8th grade math solving equations worksheets

8th Grade Free

Free 8th Grade Math Worksheets

All of the eighth grade math worksheets below are samples from the 8th Grade Math Worksheets Library on our Infinite K-8 Math Worksheet Portal .

Click any of the links below to download the corresponding 8th grade math worksheets and answer key.

▶️: Sample Worksheet Download | 🔒: Worksheet Only Available to Members | 🔽 Jump to a Topic:

Integers and Operations

Ratios & Percents

Fractions and Decimals

Probability

Lengths and Measurement

Exponents and Scientific Notation

Factors and Square Roots

Inequalities

Data and Central Tendency

Word Problems

Welcome to this complete collection of 8th Grade Math Worksheets from Mashup Math! In the library below, you will find over two hundred topic-specific 8th grade math worksheets that are available as printable pdf files. Each worksheet shares a set of problems based on a given topic and includes directions and a complete answer key so students can check their answers if desired.

Our 8th Grade Math Worksheets Library covers all math skills and topics that are covered in an 8th grade math curriculum, including ratios and percents, inequalities, scientific notation, exponents, probability, geometry, data and graphing, radicals, word problems, solving equations, graphing functions, and everything in between.

Each worksheet was carefully designed with the specific learning needs of 8th grade students in mind. The worksheet library below is an invaluable resource for parents and teachers who want to give their 8th grade students plenty of opportunities to practice and learn math in an engaging and meaningful way. They are best used for supporting students when they are practicing a new math skill, reviewing a previously learned topic, or exploring a topic that they have yet to learn.

Sharing effective math worksheets that are engaging will make a huge difference when it comes to your students’ overall development and participation, which is why our worksheets are designed to be both appropriately challenging and mentally engaging (rather than boring, monotonous, or overly repetitive).

Once you start using our 8th grade math worksheets in your lessons, you will quickly see how different they are from so many other free math worksheets that you will find online and in workbooks. Our quality-over-quantity approach to designing worksheets leads to students having opportunities to practice, explore, and learn math in a way that is engaging and encouraging of deep mathematical thinking and problem solving. Rather than focusing excessive numbers of similar problems that require students to perform monotonous mathematical tasks that are boring and rely on memorization, our worksheets include a number of problems that are appropriate for an 8th grade student’s attention span.

If this is your first experience with Mashup Math, we recommend sorting through the 8th grade math worksheets library below and downloading a handful of the available topic-specific worksheets. Once you have downloaded your worksheets, share them with your 8th graders in your upcoming lessons and see how your students react. We are highly confident that your students will love our worksheets and will have an engaging and meaningful learning experience when using them. If you find the worksheets to be useful, you can continue to revisit this page whenever you are in need of effective 8th grade math worksheets.

Also, if you want to have access to the complete Mashup Math 8th Grade Math Worksheets Library , you can use the link below to sign-up for an annual membership plan. With membership, you will gain on-demand access to the Mashup Math K-8 Math Worksheet Portal and over one thousand topic specific math worksheets for one full year.

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▶️ Blank Number Lines (positives and negatives)

▶️ Extended Practice: Rounding Decimals and Integers

▶️ Adding 4-digit numbers (vertical)

▶️ Adding 5-digit numbers (vertical)

🔒 Adding 5 and 6-digit numbers (vertical)

▶️ Adding/Subtracting 4 numbers (w/ parenthesis) (A)

🔒 Adding/Subtracting 4 numbers (w/ parenthesis) (B)

▶️ Adding/Subtracting 5 numbers (w/ parenthesis) (A)

🔒 Adding/Subtracting 5 numbers (w/ parenthesis) (B)

▶️ Adding/Subtracting 6 numbers (w/ parenthesis) (A)

🔒 Adding/Subtracting 6 numbers (w/ parenthesis) (B)

▶️ Adding/Subtracting/Multiply (no parenthesis) (3-4 numbers)

🔒 Adding/Subtracting/Multiply (w/parenthesis) (3-4 numbers)

▶️ Adding/Subtracting/Multiply (no parenthesis) (5-6 numbers)

🔒 Adding/Subtracting/Multiply (w/parenthesis) (5-6 numbers)

▶️ Multiplying 4-digit numbers by 1-digit numbers

▶️ Multiplying 5-digit numbers by 1-digit numbers

🔒 Multiplying 3-digit numbers by 2-digit numbers

▶️ Multiplying 4-digit numbers by 2-digit numbers

▶️ Multiplying 3-digit numbers by 3-digit numbers

🔒 Multiplying 4-digit numbers by 3-digit numbers

▶️ Long division with remainders (divisors 10-25) (A)

🔒 Long division with remainders (divisors 10-25) (B)

▶️ Long division with remainders (divisors 10-99) (A)

🔒 Long division with remainders (divisors 10-99) (B)

▶️ Long Division Quick Practice (1 and 2-digit divisors) (A)

▶️ Long Division Quick Practice (1 and 2-digit divisors) (B)

🔒 Long Division Quick Practice (1 and 2-digit divisors) (C)

🔒 Long Division Quick Practice (1 and 2-digit divisors) (D)

▶️ Long division estimation (multiple choice) (A)

🔒 Long division estimation (multiple choice) (B)

▶️ Commutative property of Multiplication (A)

🔒 Commutative property of Multiplication (B)

▶️ Associative property of Multiplication (A)

🔒 Associative property of Multiplication (B)

▶️ Practice with the Distributive Property (Algebra) (A)

▶️ Practice with the Distributive Property (Algebra) (B)

🔒 Practice with the Distributive Property (Algebra) (C)

▶️ Comparing integers using > or < (A)

🔒 Comparing integers using > or < (B)

▶️ Ordering integers (A)

🔒 Ordering integers (B)

▶️ Integers on the number line (A)

🔒 Integers on the number line (B)

🔒 Integers on the number line (C)

▶️ Adding integers (2-terms) (A)

🔒 Adding integers (2-terms) (B)

▶️ Adding integers (3-terms) (A)

🔒 Adding integers (3-terms) (B)

▶️ Subtracting integers (numbers to 25) (A)

🔒 Subtracting integers (numbers to 25) (B)

▶️ Subtracting integers (numbers to 100) (A)

🔒 Subtracting integers (numbers to 100) (B)

▶️ Add/Subtract Integers Using a Number Line (A)

🔒 Add/Subtract Integers Using a Number Line (B)

🔒 Add/Subtract Integers Using a Number Line (C)

▶️ Multiplying integers (A)

🔒 Multiplying integers (B)

▶️ Multiplying integers (missing factors) (A)

🔒 Multiplying integers (missing factors) (B)

▶️ Dividing integers (A)

🔒 Dividing integers (B)

▶️ Dividing integers (missing factors) (A)

🔒 Dividing integers (missing factors) (B)

▶️ Mixed multiplying and dividing integers (A)

🔒 Mixed multiplying and dividing integers (B)

▶️ Practice with Absolute Values (A)

🔒 Practice with Absolute Values (B)

🔒 Practice with Absolute Values (C)

▶️ Extra practice (order of operations up to 6 terms) (A)

🔒 Extra practice (order of operations up to 6 terms) (B)

▶️ Extra practice (order of operations up to 6 terms) (C)

▶️ Practice: Order of Operations with Exponents (A)

▶️ Practice: Order of Operations with Exponents (B)

🔒 Practice: Order of Operations with Exponents (C)

🔒 Practice: Order of Operations with Exponents (D)

▶️ Practice: Order of Operations with Nested Parenthesis (A)

🔒 Practice: Order of Operations with Nested Parenthesis (B)

🔒 Practice: Order of Operations with Nested Parenthesis (C)

▶️ Extended Practice: Order of Operations

▶️ Equivalent fractions practice (A)

▶️ Equivalent fractions practice (B)

🔒 Equivalent fractions practice (C)

▶️ Adding Fractions (common denominators) (A)

🔒 Adding Fractions (common denominators) (B)

▶️ Subtracting Fractions (common denominators) (A)

🔒 Subtracting Fractions (common denominators) (B)

▶️ Adding Fractions (unlike denominators) (A)

🔒 Adding Fractions (unlike denominators) (B)

▶️ Subtracting Fractions (unlike denominators) (A)

🔒 Subtracting Fractions (unlike denominators) (B)

▶️ Mixed Adding/Subtracting Fractions (Unlike Denominators)

▶️ Adding Mixed Numbers (A)

🔒 Adding Mixed Numbers (B)

🔒 Adding Mixed Numbers (C)

▶️ Adding Fractions and Mixed Numbers (A)

🔒 Adding Fractions and Mixed Numbers (B)

▶️ Adding Fractions Extended Practice

▶️ Subtracting Mixed Numbers (A)

🔒 Subtracting Mixed Numbers (B)

🔒 Subtracting Mixed Numbers (C)

▶️ Subtracting Mixed Fractions from Whole Numbers (A)

🔒 Subtracting Mixed Fractions from Whole Numbers (B)

▶️ Subtracting Fractions Extended Practice

▶️ Add/Subtract Fractions and Mixed Numbers Extended Practice

▶️ Converting mixed numbers to improper fractions (A)

🔒 Converting mixed numbers to improper fractions (B)

▶️ Converting improper fractions to mixed numbers (A)

🔒 Converting improper fractions to mixed numbers (B)

▶️ Multiplying fractions and whole numbers (A)

🔒 Multiplying fractions and whole numbers (B)

▶️ Multiplying Fractions and Whole Numbers Extended Practice

▶️ Multiplying fractions and whole numbers (missing factor) (A)

🔒 Multiplying fractions and whole numbers (missing factor) (B)

▶️ Multiplying fractions (intermediate) (A)

🔒 Multiplying fractions (intermediate) (B)

▶️ Multiplying fractions (missing factors) (A)

🔒 Multiplying fractions (missing factors) (B)

▶️ Multiplying Fractions by Fractions Extended Practice

▶️ Multiplying improper fractions (A)

🔒 Multiplying improper fractions (B)

▶️ Multiplying fractions by mixed numbers (A)

🔒 Multiplying fractions by mixed numbers (B)

▶️ Multiplying mixed numbers (A)

🔒 Multiplying mixed numbers (B)

▶️ Divide whole numbers by fractions (A)

🔒 Divide whole numbers by fractions (B)

▶️ Divide fractions by whole numbers (A)

🔒 Divide fractions by whole numbers (B)

▶️ Dividing fractions (easy) (A)

🔒 Dividing fractions (easy) (B)

▶️ Dividing fractions (intermediate) (A)

🔒 Dividing fractions (intermediate) (B)

▶️ Dividing Fractions Extended Practice

▶️ Dividing mixed numbers by fractions (A)

🔒 Dividing mixed numbers by fractions (B)

▶️ Dividing mixed numbers by mixed numbers (A)

🔒 Dividing mixed numbers by mixed numbers (B)

▶️ Converting fractions to decimals (A)

🔒 Converting fractions to decimals (B)

🔒 Converting fractions to decimals (C)

▶️ Converting Between Fractions & Decimals Extended Practice

▶️ Converting mixed numbers to decimals (A)

🔒 Converting mixed numbers to decimals (B)

▶️ Comparing decimals >, <, or = (A)

🔒 Comparing decimals >, <, or = (B)

▶️ Adding decimals practice (A)

🔒 Adding decimals practice (B)

🔒 Adding decimals practice (C)

▶️ Decimal addition (missing number) (A)

🔒 Decimal addition (missing number) (B)

▶️ Subtracting decimals practice (A)

🔒 Subtracting decimals practice (B)

🔒 Subtracting decimals practice (C)

▶️ Decimal subtraction (missing number) (A)

🔒 Decimal subtraction (missing number) (B)

▶️ Adding and subtracting decimals (mixed practice)

▶️ Adding and Subtracting Decimals Extended Practice

▶️ Multiply decimals by 10 or 100 (A)

🔒 Multiply decimals by 10 or 100 (B)

▶️ Multiply decimals by 10, 100, or 1,000

🔒 Multiply 3-digit decimals by 10, 100, or 1000

▶️ Multiplying Decimals by 10/100/1,000 Extended Practice

▶️ Missing factors: decimals x 10, 100 or 1,000 (missing factor) (A)

🔒 Missing factors: decimals x 10, 100 or 1,000 (missing factor) (B)

▶️ Multiplying whole numbers by decimals (1-digit)

▶️ Multiplying whole numbers by decimals (2-digit)

🔒 Multiplying whole numbers by decimals (1 and 2-digit)

▶️ Multiplying whole numbers by decimals (missing factor) (A)

🔒 Multiplying whole numbers by decimals (missing factor) (B)

▶️ Multiplying decimals by decimals (A)

🔒 Multiplying decimals by decimals (B)

▶️ Multiplying decimals by decimals (missing factor) (A)

🔒 Multiplying decimals by decimals (missing factor) (B)

▶️ Dividing decimals by whole numbers (A)

🔒 Dividing decimals by whole numbers (B)

▶️ Dividing decimals by decimals (A)

🔒 Dividing decimals by decimals (B)

▶️ Multiplying and Dividing Decimals Extended Practice

▶️ Convert between inches, feet, and yards (A)

🔒 Convert between inches, feet, and yards (B)

▶️ Convert between centimeters, millimeters, and meters (A)

🔒 Convert between centimeters, millimeters, and meters (B)

▶️ Convert between ounces and pounds (A)

🔒 Convert between ounces and pounds (B)

▶️ Convert between kilograms and grams (A)

🔒 Convert between kilograms and grams (B)

▶️ Convert between cups, pints, quarts, and gallons (A)

🔒 Convert between cups, pints, quarts, and gallons (B)

▶️ Convert between liters and milliliters (A)

🔒 Convert between liters and milliliters (B)

▶️ Practice reading a thermometer (Fahrenheit)

🔒 Practice reading a thermometer (Celsius)

▶️ Converting between Fahrenheit and Celsius (A)

🔒 Converting between Fahrenheit and Celsius (B)

▶️ Writing exponents (A)

🔒 Writing exponents (B)

▶️ Evaluating exponents (A)

🔒 Evaluating exponents (B)

▶️ Powers of 10 (A)

🔒 Powers of 10 (B)

▶️ Negative or zero exponents (A)

🔒 Negative or zero exponents (B)

▶️ Multiplying Exponents with the Same Base (A)

🔒 Multiplying Exponents with the Same Base (B)

▶️ Dividing Exponents with the Same Base (A)

🔒 Dividing Exponents with the Same Base (B)

▶️ Power to a Power (A)

🔒 Power to a Power (B)

▶️ Practice with Scientific Notation (A)

🔒 Practice with Scientific Notation (B)

🔒 Practice with Scientific Notation (C)

🔒 Extended Practice: Scientific Notation

▶️ Identifying prime numbers (A)

🔒 Identifying prime numbers (B)

▶️ Factoring numbers (up to 50) (A)

🔒 Factoring numbers (up to 50) (B)

▶️ Factoring numbers (up to 100) (A)

🔒 Factoring numbers (up to 100) (B)

🔒 Factoring numbers (up to 100) (C)

▶️ Finding Greatest Common Factor (GCF) (A)

🔒 Finding Greatest Common Factor (GCF) (B)

▶️ Finding Least Common Multiple (LCM) (A)

🔒 Finding Least Common Multiple (LCM) (B)

▶️ Extended Practice: Finding GCF and LCM

▶️ Prime factor trees (A)

🔒 Prime factor trees (B)

🔒 Prime factor trees (C)

▶️ Identifying prime factors (up to 50) (A)

🔒 Identifying prime factors (up to 50) (B)

▶️ Identifying prime factors (up to 100) (A)

🔒 Identifying prime factors (up to 100) (B)

🔒 Identifying prime factors (up to 100) (C)

▶️ Practice with square roots (A)

🔒 Practice with square roots (B)

🔒 Practice with square roots (C)

▶️ Estimating Square Roots of Non-Perfect Squares (A)

🔒 Estimating Square Roots of Non-Perfect Squares (B)

▶️ Simplifying Radicals (A)

🔒 Simplifying Radicals (B)

▶️ Adding and Subtracting Radicals (A)

🔒 Adding and Subtracting Radicals (B)

▶️ Multiplying and Dividing Radicals (A)

🔒 Multiplying and Dividing Radicals (B)

▶️ Making double bar graphs (A)

🔒 Making double bar graphs (B)

🔒 Making double bar graphs (C)

▶️ Analyzing double bar graphs (A)

🔒 Analyzing double bar graphs (B)

🔒 Analyzing double bar graphs (C)

▶️ Practice with pie charts (A)

▶️ Practice with pie charts (B)

🔒 Practice with pie charts (C)

🔒 Practice with pie charts (D)

▶️ Reading Line Plots (A)

🔒 Reading Line Plots (B)

🔒 Reading Line Plots (C)

▶️ Making Line Plots (A)

🔒 Making Line Plots (B)

▶️ Line Plots with Fractions (A)

🔒 Line Plots with Fractions (B)

▶️ Reading Venn Diagrams (A)

🔒 Reading Venn Diagrams (B)

🔒 Reading Venn Diagrams (C)

▶️ Blank Venn Diagram (2 circles)

▶️ Blank Venn Diagram (3 circles)

▶️ Making Stem-and-Lead Plots (A)

🔒 Making Stem-and-Lead Plots (B)

▶️ Reading Stem-and-Lead Plots (A)

🔒 Reading Stem-and-Lead Plots (B)

▶️ Drawing line graphs (A)

🔒 Drawing line graphs (B)

▶️ Analyzing line graphs (A)

▶️ Analyzing line graphs (B)

🔒 Analyzing line graphs (C)

🔒 Analyzing line graphs (D)

▶️ Drawing Double Line Graphs (A)

🔒 Drawing Double Line Graphs (B)

▶️ Analyzing Double Line Graphs (A)

🔒 Analyzing Double Line Graphs (B)

🔒 Analyzing Double Line Graphs (C)

▶️ Making Box-and-Whisker Plots (A)

🔒 Making Box-and-Whisker Plots (B)

🔒 Making Box-and-Whisker Plots (C)

▶️ Analyzing Box-and-Whisker Plots (A)

🔒 Analyzing Box-and-Whisker Plots (B)

🔒 Analyzing Box-and-Whisker Plots (C)

▶️ Practice with Mean, Median, and Mode (A)

▶️ Practice with Mean, Median, and Mode (B)

🔒 Practice with Mean, Median, and Mode (C)

🔒 Practice with Mean, Median, and Mode (D)

▶️ Mean, Median, and Mode Playing Cards Activity

▶️ Practice with Scatter Plots (A)

🔒 Practice with Scatter Plots (B)

▶️ Solving simple proportions (A)

🔒 Solving simple proportions (B)

🔒 Solving simple proportions (C)

▶️ Simplifying ratios (A)

🔒 Simplifying ratios (B)

▶️ Similar Triangles (A)

🔒 Similar Triangles (B)

▶️ Converting between decimals and percents (A)

🔒 Converting between decimals and percents (B)

▶️ Finding the percent of a given number (A)

🔒 Finding the percent of a given number (B)

🔒 Finding the percent of a given number (C)

▶️ A is what percent of B? (A)

🔒 A is what percent of B? (B)

🔒 A is what percent of B? (C)

▶️ Practice with Percents (Mixed) (A)

🔒 Practice with Percents (Mixed) (B)

▶️ Finding percent increase/decrease (A)

🔒 Finding percent increase/decrease (B)

▶️ Calculating Discount, Sales Tax, and Tip (A)

🔒 Calculating Discount, Sales Tax, and Tip (B)

🔒 Calculating Discount, Sales Tax, and Tip (C)

▶️ Calculating Simple Interest (A)

🔒 Calculating Simple Interest (B)

▶️ Calculating Compound Interest (A)

🔒 Calculating Compound Interest (B)

▶️ Probability diagrams with questions (A)

🔒 Probability diagrams with questions (B)

🔒 Probability diagrams with questions (C)

▶️ Probability Practice: 6-Sided Dice (x1)

▶️ Probability Practice: Spinning Wheel

🔒 Probability Practice: Playing Cards

▶️ Probability Practice: Dart Board

🔒 Probability Practice: Lottery

▶️ Estimating Probabilities Using Data (A)

🔒 Estimating Probabilities Using Data (B)

▶️ Chance Experiments (Equally Likely Outcomes)

🔒 Chance Experiments (Unequally Likely Outcomes)

▶️ Compound Probability Practice (A)

🔒 Compound Probability Practice (B)

▶️ Probability Practice: Three Coins

🔒 Probability Practice: Two Dice (6-Sided)

▶️ Naming Angles (A)

🔒 Naming Angles (B)

▶️ Angle pair relationships (A)

🔒 Angle pair relationships (B)

▶️ Parallel lines and transversals (simple) (A)

🔒 Parallel lines and transversals (simple) (B)

▶️ Parallel lines and transversals (algebraic) (A)

🔒 Parallel lines and transversals (algebraic) (B)

🔒 Naming Three-Dimensional Shapes

▶️ Extended Practice: Identifying three-dimensional figures

▶️ Drawing lines of symmetry (A)

🔒 Drawing lines of symmetry (B)

▶️ Find the perimeter (A)

🔒 Find the perimeter (B)

🔒 Find the perimeter (C)

▶️ Find the area of each rectangle (A)

🔒 Find the area of each rectangle (B)

🔒 Find the area of each rectangle (C)

▶️ Draw the figure given the area (using a grid) (A)

🔒 Draw the figure given the area (using a grid) (B)

🔒 Draw the figure given the area (using a grid) (C)

▶️ Find area/perimeter of irregular rectangular shapes (A)

🔒 Find area/perimeter of irregular rectangular shapes (B)

🔒 Find area/perimeter of irregular rectangular shapes (C)

▶️ Exploring area and perimeter using cheez-its (pdf guide)

↪ Activity Tutorial Video Link

▶️ Classifying lines, line segments, and rays (A)

🔒 Classifying lines, line segments, and rays (B)

▶️ Classifying angles: right, acute, or obtuse (A)

🔒 Classifying angles: right, acute, or obtuse (B)

▶️ Classifying parallel and perpendicular lines (A)

🔒 Classifying parallel and perpendicular lines (B)

▶️ Estimating angle measures (A)

🔒 Estimating angle measures (B)

▶️ Classifying Triangles (A)

🔒 Classifying Triangles (B)

▶️ Find area of right triangles (A)

🔒 Find area of right triangles (B)

▶️ Find area of triangles (A)

🔒 Find area of triangles (B)

▶️ Find area of parallelograms (A)

🔒 Find area of parallelograms (B)

▶️ Find area of trapezoids (A)

🔒 Find area of trapezoids (B)

▶️ Classifying Quadrilaterals (A)

🔒 Classifying Quadrilaterals (B)

▶️ Measure angles using a protractor (A)

🔒 Measure angles using a protractor (B)

▶️ Find the circumference of a circle (A)

🔒 Find the circumference of a circle (B)

▶️ Find the area of a circle (A)

🔒 Find the area of a circle (B)

▶️ Find the volume of a rectangular prism (A)

🔒 Find the volume of a rectangular prism (B)

▶️ Find the surface area of a rectangular prism (A)

🔒 Find the surface area of a rectangular prism (B)

▶️ Find the volume of a sphere (A)

🔒 Find the volume of a sphere (B)

▶️ Find the volume of a cylinder (A)

🔒 Find the volume of a cylinder (B)

▶️ Find the volume of a cone (A)

🔒 Find the volume of a cone (B)

▶️ Find the surface area of a sphere (A)

🔒 Find the surface area of a sphere (B)

▶️ Find the surface area of a cylinder (A)

🔒 Find the surface area of a cylinder (B)

▶️ Find the surface area of a cone (A)

🔒 Find the surface area of a cone (B)

▶️ Plotting Points (All Quadrants) (A)

🔒 Plotting Points (All Quadrants) (B)

▶️ Reading Points (All Quadrants) (A)

🔒 Reading Points (All Quadrants) (B)

▶️ Pokemon Coordinate Points Activity

▶️ Translations on the coordinate plane (A)

🔒 Translations on the coordinate plane (B)

▶️ Rotations on the coordinate plane (A)

🔒 Rotations on the coordinate plane (B)

▶️ Reflections on the coordinate plane (A)

🔒 Reflections on the coordinate plane (B)

▶️ Dilations on the coordinate plane (A)

🔒 Dilations on the coordinate plane (B)

▶️ Midpoint formula (A)

🔒 Midpoint formula (B)

▶️ Distance formula (A)

🔒 Distance formula (B)

▶️ Practice with the Pythagorean Theorem (A)

▶️ Practice with the Pythagorean Theorem (B)

🔒 Practice with the Pythagorean Theorem (C)

🔒 Practice with the Pythagorean Theorem (D)

🔒 Practice with the Pythagorean Theorem (E)

▶️ Translating variable expressions into words (A)

🔒 Translating variable expressions into words (B)

▶️ Translating variable equations into words (A)

🔒 Translating variable equations into words (B)

▶️ Writing algebraic expressions (one step) (A)

🔒 Writing algebraic expressions (one step) (B)

🔒 Writing algebraic expressions (one step) (C)

▶️ Writing algebraic expressions (one or two step) (A)

🔒 Writing algebraic expressions (one or two step) (B)

🔒 Writing algebraic expressions (one or two step) (C)

▶️ Evaluating expressions (add/subtract) (one variable) (A)

🔒 Evaluating expressions (add/subtract) (one variable) (B)

▶️ Evaluating expressions (multiply/divide) (one variable) (A)

🔒 Evaluating expressions (multiply/divide) (one variable) (B)

▶️ Evaluating expressions (4 operations) (one variable) (A)

🔒 Evaluating expressions (4 operations) (one variable) (B)

▶️ Evaluating expressions (w/ exponents) (one variable) (A)

🔒 Evaluating expressions (w/ exponents) (one variable) (B)

▶️ Evaluating expressions (add/subtract) (two variables) (A)

🔒 Evaluating expressions (add/subtract) (two variables) (B)

▶️ Evaluating expressions (multiply/divide) (two variables) (A)

🔒 Evaluating expressions (multiply/divide) (two variables) (B)

▶️ Evaluating expressions (4 operations) (two variables) (A)

🔒 Evaluating expressions (4 operations) (two variables) (B)

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▶️ Practice with Slope-Intercept Form (A)

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▶️ Solving linear systems of equations by graphing (A)

🔒 Solving linear systems of equations by graphing (B)

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▶️ Solving two-step inequalities (A)

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▶️ Graphing linear inequalities on the coordinate plane (A)

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▶️ Graphing systems of inequalities (A)

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▶️ Mixed multiplication and division word problems (A)

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▶️ Adding/Subtracting fractions word problems (easy) (C)

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▶️ Multiplying fractions by whole numbers word problems (A)

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▶️ Fractions and expressions word problems (A)

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▶️ Markup, discount, and tax word problems (A)

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▶️ Area of a circle word problems (A)

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▶️ Area and perimeter of a rectangle word problems (A)

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▶️ Volume of rectangular prism word problems (A)

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▶️ Pythagorean Theorem word problems (A)

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▶️ Distance, rate, and time word problems (A)

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▶️ Multi-step Word Problem: Snappy Rental Car

▶️ Multi-step Word Problem: Neil’s Square Paper

🔒 Multi-step Word Problem: Lilly Goes Shopping

🔒 Multi-step Word Problem: Pumpkins and Watermelons

🔒 Multi-step Word Problem: Alejandro’s Rock Collection

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Why Your Students Will Love Our 8th Grade Math Worksheets

Once your first introduce your 8th graders to our math worksheets, you will soon understand what makes them so effective and engaging when it comes to developing their math skills and confidence. Not all math worksheets are created equally, and, while we know that you have many options for free math worksheets online, we believe that our resources are a cut above the rest and that they will be an invaluable addition to your resource portfolio.

Our worksheets go beyond repetitively practicing math skills. Rather, they are designed with an emphasis on encouraging students to engage in deep mathematical thinking, reasoning, and problem solving. Math resources with this type of focus will have your students spending more time thinking critically and developing their math skills and less time feeling bored, frustrated, or doing busy work.

Our 8th Grade Math Worksheets are designed to give your students meaningful opportunities for thinking critically and developing their math skills

If you need a few ideas for effective ways to use our 8th grade math worksheets with your students, here are a few suggestions:

use worksheets for independent practice

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quizzes, tests, assessments, etc.

There are tons of effective ways to use our 8th grade math worksheets with your students both at home and in your classroom. Each of the suggestions above offers a great opportunity to have students practice and develop their math skills in an engaging way. By giving your students ample opportunities to interact with mathematics in a way that is challenging, yet enjoyable (and never boring), you are setting them up to be confident and interested in pursuing more challenging math topics and they move through the 8th grade and eventually into high school.

Great math teachers with effective time management skills make their own resources and also rely on outside resources such as our topic-specific practice worksheets. While you have many options, we believe that our 8th grade math worksheets are highly effective when it comes to presenting math in a way that is fun, engaging, and suitable challenging for 8th graders. By choosing resources that are designed to support your students’ math development (without making the subject seam boring or dull), you are guiding them along a path to being successful at mathematics well beyond the 8th grade!

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8th Grade Math Worksheets

First things first, prioritize major topics with our printable compilation of 8th grade math worksheets with answer keys. Pursue conceptual understanding of topics like number systems, expressions and equations, work with radicals and exponents, solve linear equations and inequalities, evaluate and compare functions, understand similarity and congruence, know and apply the Pythagorean Theorem, find volume and surface area, develop an understanding of statistics and probability and much more. Our free math worksheets for grade 8 students make sure they start right!

Select Grade 8 Math Worksheets by Topic

Explore 2,400+ Eighth Grade Math Worksheets

Converting Fractions to Decimal

Convert each fraction with a multiple of 10 as its denominator into a decimal number by placing the decimal point at the right spot.

• Download the set

Finding the Square Roots of Perfect Squares

Apply prime factorization and determine the square roots of the first fifty perfect squares offered as positive integers.

Slope of a Line passing through Two Points

Use the formula, m = (y 2 - y 1 ) / (x 1 - x 1 ) to find the slope(m) of a line passing through two points: (x 1 ,y 1 ) and (x 2 ,y 2 ).

Solving Multi-Step Equations

Follow the order of operations, rearrange to make the unknown variable the subject, and solve for its integer value.

Identifying Functions from Ordered Pairs

Observe each set of ordered pairs given in Part A, figure out ordered pairs from graphs in Part B, and state if they represent a function.

Translation on Graphs | Writing Coordinates

Slide each figure in the said direction: up or down, left or right. Write the coordinates of the shifted image.

Congruence | Congruent Parts

Complete the congruence statement for each pair of triangles by writing the corresponding side or corresponding angle.

Finding the Interior Angle

Find the measure of the indicated interior angle by subtracting the sum of the known angles from 180.

Interior Angles - Finding the Unknown

Observe whether the interior angles lie on the same side or opposite sides of the transversal and find the unknown angle.

Identifying Right Triangles

Square the adjacent and opposite sides of the triangle; take the root of their sum; if you arrive at the hypotenuse, then it's a right triangle.

Volume of Cones

Plug the given radius(r) and height(h) in the formula V = 1/3πr 2 h and find the volume of the cone.

Mean, Median, Mode, and Range

Read each word problem with a real-life scenario and find the mean, median, mode, and range for each data set.

Converting Fractions to Percent

Switch each fraction to percent by multiplying the numerator by 100, dividing the product by the denominator, and adding the % symbol.

Finding the Square of Square Roots

The square of a square root is the radicand. So, simply multiply the radicand with the square of the number outside the root.

Convert to the Standard Form

Isolate the x and y-terms to one side and the constant to the other side of the equation and rewrite it in the form: ax + by = c.

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Free Printable Solving Equations Worksheets for 8th Grade

Solving Equations just got more exciting! Discover an extensive collection of free printable Math worksheets for Grade 8 students, created by Quizizz. Enhance learning and master skills with ease.

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• Two-Step Equations
• One-Step Equations
• Multi-Step Equations

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Explore printable Solving Equations worksheets for 8th Grade

Solving Equations worksheets for Grade 8 are an essential resource for teachers looking to help their students master the fundamentals of algebra. These worksheets focus on one-variable equations, a crucial concept in Grade 8 Math curriculum. By providing a variety of problems and scenarios, these worksheets allow students to practice and hone their skills in solving algebraic equations. Teachers can use these resources to supplement their lesson plans, provide additional practice for struggling students, or even as a form of assessment to gauge students' understanding of the material. With the right set of Solving Equations worksheets for Grade 8, teachers can ensure that their students are well-prepared for the challenges of algebra and future math courses.

In addition to Solving Equations worksheets for Grade 8, Quizizz offers a comprehensive platform for teachers to create engaging and interactive quizzes, polls, and other activities to enhance their students' learning experience. Quizizz allows teachers to choose from a vast library of pre-made quizzes or create their own, tailored to their specific lesson plans and objectives. These quizzes can be assigned as homework, used for in-class review, or even as a form of assessment. With Quizizz, teachers can track their students' progress and identify areas where they may need additional support or practice. By incorporating Quizizz into their teaching strategies, teachers can not only supplement their Solving Equations worksheets for Grade 8 but also provide a dynamic and engaging learning environment for their students.

8th Grade Math Solving Equations Worksheets

Solving an equation that may need more than two steps to solve for the variable.  Generally, we use the same operation on both sides of the equation to isolate the variable. These equations involve multiple steps to get the solution. There are many ways to solve an equation. Teachers can share this amazing solving equations worksheet with their students to help them master this concept for unit tests.

Teaching Solving Equations Easily 

Things to keep in mind while solving equations unit worksheet:

• Firstly, in a parenthesis, apply the distributive property in the given equation. 
• Secondly, combine all the like terms. 
• Now, collect all the like terms on one side of the equation. 
• Lastly, isolate the variable using inverse operations. 

Here is an example of how to solve the equation problem.

Assume Tom is six years younger than Sam. After 10 years, the sum of their ages is 36. Then how old is Sam now?

Step 1: Let Sam’s age be x years old. Then Tom’s age = x - 6 years. After 10 years, the sum of their ages is 36. i.e.,

(x + 10) + (x - 6 + 10) = 36

Step 2: Combine similar terms.

2x + 14 = 36

On removing 14 from both sides,

The result is that 2x = 12

Dividing both sides by 2,

Thus, Sam's age now is 6 years old. 

Why Should You Use Solving Equation Worksheets for Your Students? 

• These worksheets provide opportunities for your students to solve multi-step word problems using variables, coefficients, and constants. 
• Solving these worksheets will help students strengthen basic skills like multiplication, division, addition, subtraction, division, BODMAS, etc.

Download Solving Equation Unit Worksheet PDFs.

You can download and print these equation worksheets in pdf here for your students.

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Solve Equations (Grade 8)

Suggested learning targets.

• I can solve linear equations with rational number coefficients.
• I can solve equations whose solutions require expanding expressions using the distributive property and/or collecting like terms.

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8th Grade Linear Equations Worksheets

Linear equations are equations that have two variables and when graphed are a straight line based on their slope and y-intercept. Hence,8th grade linear equations worksheets have a variety of questions that help students practice key concepts and build a rock-solid foundation of the concepts.

Benefits of Linear Equations Grade 8 Worksheets

Linear equation worksheets are a great resource for students to practice a large variety of problems. These 8th grade math worksheets are supported by visuals which help students get a crystal clear understanding of the topic. The variety of problems that these worksheets offer helps students approach these concepts in an engaging and fun manner.

Many websites might provide similar worksheets but the Cuemath 8th grade linear equations worksheets come with visual simulation for students to see the problems in action, an answer key that provides a detailed step-by-step solution for students to understand the process better, and a worksheet with detailed solutions.

Printable PDFs for Grade 8 Linear Equations Worksheets

Students can practice problems by downloading the linear equations grade 8 worksheets in PDF format for free.

• Math 8th Grade Linear Equations Worksheet
• 8th Grade Linear Equations Math Worksheet
• Eighth Grade Linear Equations Worksheet
• Grade 8 Math Linear Equations Worksheet

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8th Grade Mathematics Worksheets: FREE & Printable

Looking for free printable Math worksheets and exercises to help your 8th-grade students prepare for the 8th Grade Mathematics test?

Need 8th Grade Mathematics Practice exercises and activities to measure your students’ exam readiness? want great 8th Grade Math worksheets to help your students review and master math concepts? If so, then look no further.

Here is a comprehensive and perfect collection of FREE 8th Grade Mathematics worksheets that would help your students in 8th Grade Math preparation and practice.

You can download free 20+ 8th grade math worksheets from Bytelearn.

Download our free Mathematics worksheets for the 8th Grade test.

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The BEST Prep Book to Help Your Student ACE the Grade 8 Math!

Mastering Grade 8 Math The Ultimate Step by Step Guide to Acing 8th Grade Math

8th grade mathematics concepts, whole numbers.

• Whole Number Addition and Subtraction
• Whole Number Multiplication and Division
• Rounding and Estimates

Fractions and Decimals

• Simplifying Fractions
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• Factoring Numbers
• Greatest Common Factor
• Least Common Multiple

Real Numbers and Integers

• Adding and Subtracting Integers
• Multiplying and Dividing Integers
• Order of Operations
• Ordering Integers and Numbers
• Integers and Absolute Value

Proportions, Ratios, and Percent

• Simplifying Ratios
• Proportional Ratios
• Similarity and Ratios
• Ratio and Rates Word Problems
• Percentage Calculations
• Percent Problems
• Discount, Tax and Tip
• Percent of Change
• Simple Interest

Algebraic Expressions

• Simplifying Variable Expressions
• Simplifying Polynomial Expressions
• Translate Phrases into an Algebraic Statement
• The Distributive Property
• Evaluating One Variable Expressions
• Evaluating Two Variables Expressions
• Combining like Terms

Equations and Inequalities

• One-Step Equations
• Multi-Step Equations
• Graphing Single–Variable Inequalities
• One-Step Inequalities
• Multi-Step Inequalities

Systems of Equations

• Systems of Equations Word Problems
• Quadratic Equation

The Best Math Study Guide for 8th-Grade Students!

Grade 8 Math for Students The Ultimate Step by Step Guide to Preparing for the Grade 8 Math Test

Linear functions.

• Finding Slope
• Graphing Lines Using Line Equation
• Writing Linear Equations
• Graphing Linear Inequalities
• Finding Midpoint
• Finding Distance of Two Points

Exponents and Radicals

• Multiplication Property of Exponents
• Zero and Negative Exponents
• Division Property of Exponents
• Powers of Products and Quotients
• Negative Exponents and Negative Bases
• Scientific Notation
• Square Roots

Polynomials

• Writing Polynomials in Standard Form
• Simplifying Polynomials
• Adding and Subtracting Polynomials
• Multiplying Monomials
• Multiplying and Dividing Monomials
• Multiplying a Polynomial and a Monomial
• Multiplying Binomials
• Factoring Trinomials
• Operations with Polynomials

Geometry and Solid Figures

• Pythagorean Relationship
• Rectangular Prism
• Pyramids and Cone

Statistics and Probability

• Mean and Median
• Mode and Range
• Stem–and–Leaf Plot
• Probability Problems
• Combinations and Permutations

The BEST Practice Book for 8th Grade Math!

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8th grade math exercises, proportions and ratios, solid figures, function operations.

Looking for the best resources to help your students succeed on the Math test?

The Best Books to Ace Math Test!

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Mastering grade 5 math word problems the ultimate guide to tackling 5th grade math word problems, mastering grade 7 math word problems the ultimate guide to tackling 7th grade math word problems, staar grade 8 math comprehensive prep bundle a perfect resource for staar math test takers.

by: Effortless Math Team about 4 years ago (category: Blog , Free Math Worksheets )

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Algebra Worksheets

Welcome to the Algebra worksheets page at Math-Drills.com, where unknowns are common and variables are the norm. On this page, you will find Algebra worksheets for middle school students on topics such as algebraic expressions, equations and graphing functions.

This page starts off with some missing numbers worksheets for younger students. We then get right into algebra by helping students recognize and understand the basic language related to algebra. The rest of the page covers some of the main topics you'll encounter in algebra units. Remember that by teaching students algebra, you are helping to create the future financial whizzes, engineers, and scientists that will solve all of our world's problems.

Algebra is much more interesting when things are more real. Solving linear equations is much more fun with a two pan balance, some mystery bags and a bunch of jelly beans. Algebra tiles are used by many teachers to help students understand a variety of algebra topics. And there is nothing like a set of co-ordinate axes to solve systems of linear equations.

Most Popular Algebra Worksheets this Week

Algebraic Properties, Rules and Laws Worksheets

The commutative law or commutative property states that you can change the order of the numbers in an arithmetic problem and still get the same results. In the context of arithmetic, it only works with addition or multiplication operations , but not mixed addition and multiplication. For example, 3 + 5 = 5 + 3 and 9 × 5 = 5 × 9. A fun activity that you can use in the classroom is to brainstorm non-numerical things from everyday life that are commutative and non-commutative. Putting on socks, for example, is commutative because you can put on the right sock then the left sock or you can put on the left sock then the right sock and you will end up with the same result. Putting on underwear and pants, however, is non-commutative.

• The Commutative Law Worksheets The Commutative Law of Addition (Numbers Only) The Commutative Law of Addition (Some Variables) The Commutative Law of Multiplication (Numbers Only) The Commutative Law of Multiplication (Some Variables)

The associative law or associative property allows you to change the grouping of the operations in an arithmetic problem with two or more steps without changing the result. The order of the numbers stays the same in the associative law. As with the commutative law, it applies to addition-only or multiplication-only problems. It is best thought of in the context of order of operations as it requires that parentheses must be dealt with first. An example of the associative law is: (9 + 5) + 6 = 9 + (5 + 6). In this case, it doesn't matter if you add 9 + 5 first or 5 + 6 first, you will end up with the same result. Students might think of some examples from their experience such as putting items on a tray at lunch. They could put the milk and vegetables on their tray first then the sandwich or they could start with the vegetables and sandwich then put on the milk. If their tray looks the same both times, they will have modeled the associative law. Reading a book could be argued as either associative or nonassociative as one could potentially read the final chapters first and still understand the book as well as someone who read the book the normal way.

• The Associative Law Worksheets The Associative Law of Addition (Whole Numbers Only) The Associative Law of Multiplication (Whole Numbers Only)

Inverse relationships worksheets cover a pre-algebra skill meant to help students understand the relationship between multiplication and division and the relationship between addition and subtraction.

• Inverse Mathematical Relationships with One Blank Addition and Subtraction Easy Addition and Subtraction Harder All Multiplication and Division Facts 1 to 18 in color (no blanks) Multiplication and Division Range 1 to 9 Multiplication and Division Range 5 to 12 Multiplication and Division All Inverse Relationships Range 2 to 9 Multiplication and Division All Inverse Relationships Range 5 to 12 Multiplication and Division All Inverse Relationships Range 10 to 25
• Inverse Mathematical Relationships with Two Blanks Addition and Subtraction (Sums 1-18) Addition and Subtraction Inverse Relationships with 1 Addition and Subtraction Inverse Relationships with 2 Addition and Subtraction Inverse Relationships with 3 Addition and Subtraction Inverse Relationships with 4 Addition and Subtraction Inverse Relationships with 5 Addition and Subtraction Inverse Relationships with 6 Addition and Subtraction Inverse Relationships with 7 Addition and Subtraction Inverse Relationships with 8 Addition and Subtraction Inverse Relationships with 9 Addition and Subtraction Inverse Relationships with 10 Addition and Subtraction Inverse Relationships with 11 Addition and Subtraction Inverse Relationships with 12 Addition and Subtraction Inverse Relationships with 13 Addition and Subtraction Inverse Relationships with 14 Addition and Subtraction Inverse Relationships with 15 Addition and Subtraction Inverse Relationships with 16 Addition and Subtraction Inverse Relationships with 17 Addition and Subtraction Inverse Relationships with 18

The distributive property is an important skill to have in algebra. In simple terms, it means that you can split one of the factors in multiplication into addends, multiply each addend separately, add the results, and you will end up with the same answer. It is also useful in mental math, an example of which should help illustrate the definition. Consider the question, 35 × 12. Splitting the 12 into 10 + 2 gives us an opportunity to complete the question mentally using the distributive property. First multiply 35 × 10 to get 350. Second, multiply 35 × 2 to get 70. Lastly, add 350 + 70 to get 420. In algebra, the distributive property becomes useful in cases where one cannot easily add the other factor before multiplying. For example, in the expression, 3(x + 5), x + 5 cannot be added without knowing the value of x. Instead, the distributive property can be used to multiply 3 × x and 3 × 5 to get 3x + 15.

• Distributive Property Worksheets Distributive Property (Answers do not include exponents) Distributive Property (Some answers include exponents) Distributive Property (All answers include exponents)

Students should be able to substitute known values in for an unknown(s) in an expression and evaluate the expression's value.

• Evaluating Expressions with Known Values Evaluating Expressions with One Variable, One Step and No Exponents Evaluating Expressions with One Variable and One Step Evaluating Expressions with One Variable and Two Steps Evaluating Expressions with Up to Two Variables and Two Steps Evaluating Expressions with Up to Two Variables and Three Steps Evaluating Expressions with Up to Three Variables and Four Steps Evaluating Expressions with Up to Three Variables and Five Steps

As the title says, these worksheets include only basic exponent rules questions. Each question only has two exponents to deal with; complicated mixed up terms and things that a more advanced student might work out are left alone. For example, 4 2 is (2 2 ) 2 = 2 4 , but these worksheets just leave it as 4 2 , so students can focus on learning how to multiply and divide exponents more or less in isolation.

• Exponent Rules for Multiplying, Dividing and Powers Mixed Exponent Rules (All Positive) Mixed Exponent Rules (With Negatives) Multiplying Exponents (All Positive) Multiplying Exponents (With Negatives) Multiplying the Same Exponent with Different Bases (All Positive) Multiplying the Same Exponent with Different Bases (With Negatives) Dividing Exponents with a Greater Exponent in Dividend (All Positive) Dividing Exponents with a Greater Exponent in Dividend (With Negatives) Dividing Exponents with a Greater Exponent in Divisor (All Positive) Dividing Exponents with a Greater Exponent in Divisor (With Negatives) Powers of Exponents (All Positive) Powers of Exponents (With Negatives)

Knowing the language of algebra can help to extract meaning from word problems and to situations outside of school. In these worksheets, students are challenged to convert phrases into algebraic expressions.

• Translating Algebraic Phrases into Expressions Translating Algebraic Phrases into Expressions (Simple Version) Translating Algebraic Phrases into Expressions (Complex Version)

Combining like terms is something that happens a lot in algebra. Students can be introduced to the topic and practice a bit with these worksheets. The bar is raised with the adding and subtracting versions that introduce parentheses into the expressions. For students who have a good grasp of fractions, simplifying simple algebraic fractions worksheets present a bit of a challenge over the other worksheets in this section.

• Simplifying Expressions by Combining Like Terms Simplifying Linear Expressions with 3 terms Simplifying Linear Expressions with 4 terms Simplifying Linear Expressions with 5 terms Simplifying Linear Expressions with 6 to 10 terms
• Simplifying Expressions by Combining Like Terms with Some Arithmetic Adding and simplifying linear expressions Adding and simplifying linear expressions with multipliers Adding and simplifying linear expressions with some multipliers . Subtracting and simplifying linear expressions Subtracting and simplifying linear expressions with multipliers Subtracting and simplifying linear expressions with some multipliers Mixed adding and subtracting and simplifying linear expressions Mixed adding and subtracting and simplifying linear expressions with multipliers Mixed adding and subtracting and simplifying linear expressions with some multipliers Simplify simple algebraic fractions (easier) Simplify simple algebraic fractions (harder)
• Rewriting Linear Equations Rewrite Linear Equations in Standard Form Convert Linear Equations from Standard to Slope-Intercept Form Convert Linear Equations from Slope-Intercept to Standard Form Convert Linear Equations Between Standard and Slope-Intercept Form
• Rewriting Formulas Rewriting Formulas (addition and subtraction; about one step) Rewriting Formulas (addition and subtraction; about two steps) Rewriting Formulas ( multiplication and division ; about one step)

Linear Expressions and Equations

In these worksheets, the unknown is limited to the question side of the equation which could be on the left or the right of equal sign.

• Missing Numbers in Equations with Blanks as Unknowns Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Blanks in Any Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Blanks in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Blanks in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 20 ; Blanks in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Blanks in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 20 ; Blanks in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Blanks in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 20 ; Blanks in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Blanks Never in Answer Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Blanks in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 20 ; Blanks in Any Position )
• Missing Numbers in Equations with Symbols as Unknowns Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Symbols in Any Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Symbols in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Symbols in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 20 ; Symbols in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Symbols in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 20 ; Symbols in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Symbols in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 20 ; Symbols in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Symbols Never in Answer Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Symbols in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 20 ; Symbols in Any Position )
• Solving Equations with Addition and Symbols as Unknowns Equalities with Addition (0 to 9) Symbol Unknowns Equalities with Addition (1 to 12) Symbol Unknowns Equalities with Addition (1 to 15) Symbol Unknowns Equalities with Addition (1 to 25) Symbol Unknowns Equalities with Addition (1 to 99) Symbol Unknowns
• Missing Numbers in Equations with Variables as Unknowns Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Variables Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 9 ; Variables in Any Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Variables Never in Answer Position ) Missing Numbers in Equations ( All Operations ; Range 1 to 20 ; Variables in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Variables Never in Answer Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 9 ; Variables in Any Position ) Missing Numbers in Equations ( Addition Only ; Range 1 to 20 ; Variables in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Variables Never in Answer Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 9 ; Variables in Any Position ) Missing Numbers in Equations ( Subtraction Only ; Range 1 to 20 ; Variables in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Variables Never in Answer Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 9 ; Variables in Any Position ) Missing Numbers in Equations ( Multiplication Only ; Range 1 to 20 ; Variables in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Variables Never in Answer Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 9 ; Variables in Any Position ) Missing Numbers in Equations ( Division Only ; Range 1 to 20 ; Variables in Any Position )
• Solving Simple Linear Equations Solving Simple Linear Equations with Values from -9 to 9 (Unknown on Left Side) Solving Simple Linear Equations with Values from -99 to 99 (Unknown on Left Side) Solving Simple Linear Equations with Values from -9 to 9 (Unknown on Right or Left Side) Solving Simple Linear Equations with Values from -99 to 99 (Unknown on Right or Left Side)
• Determining Linear Equations from Slopes, y-intercepts and Points Determine a Linear Equation from the Slope and y-intercept Determine a Linear Equation from the Slope and a Point Determine a Linear Equation from Two Points Determine a Linear Equation from Two Points by Graphing

Graphing linear equations and reading existing graphs give students a visual representation that is very useful in understanding the concepts of slope and y-intercept.

• Graphing Linear Equations Graph Slope-Intercept Equations
• Determining Linear Equations from Graphs Determine the Equation from a Graph Determine the Slope from a Graph Determine the y-intercept from a Graph Determine the x-intercept from a Graph Determine the slope and y-intercept from a Graph Determine the slope and intercepts from a Graph Determine the slope, intercepts and equation from a Graph

Solving linear equations with jelly beans is a fun activity to try with students first learning algebraic concepts. Ideally, you will want some opaque bags with no mass, but since that isn't quite possible (the no mass part), there is a bit of a condition here that will actually help students understand equations better. Any bags that you use have to be balanced on the other side of the equation with empty ones.

Probably the best way to illustrate this is through an example. Let's use 3 x + 2 = 14. You may recognize the x as the unknown which is actually the number of jelly beans we put in each opaque bag. The 3 in the 3 x means that we need three bags. It's best to fill the bags with the required number of jelly beans out of view of the students, so they actually have to solve the equation.

On one side of the two-pan balance, place the three bags with x jelly beans in each one and two loose jelly beans to represent the + 2 part of the equation. On the other side of the balance, place 14 jelly beans and three empty bags which you will note are required to "balance" the equation properly. Now comes the fun part... if students remove the two loose jelly beans from one side of the equation, things become unbalanced, so they need to remove two jelly beans from the other side of the balance to keep things even. Eating the jelly beans is optional. The goal is to isolate the bags on one side of the balance without any loose jelly beans while still balancing the equation.

The last step is to divide the loose jelly beans on one side of the equation into the same number of groups as there are bags. This will probably give you a good indication of how many jelly beans there are in each bag. If not, eat some and try again. Now, we realize this won't work for every linear equation as it is hard to have negative jelly beans, but it is another teaching strategy that you can use for algebra.

Despite all appearances, equations of the type a/ x are not linear. Instead, they belong to a different kind of equations. They are good for combining them with linear equations, since they introduce the concept of valid and invalid answers for an equation (what will be later called the domain of a function). In this case, the invalid answers for equations in the form a/ x , are those that make the denominator become 0.

• Solving Linear Equations Combining Like Terms and Solving Simple Linear Equations Solving a x = c Linear Equations Solving a x = c Linear Equations including negatives Solving x /a = c Linear Equations Solving x /a = c Linear Equations including negatives Solving a/ x = c Linear Equations Solving a/ x = c Linear Equations including negatives Solving a x + b = c Linear Equations Solving a x + b = c Linear Equations including negatives Solving a x - b = c Linear Equations Solving a x - b = c Linear Equations including negatives Solving a x ± b = c Linear Equations Solving a x ± b = c Linear Equations including negatives Solving x /a ± b = c Linear Equations Solving x /a ± b = c Linear Equations including negatives Solving a/ x ± b = c Linear Equations Solving a/ x ± b = c Linear Equations including negatives Solving various a/ x ± b = c and x /a ± b = c Linear Equations Solving various a/ x ± b = c and x /a ± b = c Linear Equations including negatives Solving linear equations of all types Solving linear equations of all types including negatives

Algebra rectangles are rectangles that use linear expressions for the side measurements. With a known value (such as the perimeter), students create an algebraic equation that they can solve to determine the value of the unknown (x) and use it to determine the side lengths and area of the rectangle. The terminology in identifying the various options for worksheets use the standard equation y = mx + b where m is the coeffient of x that is generally a known value.

• Algebra Rectangles Algebra Rectangles -- Determining the Value of x, Length, Width and Area Using Algebraic Sides and the Perimeter -- m Range [1,1] Algebra Worksheet -{}- Algebra Rectangles -- Determining the Value of x, Length, Width and Area Using Algebraic Sides and the Perimeter -- m Range [2,9] Algebra Worksheet -{}- Algebra Rectangles -- Determining the Value of x, Length, Width and Area Using Algebraic Sides and the Perimeter -- m Range [2,9] or [-9,-2] Algebra Worksheet -{}- Algebra Rectangles -- Determining the Value of x, Length, Width and Area Using Algebraic Sides and the Perimeter -- m Range [2,9] or [-9,-2] -- Inverse m Possible

Linear Systems

• Solving Systems of Linear Equations Easy Linear Systems with Two Variables Easy Linear Systems with Two Variables including negative values Linear Systems with Two Variables Linear Systems with Two Variables including negative values Easy Linear Systems with Three Variables; Easy Easy Linear Systems with Three Variables including negative values Linear Systems with Three Variables Linear Systems with Three Variables including negative values
• Solving Systems of Linear Equations by Graphing Solve Linear Systems by Graphing (Solutions in first quadrant only) Solve Standard Linear Systems by Graphing Solve Slope-Intercept Linear Systems by Graphing Solve Various Linear Systems by Graphing Identify the Dependent Linear System by Graphing Identify the Inconsistent Linear System by Graphing

Quadratic Expressions and Equations

• Simplifying (Combining Like Terms) Quadratic Expressions Simplifying quadratic expressions with 5 terms Simplifying quadratic expressions with 6 terms Simplifying quadratic expressions with 7 terms Simplifying quadratic expressions with 8 terms Simplifying quadratic expressions with 9 terms Simplifying quadratic expressions with 10 terms Simplifying quadratic expressions with 5 to 10 terms
• Adding/Subtracting and Simplifying Quadratic Expressions Adding and simplifying quadratic expressions. Adding and simplifying quadratic expressions with multipliers. Adding and simplifying quadratic expressions with some multipliers. Subtracting and simplifying quadratic expressions. Subtracting and simplifying quadratic expressions with multipliers. Subtracting and simplifying quadratic expressions with some multipliers. Mixed adding and subtracting and simplifying quadratic expressions. Mixed adding and subtracting and simplifying quadratic expressions with multipliers. Mixed adding and subtracting and simplifying quadratic expressions with some multipliers.
• Multiplying Factors to Get Quadratic Expressions Multiplying Factors of Quadratics with Coefficients of 1 Multiplying Factors of Quadratics with Coefficients of 1 or -1 Multiplying Factors of Quadratics with Coefficients of 1, or 2 Multiplying Factors of Quadratics with Coefficients of 1, -1, 2 or -2 Multiplying Factors of Quadratics with Coefficients up to 9 Multiplying Factors of Quadratics with Coefficients between -9 and 9

The factoring quadratic expressions worksheets in this section provide many practice questions for students to hone their factoring strategies. If you would rather worksheets with quadratic equations, please see the next section. These worksheets come in a variety of levels with the easier ones are at the beginning. The 'a' coefficients referred to below are the coefficients of the x 2 term as in the general quadratic expression: ax 2 + bx + c. There are also worksheets in this section for calculating sum and product and for determining the operands for sum and product pairs.

• Factoring Quadratic Expressions Factoring Quadratic Expressions with Positive 'a' coefficients of 1 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients of 1 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients of 1 with a Common Factor Step Factoring Quadratic Expressions with Positive 'a' coefficients up to 4 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 4 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 4 with a Common Factor Step Factoring Quadratic Expressions with Positive 'a' coefficients up to 5 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 5 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 5 with a Common Factor Step Factoring Quadratic Expressions with Positive 'a' coefficients up to 9 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 9 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 9 with a Common Factor Step Factoring Quadratic Expressions with Positive 'a' coefficients up to 81 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 81 Factoring Quadratic Expressions with Positive or Negative 'a' coefficients up to 81 with a Common Factor Step Calculating Sum and Product (Operand Range 0 to 9 ) ✎ Calculating Sum and Product (Operand Range 1 to 9 ) ✎ Calculating Sum and Product (Operand Range 0 to 9 Including Negatives ) ✎ Calculating Sum and Product (Operand Range 1 to 9 Including Negatives ) ✎ Calculating Sum and Product (Operand Range -20 to 20 ) ✎ Calculating Sum and Product (Operand Range -99 to 99 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 0 to 9 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 1 to 9 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 0 to 12 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 1 to 12 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 0 to 9 Including Negatives ) ✎ Determining Operands from Sum and Product Pairs (Operand Range 1 to 9 Including Negatives ) ✎ Determining Operands from Sum and Product Pairs (Operand Range -20 to 20 ) ✎ Determining Operands from Sum and Product Pairs (Operand Range -99 to 99 ) ✎

Whether you use trial and error, completing the square or the general quadratic formula, these worksheets include a plethora of practice questions with answers. In the first section, the worksheets include questions where the quadratic expressions equal 0. This makes the process similar to factoring quadratic expressions, with the additional step of finding the values for x when the expression is equal to 0. In the second section, the expressions are generally equal to something other than x, so there is an additional step at the beginning to make the quadratic expression equal zero.

• Solving Quadratic Equations that Equal Zero Solving Quadratic Equations with Positive 'a' coefficients of 1 Solving Quadratic Equations with Positive or Negative 'a' coefficients of 1 Solving Quadratic Equations with Positive or Negative 'a' coefficients of 1 with a Common Factor Step Solving Quadratic Equations with Positive 'a' coefficients up to 4 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 4 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 4 with a Common Factor Step Solving Quadratic Equations with Positive 'a' coefficients up to 5 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 5 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 5 with a Common Factor Step Solving Quadratic Equations with Positive 'a' coefficients up to 9 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 9 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 9 with a Common Factor Step Solving Quadratic Equations with Positive 'a' coefficients up to 81 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 81 Solving Quadratic Equations with Positive or Negative 'a' coefficients up to 81 with a Common Factor Step
• Solving Quadratic Equations that Equal an Integer Solving Quadratic Equations for x ("a" coefficients of 1) Solving Quadratic Equations for x ("a" coefficients of 1 or -1) Solving Quadratic Equations for x ("a" coefficients up to 4) Solving Quadratic Equations for x ("a" coefficients between -4 and 4) Solving Quadratic Equations for x ("a" coefficients up to 81) Solving Quadratic Equations for x ("a" coefficients between -81 and 81)

Other Polynomial and Monomial Expressions & Equations

• Simplifying Polynomials That Involve Addition And Subtraction Addition and Subtraction; 1 variable; 3 terms Addition and Subtraction; 1 variable; 4 terms Addition and Subtraction; 2 variables; 4 terms Addition and Subtraction; 2 variables; 5 terms Addition and Subtraction; 2 variables; 6 terms
• Simplifying Polynomials That Involve Multiplication And Division Multiplication and Division; 1 variable; 3 terms Multiplication and Division; 1 variable; 4 terms Multiplication and Division; 2 variables; 4 terms Multiplication and Division; 2 variables; 5 terms
• Simplifying Polynomials That Involve Addition, Subtraction, Multiplication And Division All Operations; 1 variable; 3 terms All Operations; 1 variable; 4 terms All Operations; 2 variables; 4 terms All Operations; 2 variables; 5 terms All Operations (Challenge)
• Factoring Expressions That Do Not Include A Squared Variable Factoring Non-Quadratic Expressions with No Squares, Simple Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with No Squares, Simple Coefficients, and Negative and Positive Multipliers Factoring Non-Quadratic Expressions with No Squares, Compound Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with No Squares, Compound Coefficients, and Negative and Positive Multipliers
• Factoring Expressions That Always Include A Squared Variable Factoring Non-Quadratic Expressions with All Squares, Simple Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with All Squares, Simple Coefficients, and Negative and Positive Multipliers Factoring Non-Quadratic Expressions with All Squares, Compound Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with All Squares, Compound Coefficients, and Negative and Positive Multipliers
• Factoring Expressions That Sometimes Include Squared Variables Factoring Non-Quadratic Expressions with Some Squares, Simple Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with Some Squares, Simple Coefficients, and Negative and Positive Multipliers Factoring Non-Quadratic Expressions with Some Squares, Compound Coefficients, and Positive Multipliers Factoring Non-Quadratic Expressions with Some Squares, Compound Coefficients, and Negative and Positive Multipliers
• Multiplying Polynomials With Two Factors Multiplying a monomial by a binomial Multiplying two binomials Multiplying a monomial by a trinomial Multiplying a binomial by a trinomial Multiplying two trinomials Multiplying two random mon/polynomials
• Multiplying Polynomials With Three Factors Multiplying a monomial by two binomials Multiplying three binomials Multiplying two binomials by a trinomial Multiplying a binomial by two trinomials Multiplying three trinomials Multiplying three random mon/polynomials

Inequalities

• Writing The Inequality That Matches The Graph Writing Inequalities for Graphs
• Graphing Inequalities On Number Lines Graphing Inequalities (Basic)
• Solving Linear Inequalities Solving Inequalities Including a Third Term Solving Inequalities Including a Third Term and Multiplication Solving Inequalities Including a Third Term, Multiplication and Division

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Square root

Square roots

Here is everything you need to know about square numbers and square roots. You will learn what a square number is and how to find the square roots of numbers and expressions. You will also apply this knowledge to problem solve.

Students first work with square roots in 8 th grade math and expand that knowledge as they move into high school math classes.

What is a square number?

A square number is a number that is the result of multiplying that number to itself, or “squared”. In other words, a square number is found when multiplying any number by itself. The solution when a number is multiplied to itself is called a perfect square.

Look at this table to see the relationship.

Square numbers can also be represented by an array that forms squares.

You can arrange 1^2 as a square which has side lengths 1 unit.

You can arrange 2^2 as a square which has side lengths 2 units.

You can arrange 3^2 as a square which has side lengths 3 units.

You can arrange 4^2 as a square which has side lengths 4 units.

There are an infinite number of perfect square numbers, which makes it impossible to know all of them. However, remembering the perfect squares up to 15 \times 15 is extremely helpful for problem solving purposes.

Squaring negative numbers

Negative numbers can be squared like positive numbers.

For example:

Notice how (- \; 5)^2=(5)^2=25

The square of any negative number is always positive as you are multiplying a negative by a negative, which gives you a positive answer.

What is a square root?

The square root is a factor of a number that, when multiplied to itself, gives the original number. In other words, square rooting a number is the inverse operation of squaring a number. Taking a square root undoes squaring a number. The square root symbol (square root function) looks like this:

Its mathematical name is a radical or radical symbol.

The square root of a number is represented by:

\sqrt{4} where 4 is considered the radicand because it is the number under the radical symbol.

\sqrt{4}=2. In this case, 2 is the principal square root because it is the positive square root.

Since 2\times{2}=4, and (- \; 2)\times(- \; 2)=4, then \sqrt{4}=2 or - \; 2. This is sometimes written as \sqrt{4}=\pm \; {2}.

Algebraic expressions such as variables can be squared. For example, x^2 means x\times{x}. So, \sqrt{x^2}=x. Taking the square root undoes the squaring.

x^4 is also a square term because x^{2}\times{x}^{2}=x^{4} so, \sqrt{x^{4}}=x^{2}

You can simplify square root expressions by breaking the expression down into perfect square factors.

Notice how \sqrt{32} is not a perfect square. The expression can still be simplified by breaking the number into perfect square factors. Specifically, look for the largest square factor of the number under the radical.

In this case, the largest square factor of 32 is 16. So, \sqrt{32} can be rewritten as \sqrt{16\times{2}} which is \sqrt{16}\times\sqrt{2}.

Since 16 is a perfect square, you can take the square root, but \sqrt{2} is not a perfect square, so you cannot take the square root without a calculator; it’s considered to be an irrational number.

\sqrt{32} fully simplified is 4\sqrt{2}.

Step-by-step guide How to simplify radicals

Common Core State Standards

How does this relate to 8 th grade math?

• Grade 8: Expressions and Equations (8.EE.A.2) Use square root and cube root symbols to represent solutions to equations of the form x^{2}=p and x^{3}=p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that \sqrt{2} is irrational.

[FREE] Square Roots Worksheet (Grade 6 to 8)

Use this worksheet to check your grade 6 to 8 students’ understanding of square roots. 15 questions with answers to identify areas of strength and support!

How to find square roots

In order to find square roots:

Write an expression using the \bf{\sqrt{\;}} (radical sign).

Find the square root, simplify if necessary.

Write the simplified answer.

Square numbers and square roots examples

Example 1: square root of a perfect square.

Find the square root of 81.

The square root of 81 is expressed as \sqrt{81} .

2 Find the square root, simplify if necessary.

\sqrt{81} is a whole number because 81 is a perfect square.

3 Write the simplified answer.

\sqrt{81}=9 and \sqrt{81}=- \; 9 because 9\times{9}=81 and - \; 9\times{- \; 9}=81

Example 2: square root of a fraction

Find the square root of \cfrac{1}{16}.

The square root of \cfrac{1}{16} is represented by \sqrt{\cfrac{1}{16}} .

\sqrt{\cfrac{1}{16}} is a perfect square because 1 and 16 are perfect square numbers. You can rewrite it with the radical in the numerator and the radical in the denominator.

\sqrt{\cfrac{1}{16}}=\cfrac{\sqrt{1}}{\sqrt{16}}

\cfrac{\sqrt{1}}{\sqrt{16}}=\cfrac{1}{4} or - \; \cfrac{1}{4}.

\sqrt{\cfrac{1}{16}}=\cfrac{\sqrt{1}}{\sqrt{16}}=\cfrac{1}{4} or - \; \cfrac{1}{4}.

Example 3: square root of an algebraic expression

Find the square root of 225s^{4}.

The square root of 225s^{4} is represented by \sqrt{225s^{4}}

\sqrt{225s^{4}} is a perfect square expression because 225 is a perfect square number and s^4 is a perfect square expression.

15\times{15}=225

s^{2}\times{s}^{2}=s^{4}

How to find square roots of algebraic expressions with non-perfect squares

In order to find square roots of algebraic expressions with non-perfect squares:

Find the largest square factor(s) of the term under the root.

Rewrite the radical as a product of the square factor(s) and the other factors.

Simplify the radical expression.

Example 4: square root of an algebraic expression

Simplify \sqrt{8x^{3}}.

Square numbers are 1, 4, 9, 16, 25, …

The largest square factor of 8 is 4 because 4\times{2}=8

The largest square factor of x^3 is x^2 because x^{2}\times{x}=x^{3}

Take the square root of 4 and x^2 because both are perfect squares.

How to solve problems involving square numbers and square roots

In order to problem solve with square numbers and square roots:

Identify whether you need to square or square root the number/variable.

Perform the operation.

Clearly state the answer within the context of the question.

Example 5: word problems with square numbers

The area of a square is 36\mathrm{~in}^{2}. Using the formula to find area of a square, \text{Area}=s^{2}, find the side length of the square.

Identify whether you need to square or square root the number/ variable.

The question is to find the side length, so using the formula you are taking the square root.

\text{Area}=s^{2} where the area is 36\mathrm{~in}^{2}.

Since the question is asking for side length, the positive value is the solution not the negative value.

The side length of the square is 6 inches.

Example 6: word problems with square roots

Two times a number squared is 32. Calculate the possible value(s) of the number.

In this case, you will have to take the square root to find the solution.

Two times a number squared is 32 can be written as the equation 2\times{x}^{2}=32.

For this problem, both + \; 4 and - \; 4 are the solutions.

Check both values in the original equation to validate your answer.

2\times(4)^{2}=32

2\times(- \; 4)^{2}=32

Teaching tips for square numbers and square roots

• Incorporate discovery based learning activities so that students can be like mathematicians and explore perfect square numbers and square roots on their own.
• If students struggle with multiplication tables, have them use a digital, online square root calculator.

Easy mistakes to make

• Squaring numbers incorrectly For example, thinking that squaring a number means to double it. 3^{2} ≠ {6} 3^{2}=3\times{3}=9
• Forgetting about the negative root when taking a square root For example, only recognizing positive values of square roots of integers. \sqrt{100}=10 (only thinking the answer is 10 ) \sqrt{100}=\pm \; {10}

Related square root lessons

• Laws of exponents
• Exponential notation
• Anything to the power of 0
• Exponent rules
• Negative exponents
• Multiplying exponents
• Dividing exponents
• Distributing exponents

Practice square numbers and square roots questions

1. What is the square root of the number, 169?

Taking the square root of 169 means \sqrt{169}. 169 is a perfect square number because 13\times13=169 and – \; 13\times{- \; 13}=169

So, \sqrt{169}=\pm \; {13}

2. What is the square root of a^{6}?

The square root of a^6 is represented by \sqrt{a^6}. a^6 is a perfect square term because a^{3}\times{a^{3}}=a^{6} so, \sqrt{a^{6}}=a^{3}

3. What are the values of \sqrt{144}?

12 and – \; 12

72 and – \; 72

12 and – \; 11

\sqrt{\;} means square root, so, \sqrt{144} means to take the square root of 144. In other words, what number multiplied to itself is 144?

12\times{12}=144 and – \; 12\times{- \; 12}=144.

4. Simplify the square root expression, \sqrt{36 y^{3}}.

Look for the perfect square factors of 36y^3 in order to simplify it.

36 is a perfect square and y^{3}=y^{2}\times{y} where y^{2} is a perfect square term.

Take the square root of the perfect square terms

\sqrt{36y^{3}} simplified is 6y\sqrt{y}

5. Find the side length of a square with an area of 81\mathrm{~cm}^{2}.

A square has four equal sides and to find the area of a square you take the side length and square it. So, if you have the area and need to find the side length, take the square root.

Since this is the length of the side of a square only the positive value works. So the side length of the square is 9 \, cm.

6. 3 times a number squared is 363. Find the number(s).

3 times a number squared is 363 translates to be:

In this case, both + \; 11 and – \; 11 work. Check both solutions to verify.

Square numbers and square roots FAQs

If you take the square root of a negative number on a calculator, you will get “error.” The reason being that the square root of a negative number is not a real number, it is an imaginary number which is part of the complex number system. Typically in 8 th grade math, you will be asked to find the square root of natural numbers, positive whole numbers, positive integers, and positive real numbers (decimals and fractions).

In algebra 1 and algebra 2 classes you will learn how to find the square root of polynomials. There are polynomials that are considered to be perfect square expressions such as perfect square trinomials.

To solve for the missing side of right triangles you will use the Pythagorean Theorem (Pythagoras’ Theorem), a^2+b^2=c^2. Since the theorem has square terms, you will have to use square root to find missing side lengths.

Quadratic equations have a squared term and square root undoes squaring. So, you will need to sometimes use square root to solve quadratic equations.

Yes, you can take the square root of prime numbers but they will be considered irrational numbers. So, either leave them under the radial symbol such as \sqrt{5} or use a square root calculator to find the answer. Remember the answer in a calculator will have many decimal places because irrational numbers are non-repeating, non-terminating numbers, so you will have to round the answer.

The next lessons are

• Scientific notation
• Quadratic graphs

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[FREE] Common Core Practice Tests (Grades 3 to 6)

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Unit 4: Systems of equations

About this unit.

If one line is useful, let's see what we can do with two lines. In this unit, we learn how to write systems of equations, solve those systems, and interpret what those solutions mean in a real-world context.

Intro to systems of equations

• Systems of equations: trolls, tolls (1 of 2) (Opens a modal)
• Systems of equations: trolls, tolls (2 of 2) (Opens a modal)
• Testing a solution to a system of equations (Opens a modal)
• Solutions of systems of equations Get 3 of 4 questions to level up!

Systems of equations with graphing

• Systems of equations with graphing (Opens a modal)
• Systems of equations with graphing: y=7/5x-5 & y=3/5x-1 (Opens a modal)
• Systems of equations with graphing: 5x+3y=7 & 3x-2y=8 (Opens a modal)
• Systems of equations with graphing: chores (Opens a modal)
• Systems of equations with graphing: exact & approximate solutions (Opens a modal)
• Systems of equations with graphing Get 3 of 4 questions to level up!

Solving systems with substitution

• Systems of equations with substitution: 2y=x+7 & x=y-4 (Opens a modal)
• Systems of equations with substitution (Opens a modal)
• Systems of equations with substitution: y=4x-17.5 & y+2x=6.5 (Opens a modal)
• Systems of equations with substitution: -3x-4y=-2 & y=2x-5 (Opens a modal)
• Systems of equations with substitution: 9x+3y=15 & y-x=5 (Opens a modal)
• Systems of equations with substitution: y=-5x+8 & 10x+2y=-2 (Opens a modal)
• Systems of equations with substitution: y=-1/4x+100 & y=-1/4x+120 (Opens a modal)
• Substitution method review (systems of equations) (Opens a modal)
• Systems of equations with substitution Get 3 of 4 questions to level up!

Number of solutions to systems of equations

• Systems of equations number of solutions: fruit prices (1 of 2) (Opens a modal)
• Systems of equations number of solutions: fruit prices (2 of 2) (Opens a modal)
• Solutions to systems of equations: dependent vs. independent (Opens a modal)
• Number of solutions to a system of equations (Opens a modal)
• Number of solutions to a system of equations graphically (Opens a modal)
• Number of solutions to a system of equations algebraically (Opens a modal)
• How many solutions does a system of linear equations have if there are at least two? (Opens a modal)
• Number of solutions to system of equations review (Opens a modal)
• Number of solutions to a system of equations graphically Get 3 of 4 questions to level up!
• Number of solutions to a system of equations algebraically Get 3 of 4 questions to level up!

Systems of equations word problems

• Age word problem: Imran (Opens a modal)
• Age word problem: Ben & William (Opens a modal)
• Age word problem: Arman & Diya (Opens a modal)
• System of equations word problem: walk & ride (Opens a modal)
• System of equations word problem: no solution (Opens a modal)
• System of equations word problem: infinite solutions (Opens a modal)
• Systems of equations with substitution: coins (Opens a modal)
• Systems of equations: FAQ (Opens a modal)
• Age word problems Get 3 of 4 questions to level up!
• Systems of equations word problems Get 3 of 4 questions to level up!

CBSE Class 8 Maths Worksheets for Linear Equations

Table of Contents

Prepare for success in CBSE Class 8 Linear Equations by utilizing our comprehensive PDF worksheets containing crucial chapter-wise and topic-wise questions. Daily practice of these CBSE NCERT Class 8 Linear Equations resources, including worksheets , question banks, workbooks, and exercises with solutions, will aid in concept mastery and effective revision. These materials are aligned with the latest CBSE syllabus 2024 -25 from NCERT, and CBSE , ensuring thorough coverage of all essential topics.

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• Click the links below to download our extensive collection of CBSE NCERT Worksheets for Class 8 Linear Equations , designed to help you excel in your studies.
• These free worksheets , complete with questions and solutions, are based on the latest CBSE NCERT Books and Syllabus , providing a valuable resource for exam preparation.
• Download chapter-wise test papers to further enhance your understanding and preparation for Class 8 Linear Equations examinations.

CBSE Class 8 Linear Equations Worksheet Questions with Answers

Question 1: Solve the equation: 2x + 5 = 11

Starting with the given equation:

2x + 5 = 11

Subtracting 5 from both sides:

2x = 11 – 5

Dividing by 2 on both sides:

Explanation: In this question, we first isolate the variable x by performing inverse operations. By subtracting 5 from both sides and then dividing by 2, we find the value of x to be 3, satisfying the equation.

Question 2: Find the solution to the equation: 3(x – 4) = 15

Expanding the equation:

3x – 12 = 15

Adding 12 to both sides:

3x = 15 + 12

Dividing by 3 on both sides:

Explanation: In this question, we first distribute the 3 to both terms inside the parentheses. Then, by simplifying and isolating the variable x, we find the solution x = 9 that satisfies the equation.

Question 3: Solve the equation: 4(2x + 3) = 32

8x + 12 = 32

Subtracting 12 from both sides:

8x = 32 – 12

Dividing by 8 on both sides:

Explanation:

In this question, we first distribute the 4 to both terms inside the parentheses. By simplifying and isolating the variable x, we find the solution x = 2.5 that satisfies the equation.These questions and answers provide practice in solving linear equations in one variable.

By understanding the steps involved in solving these equations, students can enhance their problem-solving skills and grasp the concepts of linear equations effectively.

Question 4: Solve the equation: 5(x – 2) = 3(x + 1)

Expanding both sides:

5x – 10 = 3x + 3

Subtracting 3x from both sides:

2x – 10 = 3

Adding 10 to both sides:

x = 13/2 or x = 6.5

Explanation: In this question, we first distribute the coefficients on both sides of the equation. Then, by simplifying and isolating the variable x, we find the solution x = 6.5 that satisfies the equation.

Question 5: Solve the equation: 2(x + 3) – 4(x – 1) = 0

2x + 6 – 4x + 4 = 0

-2x + 10 = 0

Explanation: In this question, we first distribute the coefficients on both sides of the equation. Then, by combining like terms and isolating the variable x, we find the solution x = 5 that satisfies the equation.

Question 6: Solve the equation: 3(2x – 1) = 2(3x + 1)

6x – 3 = 6x + 2

This equation has no solution, as -3 is not equal to 2.

Explanation: In this question, we first distribute the coefficients on both sides of the equation. Then, by simplifying and isolating the variable x, we find that the equation has no solution, as -3 is not equal to 2.

Steps to Excel in Class 8 Mathematics Linear Equations

Follow these expert-recommended steps from Infinity Learn to optimize your preparation for final exams:

• Create a Study Schedule: Organize your study time by prioritizing topics based on their importance and mark distribution in the Class 8 Mathematics syllabus.
• Select Quality Worksheets: Choose worksheets that cover a variety of question types related to each Linear Equations topic, ensuring comprehensive practice.
• Thorough Revision: Before tackling worksheets, revise the entire Class 8 Mathematics syllabus to maximize your performance.
• Focus on High-Weightage Topics: Begin with worksheets focusing on topics with higher marks weight-age to enhance your preparation.
• Time Management: Evaluate your performance based on the time taken to solve different types of questions, improving efficiency and accuracy.

Benefits of Using Linear Equations Worksheets

• Concept Clarity: These worksheets aid in clearing concepts and improving exam scores.
• Skill Enhancement: Practice with printable worksheets enhances analytical skills and understanding of Linear Equations.
• Expertly Crafted Resources: Developed by experienced teachers at Infinity Learn, these worksheets cater to students of all levels, ensuring comprehensive preparation.

Advantages of Class 8 Linear Equations Worksheets

• Concept Clarity: These worksheets help in clearing concepts and achieving higher scores in examinations.
• Skill Development: Practice with these printable worksheets enhances conceptual understanding and analytical skills.
• Comprehensive Coverage: Our worksheets cover all topics from the NCERT textbook for Class 8 Linear Equations, aiding in thorough preparation.

Class 8 Linear Equations with Our Comprehensive Study Materials

Get ready to excel in Class 8 Linear Equations with our extensive collection of study materials, available for free download in PDF format. Our resources include sample papers, previous year question papers, the latest NCERT books, and NCERT solutions , all tailored to the CBSE syllabus. These materials have been carefully crafted by experienced teachers from leading schools in India, ensuring high-quality content for your academic success.

The Power of Worksheets in Linear Equations

Our Class 8 Linear Equations worksheets are designed to help you apply your understanding of the subject by solving a variety of questions. We also offer a vast collection of MCQ tests to aid your daily practice. These worksheets are essential for students as they help in:

• Applying Knowledge: By solving questions, you can apply your understanding of Linear Equations concepts.
• Identifying Weaknesses: Our worksheets help you identify areas where you need improvement.
• Building Confidence: Regular practice with our worksheets will boost your confidence in Linear Equations.

Comprehensive Coverage of Linear Equations Topics

Our worksheets for Class 8 Linear Equations cover all important topics from each chapter of your NCERT book . They include a wide range of question types, such as:

• MCQ Questions: Multiple-choice questions to test your understanding of concepts.
• Short Answer Questions: Questions that require brief answers to assess your knowledge.
• Long Answer Questions: In-depth questions that evaluate your understanding of complex concepts.
• Fill in the Blanks: Questions that test your ability to recall important information.
• Match the Following: Questions that assess your ability to relate concepts.

The Benefits of Using Our Worksheets

Regular practice with our worksheets can significantly improve your knowledge and conceptual understanding of Linear Equations. Our worksheets are designed to:

• Cover All Topics: We ensure that all topics from your NCERT textbook are covered.
• Follow the Latest Syllabus: Our worksheets are aligned with the latest CBSE syllabus.
• Provide Diverse Question Types: Our worksheets include a variety of question types to test your understanding from different angles.

Easy Access to Printable Worksheets

All our Linear Equations worksheets for Class 8 are available in PDF format, making it easy for you to download and print them. You can access these printable worksheets for free and use them whenever you want. Our expert teachers have designed these PDF worksheets to be easy to read and solve on any computer or mobile device.

Free Access to Study Materials

If you’re a parent or student studying Class 8 Linear Equations, you’ve come to the right place. We offer free downloadable worksheets for Class 8 Linear Equations and all other subjects. Our study materials are designed to improve your overall knowledge and understanding of the subject. All our printable test papers for Linear Equations in Class 8 are available in PDF format for free access.Visit Infinity Learn, the leading portal for Class 8 students, to access our comprehensive study materials and unlock your full academic potential.

CBSE Class 8 Maths Linear Equations Worksheets FAQs

What are linear equations in one variable.

Linear equations in one variable are algebraic expressions where the variable appears only to the power of 1. They can be represented in the form ax + b = c, where a, b, and c are constants, and x is the variable.

How do I Solve Linear Equations in One Variable?

To solve linear equations in one variable, apply inverse operations to isolate the variable. Perform operations such as addition, subtraction, multiplication, and division on both sides of the equation to find the value of the variable that satisfies the equation.

Why are Linear Equations Important in Mathematics?

Linear equations play a crucial role in mathematics as they model real-world situations, help in problem-solving, and form the foundation for more complex algebraic concepts. They are fundamental in understanding relationships between variables and making predictions.

What is the Importance of Practicing Linear Equations Worksheets?

Practicing linear equations worksheets helps in reinforcing concepts, improving problem-solving skills, and enhancing understanding of algebraic principles. Regular practice with worksheets aids in mastering the techniques required to solve linear equations effectively.

How Can I Improve My Performance in Class 8 Maths Linear Equations?

To enhance your performance in Class 8 Maths Linear Equations, create a study schedule, practice regularly with worksheets, revise the syllabus thoroughly, focus on high-weightage topics, and evaluate your performance to identify areas for improvement. Consistent practice and understanding of concepts are key to excelling in linear equations.

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Solving Inequalities Notes, Assessments, Games, and Worksheets 7th Grade Math

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