<meta http-equiv="refresh" content="1; url=/nojavascript/">

# Distributive Property

## The distributive property dictates that when multiplying, the multiplication of real numbers distributes over two or more terms in parentheses. Learn more.

0%
Progress
Practice Distributive Property
Progress
0%
Distributive Property

Credit: Julie/hello-julie
Source: https://www.flickr.com/photos/roosterfarm/327228804/

Josh is at the yarn store for their annual sale. Each bundle of yarn is on sale for 3.49. He buys 10 bundles of red yarn, 8 bundles of green, 6 bundles of blue, and another 6 bundles of yellow. How much did Josh spend on yarn? In this concept, you will learn to use the distributive property to evaluate numerical expressions. ### Guidance To evaluate an expression means to simplify an expression to find the value or quantity. Expressions of the product of a number and a sum can be evaluated using the distributive property. Distributive Property The distributive property is a property that allows you to multiply a number and a sum by distributing the multiplier outside the parentheses with each addend inside the parentheses. a(b+c)=ab+bc Then you can evaluate the expression by finding the sum of the products. Here an expression of the product of a number and a sum. 4(3+2)\begin{align*}4(3+2)\end{align*} To use the distributive property, take the 4 and distribute the multiplier to the addends inside the parentheses. 4(3+2)=4(3)+4(2) Then, find the sum of the products. 4(3)+4(2)12+820 Therefore, the value of the product of 4 times the sum of 3 plus 2 is 20. Here is another example, this time with a variable. 8(9+a)\begin{align*}8(9+a)\end{align*} Evaluate the expression using the distributive property. First, distribute the 8 to each addend inside the parentheses. 8(9+a)=8(9)+8(a) Then, find the sum of the products. 8(9)+8(a)72+8a This is as far as this expression can be evaluated. If there is a known value for a\begin{align*}a\end{align*}, you can substitute a\begin{align*}a\end{align*} with the value to continue evaluating the expression. Evaluate the expression if a=4\begin{align*}a = 4\end{align*}. 72+8(4)72+32104 The value of the product of 8 times the sum of 9 plus a\begin{align*}a\end{align*}, when a\begin{align*}a\end{align*} equals 4, is 104. ### Guided Practice Use the distributive property to evaluate the expression. 4(9+2)\begin{align*}4(9 + 2)\end{align*} First, distribute the 4 and multiply it by each value in the parentheses. 4(9+2)=4(9)+4(2) Then, find the sum of the products. 4(9)+4(2)36+844 The value of the product of 4 times the sum of 9 plus 2 is 44. ### Examples Use the distributive property to evaluate the following expressions. #### Example 1 5(6+3)\begin{align*}5(6 + 3)\end{align*} First, distribute the multiplier to each value in the parentheses. 5(6+3)=5(6)+5(3) Then, find the sum of the products. 5(6)+5(3)30+1545 The value of the product of 5 times the sum of 6 plus 3 is 45. #### Example 2 2(8+1)\begin{align*}2(8 + 1)\end{align*} First, distribute the multiplier to each value in the parentheses. 2(8+1)=2(8)+2(1) Then, find the sum of the products. 2(8)+2(1)16+218 The value of the product of 2 times the sum of 8 plus 1 is 18. #### Example 3 12(3+2)\begin{align*}12(3 + 2)\end{align*} First, distribute the multiplier to each value in the parentheses. 12(3+2)=12(3)+12(2) Then, find the sum of the products. 12(3)+12(2)36+2460 The value of the product of 12 times the sum of 3 plus 2 is 60. ### Follow Up Credit: Sherrie Thai Source: https://www.flickr.com/photos/shaireproductions/5506878010/ License: CC BY-NC 3.0 Remember Josh at the yarn store? Josh buys 10 bundles of red yarn, 8 bundles of green, 6 bundles of blue, and another 6 bundles of yellow for3.49 each. Multiply the sum of bundles of yarn by $3.49 to find the total cost of the yarn. First, write an expression to find the total cost of the yarn.$3.49(10+8+6+6)\begin{align*}\3.49(10 + 8 + 6 + 6)\end{align*}

Then, distribute the multiplier to each value in the parentheses.

$3.49(10+8+6+6)=$3.49(10)+$3.49(8)+$3.49(6)+$3.49(6) Then, find the sum of the products.$3.49(10)+$3.49(8)+$3.49(6)+$3.49(6)$34.90+$27.92+$20.94+$20.94$104.70

Josh spent \$104.70 on yarn.

### Video Review

This video presents the distributive property from whole numbers to more complicated algebraic expressions.

The Distributive Property

### Explore More

Evaluate each expression using the distributive property.

1. 4(3+6)\begin{align*}4(3 + 6)\end{align*}
2. 5(2+8)\begin{align*}5(2 + 8)\end{align*}
3. 9(12+11)\begin{align*}9(12 + 11)\end{align*}
4. 7(8+9)\begin{align*}7(8 + 9)\end{align*}
5. \begin{align*}8(7 + 6)\end{align*}
6. \begin{align*}5(12 + 8)\end{align*}
7. \begin{align*}7(9 + 4)\end{align*}
8. \begin{align*}11(2 + 9)\end{align*}
9. \begin{align*}12(12 + 4)\end{align*}
10. \begin{align*}12(9 + 8)\end{align*}
11. \begin{align*}10(9 + 7)\end{align*}
12. \begin{align*}13(2 + 3)\end{align*}
13. \begin{align*}14(8 + 6)\end{align*}
14. \begin{align*}14(9 + 4)\end{align*}
15. \begin{align*}15(5 + 7)\end{align*}

### Vocabulary Language: English

Evaluate

Evaluate

To evaluate an expression or equation means to perform the included operations, commonly in order to find a specific value.
Numerical expression

Numerical expression

A numerical expression is a group of numbers and operations used to represent a quantity.
Product

Product

The product is the result after two amounts have been multiplied.
Property

Property

A property is a rule that works for a given set of numbers.
Sum

Sum

The sum is the result after two or more amounts have been added together.