Have you ever had to use a formula to figure something out? Well sometimes when you work with properties, it is necessary.

Let's say that you had a rectangle that was half as large as this one. That would mean that the side lengths of the rectangle would be 6 inches and 3.5 inches.

Now what if you had two of them? What would be the area of the two rectangles?

2(6 x 3.5)

Do you know how to figure this out?

**This Concept is about the distributive property and formulas. By the end of it, you will know how to tackle this problem.**

### Guidance

We can also use and apply the Distributive Property when working with a formula. Let’s think about the formula for finding the area of a rectangle.

**We know that the area of a rectangle can be found by using the formula:**

\begin{align*}A = lw (\text{length}\times \text{width})\end{align*}

For this example, we would multiply 12 times 4 and get an area of 48 square inches.

**How can we find the area of both of these rectangles?**

You can see that they have the same width. The width is four and a half inches. However, there are two lengths.

**We need to find the product of a number and a sum.**

**Here is our expression.**

\begin{align*}A = 4.5(12 + 7)\end{align*}

Now we can use the Distributive Property to find the area of these two rectangles.

\begin{align*}A & = 4.5(12) + 4.5(7) \\ A & = 54 + 31.5 \\ A & = 85.5\ square\ inches\end{align*}

**Notice that we used what we have already learned about multiplying decimals and whole numbers with the Distributive Property.** **When we distributed 4.5 with each length, we were able to find the sum of the products.** **This gives us the area of the two rectangles.**

Use what you have learned to answer these questions about formulas, area and the distributive property.

#### Example A

What is the formula for finding the area of a square?

**Solution: A = s^2**

#### Example B

Which property is being illustrated: 4(a + b) = 4a + 4b

**Solution: The Distributive Property**

#### Example C

What is the formula for finding the area of a rectangle?

**Solution: A = length x width**

Remember the rectangle from the beginning of the Concept? Now you are ready to work on that problem. Take a look.

Let's say that you had a rectangle that was half as large as this one. That would mean that the side lengths of the rectangle would be 6 inches and 3.5 inches.

Now what if you had two of them? What would be the area of the two rectangles?

2(6 x 3.5)

Do you know how to figure this out?

To figure this out, we have to multiply the value outside the parentheses by both values inside the parentheses.

\begin{align*}2(6) \times 2(3.5)\end{align*}

\begin{align*}12 \times 7 = 84\end{align*}

**The area of the two rectangles is 84 square inches.**

### Vocabulary

- 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

- 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.

- Area
- the space inside a figure.

### Guided Practice

Here is one for you to try on your own.

Use the Distributive Property to find the area of the rectangles.

**Answer**

First, we can write an expression to solve it.

\begin{align*}A = 2.5(10 + 4)\end{align*}

Next, we can solve it.

\begin{align*} A = 2.5(14)\end{align*}

\begin{align*} A = 35\end{align*}

**The area of the two rectangles is \begin{align*} 35 mm^2\end{align*}.**

### Video Review

Khan Academy The Distributive Property

Khan Academy: Area and Perimeter

### Practice

Directions: Practice using the Distributive Property to solve each problem.

1. 3.2(4 + 7)

2. 2.5(6 + 8)

3. 1.5(2 + 3)

4. 3.1(4 + 15)

5. 6.5(2 + 9)

6. 7.5(2 + 3)

7. 8.2(9 + 3)

8. 4(5.5 + 9)

9. 5(3.5 + 7)

10. 2(4.5 + 5)

11. 3.5(2.5 + 3)

12. 2.5(9 + 1.5)

13. 3.2(7 + 8.3)

14. 1.5(8.9 + 2.5)

15. 3.5(2.5 + 8.2)