How to Use the Distributive Property with Fractions

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  • 0:00 Distributive Property…
  • 1:23 Real World Application
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Lesson Transcript
Instructor: Maria Airth

Maria has a Doctorate of Education and over 15 years of experience teaching psychology and math related courses at the university level.

The distributive property works the same with or without fractions. In this lesson, you'll learn how to use the distributive property on fractions, step by step.

Distributive Property & Fractions

Fractions can strike fear in the hearts of many students. But take heart and know that fractions are just as easy to work with as any other number type.

The distributive property allows us to multiply one number or term with a set of terms in parentheses. All you do is multiply the term outside the parenthesis by each term inside the parentheses. Fractions follow the same rules as any other kind of term in algebra. They do not change the general procedures for how to simplify an algebraic expression using the distributive property.

It's best to learn math with an example, so let's take a look at one:

  • 1/3 ( x + 3)

Step 1:

Multiply the term on the outside of the parenthesis by the first term on the inside of the parenthesis.

  • 1/3*x= 1/3x

Step 2:

Continue multiplying the outside term by each term inside until all terms inside the parentheses have been multiplied.

  • 1/3 * 3 = 1

Step 3:

Simplify the results by collecting like terms and reducing all fractions, where necessary.

  • 1/3x + 1

The solution to this example is simply 1/3x + 1.

Real World Application

Word problems add an extra step to the process of simplifying distributive property problems. First you must translate the words into an algebraic function, after which you can simplify it.

Let's look at an example. A recipe calls for 3/4 cups flour, 1/2 cup milk, and 4 eggs, to serve 4 people. Jane wants to make the recipe for only herself and her husband. How much of each item will she need?

Step 1:

Let f= flour, m= milk, and e= eggs.

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