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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.
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,
Examples of Whole Numbers  Examples of NonWhole Numbers 

0 \quad \quad \quad \quad 100 \quad \quad \quad \quad 857 \quad 1,524 \quad \quad 125,031 \quad \quad 1,000,000  5 \quad \quad \quad \quad \cfrac{1}{2} \quad \quad \quad \quad 0.75 \quad 0.\overline{88} \quad \quad \quad \;\, 2\cfrac{1}{4} \,\;\; \quad \quad \quad \quad \pi \quad \quad 
Commutative property of whole numbers
For example,
Commutative property of addition  Commutative property of multiplication 

a+b=b+a 4+5=5+4
 a \times b=b \times a 6 \times 3=3 \times 6

See also: Commutative property
Associative property of whole numbers
For example,
Associative property of addition  Associative property of multiplication 

(a+b)+c=a+(b+c) (8+4)+6=8+(4+6)
 (a \times b) \times c=a \times(b \times c) (2 \times 5) \times 7=2 \times(5 \times 7)

See also: Associative property
Distributive property
For example,
Distributive property of multiplication
over addition  Distributive property of multiplication
over subtraction 

a(b+c)=(a \times b)+(a \times c) \begin{aligned}
5(3+9) & =(5 \times 3)+(5 \times 9) \\
& =15+45 \\
& =60
\end{aligned}
 a(bc)=(a \times b)(a \times c) \begin{aligned}
8(101) & =(8 \times 10)(8 \times 1) \\
& =808 \\
& =72
\end{aligned}

See also: Distributive property
Closure property
For example,
Closure property of addition  Closure property of multiplication 

a+b=c If a and b are whole numbers, c will be a whole number. 9+6=15
 a \times b=c If a and b are whole numbers, c will be a whole number. 8 \times 4=32

How does this relate to Kindergarten math through 6th grade math?
In order to identify whole numbers:
In order to apply a property of whole numbers:
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!
DOWNLOAD FREEUse 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!
DOWNLOAD FREEWhich 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.
2Show 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
Maya says 4 is a whole number since it doesn’t have a decimal or fractional part. Is she correct?
Recall the definition of the type of number needed.
The set of whole numbers includes all positive integers starting at zero. Whole numbers do not include negative numbers, fractions, or decimals.
Show whether the number fits or does not fit the definition.
4 is not a whole number since it is not a positive number. Negative numbers are not whole numbers. Therefore, Maya is incorrect.
Which point on the number line represents a whole number?
Recall the definition of the type of number needed.
The set of whole numbers includes all positive integers starting at zero. Whole numbers do not include negative numbers, fractions, or decimals.
Show whether the number fits or does not fit the definition.
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.
Which whole number fills in the blank in the sequence?
26, \, 27, \, 28, \, \rule{0.5cm}{0.15mm} \, , \, 30, \, 31
Recall the definition of the type of number needed.
The set of whole numbers includes all positive integers starting at zero. Whole numbers do not include negative numbers, fractions, or decimals.
Show whether the number fits or does not fit the definition.
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.
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
Recall the property.
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
Use the property to get an answer.
\underline{3} \times 15=15 \times 3
The number 3 makes the equation true.
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
Recall the property.
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)
Use the property to get an answer.
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
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 stepbystep guides below for further detail on individual topics. Other topic guides in this series include:
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
Distributive property
Closure 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 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 nonnegative 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.
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40 multiple choice questions and detailed answers to support test prep, created by US math experts covering a range of topics!