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In addition and/or subtraction: Value 1 and Value 2 are the two numbers to be added or subtracted, and Value 3 is the answer.
In multiplication: Value 1 is one factor, Value 2 is second factor, and Value 3 is the answer.
In division: Value 1 is the dividend, Value 2 is the divisor, and Value 3 is the answer.
In Multiplication/Division things are different: In this option, Value 3 is the largest number (the answer for multiplication, and the dividend for division). Values 1 and 2 are the other two numbers (factors in multiplication, and divisor & answer for division). I am sorry for this discrepancy; however it allows for you to make, for example, multiplication/division equations based on basic multiplication tables by setting values 1 and 2 both to be from 2 to 12.

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1.E: Whole Numbers (Exercises)

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1.1 - Introduction to Whole Numbers

Identify counting numbers and whole numbers.

In the following exercises, determine which of the following numbers are (a) counting numbers (b) whole numbers.

Model Whole Numbers

In the following exercises, model each number using base-10 blocks and then show its value using place value notation.

Identify the Place Value of a Digit

In the following exercises, find the place value of the given digits.

(a) 8 (b) 4 (c) 1 (d) 7 (e) 2

(a) 4 (b) 0 (c) 1 (d) 9 (e) 3

Use Place Value to Name Whole Numbers

In the following exercises, name each number in words.

Use Place Value to Write Whole Numbers

In the following exercises, write each number as a whole number using digits.

six hundred two
fifteen thousand, two hundred fifty-three
three hundred forty million, nine hundred twelve thousand, sixty-one
two billion, four hundred ninety-two million, seven hundred eleven thousand, two

Round Whole Numbers

In the following exercises, round to the nearest ten.

In the following exercises, round to the nearest hundred.

1.2 - Add Whole Numbers

Use addition notation.

In the following exercises, translate the following from math notation to words.

10,085 + 3,492

Model Addition of Whole Numbers

In the following exercises, model the addition.

Add Whole Numbers

In the following exercises, fill in the missing values in each chart.

$A table with 11 rows down and 11 rows across. The first row and first column are headers and include the numbers 0 through 9 both across and down, with a plus sign in the first cell. The numbers across in the second row down appear as follows: 0,0, 1, null, 3, 4, null, 6, 7, null, 9. The numbers across in the third row down appear as follows: 1, 1, 2, 3, 4, null, null, 7, 8, 9, null. The numbers in the fourth row down appear across as follows: 2, null, 3,4,5,6,7,8, null, 10, 11. The numbers across in the fifth row down appear as follows: 3, 3, null, 5, null, 7, 8, null, 10, null 12. The numbers across in the sixth row down appear as follows: 4, 4, 5, null, null, 8, 9,null, null, 12, null. The numbers across in the seventh row down appear as follows: 5, 5, null, 7, 8, null null, 11, null, 13, null. The numbers across in the eighth row down appear as follows:6, 6, 7, 8, null, 10, null, null, 13, null, 15. The numbers across in the ninth row down appear as follows: null, null, 9, null, null, 12, 13, null, 15, 16. The numbers across in the tenth row down appear as follows: 8,8,9,null, 11, null, null, 14, null, eleventh row down appear as follows: 9, 9, 10, 11, null, 13, 14, null, null, 17, null.$

In the following exercises, add.

(a) 0 + 19 (b) 19 + 0
(a) 0 + 480 (b) 480 + 0
(a) 7 + 6 (b) 6 + 7
(a) 23 + 18 (b) 18 + 23
7,281 + 12,546
5,280 + 16,324 + 9,731

Translate Word Phrases to Math Notation

In the following exercises, translate each phrase into math notation and then simplify.

the sum of 30 and 12
11 increased by 8
25 more than 39
total of 15 and 50

Add Whole Numbers in Applications

In the following exercises, solve.

Shopping for an interview Nathan bought a new shirt, tie, and slacks to wear to a job interview. The shirt cost $24, the tie cost $14, and the slacks cost $38. What was Nathan’s total cost?
Running Jackson ran 4 miles on Monday, 12 miles on Tuesday, 1 mile on Wednesday, 8 miles on Thursday, and 5 miles on Friday. What was the total number of miles Jackson ran?

In the following exercises, find the perimeter of each figure.

$An image of a rectangle that is 8 feet tall and 15 feet wide.$

1.3 - Subtract Whole Numbers

Use subtraction notation.

14 − 5
40 − 15
351 − 249
5,724 − 2,918

Model Subtraction of Whole Numbers

In the following exercises, model the subtraction.

18 − 4
41 − 29

Subtract Whole Numbers

In the following exercises, subtract and then check by adding.

8 − 5
12 − 7
23 − 9
. 46 − 21
82 − 59
110 − 87
539 − 217
415 − 296
1,020 − 640
8,355 − 3,947
10,000 − 15
54,925 − 35,647

In the following exercises, translate and simplify.

the difference of nineteen and thirteen
subtract sixty-five from one hundred
seventy-four decreased by eight
twenty-three less than forty-one

Subtract Whole Numbers in Applications

Temperature The high temperature in Peoria one day was 86 degrees Fahrenheit and the low temperature was 28 degrees Fahrenheit. What was the difference between the high and low temperatures?
Savings Lynn wants to go on a cruise that costs $2,485. She has $948 in her vacation savings account. How much more does she need to save in order to pay for the cruise?

1.4 - Multiply Whole Numbers

Use multiplication notation.

In the following exercises, translate from math notation to words.

8 × 5
6 • 14

Model Multiplication of Whole Numbers

In the following exercises, model the multiplication.

2 × 4
3 × 8

Multiply Whole Numbers

$A table with 10 rows down and 10 rows across. The first row and first column are headers and include the numbers 0 through 9 both across and down, with a plus sign in the first cell. The numbers across in the second row down appear as follows: 0, 0, 0, 0, 0, 0, null, 0, null, 0,0. The numbers across in the third row down appear as follows: 1, 0, 1, 2, null, 4, 5, 6, 7, null, 9. The numbers across in the fourth row down appear as follows: 2, 0, null, 4, null, 8, 10, null, 14, 16, null. The numbers across in the fifth row down appear as follows: 3, null, 3, null, 9, null, null, 18, null, 24, null. The numbers across in the sixth row down appear as follows: 4, 0, 4, 0, 12, null, null, 24, null, null, 36. The numbers across in the seventh row down appear as follows:5, 0, 5, 10, null, 20, null, 30, 35, 40, 45. The numbers across in the eighth row down appear as follows: 6, null, null, 12, 18, null, null, 36, 42, null, 54. The numbers across in the ninth row down appear as follows: 7, 0, 7, null, 21, null, 35, null, null, 56, 63. The numbers in the tenth row down appear as follows: 8, 0, 8, 16, null, 32, null, 48, null, 64, null. The numbers in the eleventh row down appear across as follows: 9, null, null, 18, 27, 36, null, null, 63, 72, null.$

In the following exercises, multiply.

0 • 14
1 • 99
(a) 7 • 4 (b) 4 • 7
9,261 × 3
48 • 76
64 • 10
162 × 493
3,624 × 517
10,538 • 22
the product of 15 and 28
ninety-four times thirty-three
ten times two hundred sixty-four

Multiply Whole Numbers in Applications

Gardening Geniece bought 8 packs of marigolds to plant in her yard. Each pack has 6 flowers. How many marigolds did Geniece buy?
Cooking Ratika is making rice for a dinner party. The number of cups of water is twice the number of cups of rice. If Ratika plans to use 4 cups of rice, how many cups of water does she need?
Multiplex There are twelve theaters at the multiplex and each theater has 150 seats. What is the total number of seats at the multiplex?
Roofing Lewis needs to put new shingles on his roof. The roof is a rectangle, 30 feet by 24 feet. What is the area of the roof?

1.5 - Divide Whole Numbers

Use division notation.

Translate from math notation to words.

54 ÷ 9
$\dfrac{72}{8}$
$6 \overline{\smash{)}48}$

Model Division of Whole Numbers

In the following exercises, model.

8 ÷ 2
$3 \overline{\smash{)}12}$

Divide Whole Numbers

In the following exercises, divide. Then check by multiplying.

14 ÷ 2
$\dfrac{32}{8}$
52 ÷ 4
$26 \overline{\smash{)}26}$
$\dfrac{97}{1}$
0 ÷ 52
100 ÷ 0
$\dfrac{355}{5}$
3828 ÷ 6
$31 \overline{\smash{)}1,519}$
$\dfrac{7505}{25}$
5,166 ÷ 42
the quotient of 64 and 16
the quotient of 572 and 52

Divide Whole Numbers in Applications

Ribbon One spool of ribbon is 27 feet. Lizbeth uses 3 feet of ribbon for each gift basket that she wraps. How many gift baskets can Lizbeth wrap from one spool of ribbon?
Juice One carton of fruit juice is 128 ounces. How many 4 ounce cups can Shayla fill from one carton of juice?

PRACTICE TEST

Determine which of the following numbers are (a) counting numbers (b) whole numbers. $$0, 4, 87$$
Find the place value of the given digits in the number 549,362.

(a) 9 (b) 6 (c) 2 (d) 5

Write each number as a whole number using digits.

(a) six hundred thirteen (b) fifty-five thousand two hundred eight

Round 25,849 to the nearest hundred.
65 − 42
85 ÷ 5
1,000 × 8
90 − 58
(0)(12,675)
$\dfrac{0}{9}$
$8 \overline{\smash{)}128}$
145 − 79
7 • 475
8,528 + 704
$\dfrac{26}{0}$
733 − 291
4,916 − 1,538
495 ÷ 45
52 × 983

Translate each phrase to math notation and then simplify.

The sum of 16 and 58
The product of 9 and 15
The difference of 32 and 18
The quotient of 63 and 21
29 more than 32
50 less than 300
LaVelle buys a jumbo bag of 84 candies to make favor bags for her son’s party. If she wants to make 12 bags, how many candies should she put in each bag?
Last month, Stan’s take-home pay was $3,816 and his expenses were $3,472. How much of his take-home pay did Stan have left after he paid his expenses?
Each class at Greenville School has 22 children enrolled. The school has 24 classes. How many children are enrolled at Greenville School?
Clayton walked 12 blocks to his mother’s house, 6 blocks to the gym, and 9 blocks to the grocery store before walking the last 3 blocks home. What was the total number of blocks that Clayton walked?

Contributors and Attributions

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Understanding multiplication

Whole numbers

Here you will learn about whole numbers, including how to identify whole numbers, whole numbers on a number line, and the properties of whole numbers.

Students will first learn about whole numbers as part of counting and cardinality in Kindergarten and will expand their knowledge of whole numbers throughout elementary and middle school when learning about the properties of whole numbers and performing the four operations with whole numbers.

What are whole numbers?

Whole numbers are a set of numbers starting at zero and increasing by one each time.

Whole numbers do not include fractions, decimals, or negative numbers. They are positive integers.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10….

All whole numbers are integers, but not all integers are whole numbers since integers also include negative numbers. Both whole numbers and integers are rational numbers.

For example,

Properties of whole numbers

Commutative property of whole numbers

The commutative property of whole numbers states that the order of two numbers being added or multiplied together does not matter and that changing the order of the numbers will still give the same result.

Common Core State Standards

How does this relate to Kindergarten math through 6th grade math?

Kindergarten – Counting and Cardinality (K.CC.1, K.CC.2, K.CC.3) Count to 100 by ones and by tens; Count forward beginning from a given number within the known sequence (instead of having to begin at 1 ); Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects).
Grade 1 – Operations and Algebraic Thinking (1.0A.B.3 ) Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition). To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition).
Grade 2 – Operations and Algebraic Thinking (2.OA.C.3) Determine whether a group of objects (up to 20 ) has an odd or even number of members, for example, by pairing objects or counting them by 2 s; write an equation to express an even number as a sum of two equal addends.
Grade 3 – Operations and Algebraic Thinking (3.OA.B.5) Apply properties of operations as strategies to multiply and divide. Examples: If 6 \times 4 = 24 is known, then 4 \times 6 = 24 is also known. (Commutative property of multiplication). 3 \times 5 \times 2 can be found by 3 \times 5 = 15, then 15 \times 2 = 30, or by 5 \times 2 = 10, then 3 \times 10 = 30. (Associative property of multiplication). Knowing that 8 \times 5 = 40 and 8 \times 2 = 16, one can find 8 \times 7 as 8 \times (5 + 2) = (8 \times 5) + (8 \times 2) = 40 + 16 = 56. (Distributive property).
Grade 4 – Number and Operations Base Ten (4.NBT.B.5) Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Grade 6 – Number Systems (6.NS.B.4) Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 \, (9 + 2).

How to use whole numbers

In order to identify whole numbers:

Recall the definition of the type of number needed.

Show whether the number fits or does not fit the definition.

In order to apply a property of whole numbers:

Recall the property.

Use the property to get an answer.

[FREE] Types of Number Check for Understanding Quiz (Grade 2, 4 and 6)

Use this quiz to check your grade 6 students’ understanding of types of numbers. 10+ questions with answers covering a range of 2nd, 4th and 6th grade types of numbers topics to identify areas of strength and support!

Identifying whole numbers examples

Example 1: identifying whole numbers.

Which of the following are whole numbers?

0, \, 8.5, \, -1, \, 32, \, 6 \cfrac{1}{4} \, , \, 3.05, \, 927

Since the set of whole numbers does not include decimals, fractions, and negative numbers, you can eliminate 8.5, -1, 6 \cfrac{1}{4} \, , and 3.05 from the list.

2 Show whether the number fits or does not fit the definition.

The remaining numbers are 0, 32, and 927. All three fit the definition and are whole numbers.

Answer: 0, 32, and 927

Example 2: identifying whole numbers

Maya says -4 is a whole number since it doesn’t have a decimal or fractional part. Is she correct?

The set of whole numbers includes all positive integers starting at zero. Whole numbers do not include negative numbers, fractions, or decimals.

-4 is not a whole number since it is not a positive number. Negative numbers are not whole numbers. Therefore, Maya is incorrect.

Example 3: identifying whole numbers

Which point on the number line represents a whole number?

The only point on the number line that shows a whole number is B, which represents 5.

Point A represents 3 \cfrac{1}{2} \, , point C represents 6 \cfrac{1}{2} \, and point D represents a fraction or decimal between 7 \cfrac{1}{2} and 8.

Since whole numbers do not include fractions or decimals, point B is the only whole number.

Example 4: identifying whole numbers

Which whole number fills in the blank in the sequence?

26, \, 27, \, 28, \, \rule{0.5cm}{0.15mm} \, , \, 30, \, 31

26, \, 27, \, 28, \, {\bf{29}}, \, 30, \, 31

Although there are many fractions and decimals in between 28 and 30, there is only one whole number, which is 29.

Example 5: apply a property of whole numbers

Fill in the blank using your knowledge of the commutative property of multiplication to make the equation true.

\rule{0.5cm}{0.15mm} \, \times 15=15 \times 3

The commutative property of multiplication states that the order of two numbers being multiplied together does not matter and that changing the order of the numbers will still give the same result.

a \times b = b \times a

\underline{3} \times 15=15 \times 3

The number 3 makes the equation true.

Example 6: apply a property of whole numbers

Fill in the blank using your knowledge of the distributive property to make the equation true.

3 \times(7 + 9)= \, \rule{0.5cm}{0.15mm} \, +27

The distributive property states that multiplication is distributive over addition. This means that when multiplying a number by a sum of 2 numbers, you can multiply by each number separately and then add the products.

a(b + c) =(a \times b) + (a \times c)

Since this equation can also be solved as (3 \times 7) + (3 \times 9), I know that the missing number is 21.

3 \times(7 + 9)=\underline{21}+27

Teaching tips for whole numbers

Allow students to use concrete manipulatives to explore whole numbers when first building number sense.
Use a number line to give students a visual representation of whole numbers. As they progress to higher grades, the number line can be partitioned into fractional and decimal parts as well, so students can see the difference between whole numbers and fractions/decimals. Later, a number line can also be extended past the number zero to show negative numbers. Students will gain better number sense when they are able to see non-examples of whole numbers.
Display a chart or poster in the classroom showing the different types of numbers – whole numbers, natural numbers, integers, real numbers, etc. New types of numbers can be added to these displays in higher grade levels. This will help students differentiate between the sets of numbers.

Easy mistakes to make

Thinking that zero is not a whole number Zero is the first and smallest whole number. The set of whole numbers begins at zero and increases by one with each number.
Thinking that whole numbers are the same as integers Whole numbers are a subset of integers. Integers include all negative numbers, positive numbers, and zero, while whole numbers include only non-negative integers.

Related types of numbers lessons

This whole numbers topic guide is part of our series on types of numbers. You may find it helpful to start with the main types of numbers topic guide for a summary of what to expect or use the step-by-step guides below for further detail on individual topics. Other topic guides in this series include:

Types of numbers
Irrational numbers
Rational numbers
Prime numbers
Natural numbers
Prime and composite numbers
Number sets
Even numbers
Odd numbers
Absolute value

Practice identifying whole numbers questions

1. What is the smallest whole number?

The set of whole numbers starts at zero. Whole numbers do not include negative numbers, fractions, or decimals. Therefore, the smallest whole number listed is zero.

2. Look at the number line. What is the missing whole number?

When counting whole numbers by ones, the number after 19 will be 20.

3. Colin wrote a set of whole numbers on the whiteboard using the numbers 0, 1, 3, and 9. What number should he not have included?

1.039 should not have been included because it is a decimal, not a whole number.

4. Select the group of numbers made up of only whole numbers.

101, \, 556, \, 18,000, \, 1 is the only group of numbers comprised of only whole numbers. The other groups include at least one fraction or decimal.

5. Which property is demonstrated by the following equation?

5(9+8)=(5 \times 9)+(5 \times 8)

Associative property

Commutative property

This shows the distributive property because multiplication is being distributed over addition. The distributive property allows you to perform the multiplication separately, then add the products.

6. Fill in the blank to make the equation true.

8 \times\left(6 \times \, \rule{0.5cm}{0.15mm} \, \right)=(8 \times 6) \times 4

This equation shows the associative property of multiplication, which states that when multiplying three numbers, the grouping of two numbers within the expression can change and still give the same result.

Therefore, since the right side shows 8, 6, and 4 being multiplied, I know the same 3 numbers are being multiplied on the left side of the equation.

Whole numbers FAQs

Whole numbers are a set of numbers (also known as natural numbers or counting numbers) starting at the number zero and increasing by one each time. Whole numbers do not include fractions, decimals, or negative numbers.

Whole numbers and natural numbers are very similar but not the same. The set of natural numbers starts at one instead of zero.

Whole numbers are a subset of integers. Integers include positive whole numbers, negative whole numbers, and zero, while whole numbers only include non-negative integers.

If the fraction has the same numerator and denominator, or if its numerator is a multiple of its denominator, it can be written as a whole number. For example, the fraction \cfrac{4}{2} can be written as the whole number 2.

The next lessons are

Rounding numbers
Factors and multiples

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Order of Operations with Whole Numbers (Six Steps) (A)

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