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4.7: Distributive Property to Evaluate Formulas with Decimals

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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:

A = lw (\text{length}\times \text{width})

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.

A = 4.5(12 + 7)

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

A & = 4.5(12) + 4.5(7) \\A & = 54 + 31.5 \\A & = 85.5\ square\ inches

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.

2(6) \times 2(3.5)

12 \times 7 = 84

The area of the two rectangles is 84 square inches.

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
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.

A = 2.5(10 + 4)

Next, we can solve it.

 A = 2.5(14)

 A = 35

The area of the two rectangles is  35 mm^2 .

Video Review

Here are two videos for 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)

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Difficulty Level:

Basic

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Date Created:

Oct 29, 2012

Last Modified:

Jun 25, 2014
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