# 4.5: Distributive Property

**Basic**Created by: CK-12

**Practice**Distributive Property

Remember Kyle from the last Concept? Well, he wrote a numerical expression for the situation at the science museum, but he didn't evaluate it, which means that he doesn't have an answer to his teacher's question about cost.

Here is what Kyle wrote.

**\begin{align*}22(8.95 + 2.00)\end{align*} 22(8.95+2.00)**

But there was more to the problem. Kyle also needed to figure out additional costs.

Kyle knows that there is a way to solve this with the Distributive Property, but he can’t remember exactly what to do.

**In this Concept, you will learn how to use the Distributive Property to evaluate numerical expressions. Then we'll revisit this problem.**

### Guidance

In the last Concept, you learned how to write numerical expressions, and now you are going to learn how to evaluate those expressions.

**What does the word “evaluate” mean?**

When we ** evaluate** an expression, we figure out the value of that expression or the quantity of the expression.

When we evaluate expressions that have a product and a sum, we use a ** property** called the Distributive Property.

**What is the Distributive Property?**

** The Distributive Property** is a property that is a true statement about how to multiply a number with a sum. Multiply the number outside the parentheses with each number inside the parentheses. Then figure out the sum of those products.

*In other words, we distribute the number outside the parentheses with both of the values inside the parentheses and find the sum of those numbers.*

Let’s see how this works.

\begin{align*}4(3 + 2)\end{align*}

To use the Distributive Property, we take the four and multiply it by both of the numbers inside the parentheses. Then we find the sum of those products.

\begin{align*}& 4(3) + 4(2) \\
& 12 + 8 \\
& 20\end{align*}

**Our answer is 20.**

Here is another one.

\begin{align*}8(9 + 4)\end{align*}

Multiply the eight times both of the numbers inside the parentheses. Then find the sum of the products.

\begin{align*}& 8(9) + 8(4) \\
& 72 + 32 \\
& 104\end{align*}

**Our answer is 104.**

Now it is your turn. Evaluate these expressions using the Distributive Property.

#### Example A

\begin{align*}5(6 + 3)\end{align*}

**Solution: 45**

#### Example B

\begin{align*}2(8 + 1)\end{align*}

**Solution: 18**

#### Example C

\begin{align*}12(3 + 2)\end{align*}

**Solution: 60**

**Now we can take the expression that Kyle wrote and use the Distributive Property to figure out the total amount of money needed for the trip.**

\begin{align*}& 22(8.95 + 2) \\
& 22(8.95) + 22(2)\end{align*}

**Next, we can multiply 22 by 8.95.**

\begin{align*}& \quad \ \ \ \ 895 \\
& \underline{\times \quad \ \ \ 22 \;} \\
& \quad \ \ 1790 \\
& \underline{+ \ 1790 \; \; \;} \\
& \ \ \ 196.90 \ \text{this is the amount of all of the tickets}.\end{align*}

**Next, we complete the second part of the problem.**

2(22) = 44

It will cost the students an additional $44.00 to attend the Omni Theater.

The good news is that there is enough money in the student account to help cover the additional costs. There are fifty dollars in the account and the class only needs $44.00 to help cover the costs.

**The total amount of money needed is $240.90.**

Kyle gives his information to Mrs. Andersen and she is thrilled! Now the students are off to the Science Museum and the Omni Theater!

### Vocabulary

Here are the vocabulary words in this Concept.

- Numerical expression
- a number sentence that has at least two different operations in it.

- Product
- the answer in a multiplication problem

- Sum
- the answer in an addition problem

- Property
- a rule that works for all numbers

- Evaluate
- to find the quantity of values in an expression

- The Distributive Property
- the property that involves taking the product of the sum of two numbers. Take the number outside the parentheses and multiply it by each term in the parentheses.

### Guided Practice

Here is one for you to try on your own.

Use the distributive property to evaluate this expression.

\begin{align*}4(9 + 2)\end{align*}

First, we can distribute the four and multiply it by each value in the parentheses. Then we can add.

\begin{align*}36 + 8 = 44\end{align*}

**This is our answer.**

### Video Review

Here are videos for review.

Khan Academy The Distributive Property

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

### Practice

Directions: Evaluate each expression using the Distributive Property.

1. 4(3 + 6)

2. 5(2 + 8)

3. 9(12 + 11)

4. 7(8 + 9)

5. 8(7 + 6)

6. 5(12 + 8)

7. 7(9 + 4)

8. 11(2 + 9)

9. 12(12 + 4)

10. 12(9 + 8)

11. 10(9 + 7)

12. 13(2 + 3)

13. 14(8 + 6)

14. 14(9 + 4)

15. 15(5 + 7)

Evaluate

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

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

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

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

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

Here you'll learn to identify and apply the Distributive Property to evaluate numerical expressions.

## Concept Nodes:

Evaluate

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

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

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

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

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