How to Multiply Fractions with Unlike Denominators

Instructor: Emily Hume

Emily is a Reading Specialist and Literacy coach in a public elementary school with a Master's Degree in Elementary Education.

Multiplying fractions doesn't have to be difficult, even when they have unlike denominators! In this lesson, you will learn how to multiply fractions with unlike denominators as well as how to simplify your answer.

Fractions in Real Life

You encounter fractions every day. Don't believe it? Check this story out!

You are throwing a pizza party for your friends! When the pizza comes, your little brother sneaks in and grabs 1/3 of the pizza! Mom tells him he has to share 1/2 (half) of his pizza with your sister. What fraction of his share will they both get to eat? You will have to multiply fractions to find out!

Steps to Multiply Fractions

Let's take a look at that pizza party problem. There are just a few simple steps involved in multiplying fractions.

Step 1: Set up your problem. 1/2 of 1/3 = 1/2 x 1/3. You will notice that your problem has unlike denominators, meaning the bottom numbers are different from each other. Although this is important when adding or subtracting fractions, it is not a problem when multiplying.

Step 2: Multiply the top numbers, called the numerators. 1 x 1 = 1. This is the numerator for your answer.

Step 3: Multiply the denominators. 2 x 3 = 6. This is the denominator for your answer.

Step 4: Put your answer together: 1/6. Your brother and sister will end up with 1/6 of the pizza each!

Pizza Fraction Multiplication
Pizza Fraction Multiplication

Simplifying Fractions

Sometimes you end up with a fraction that needs to be simplified. This means that the numerator and denominator are not the smallest whole numbers they can be. It doesn't change the size of the fraction (the piece of pizza in the previous example), it just makes it more simple.

Here's an example! You share a room with your little sister. Mom says you have to clean up at least 2/3 of your half of the room today, and then you may go outside to play. What fraction of the entire room will you clean today? Multiply and then simplify!

Step 1: Set up your problem: 2/3 x 1/2 =

Step 2: Multiply the numerators: 2 x 1 = 2

Step 3: Multiply the denominators: 3 x 2 = 6

Step 4: Put your answer together: 2/6. These are not the smallest possible numbers, so you will need to simplify!

Step 5: Divide both the numerator and denominator by 2.

2 ÷ 2 = 1. This is your new numerator.

6 ÷ 2 = 3. This is your new denominator.

So, 2/6 simplifies to 1/3. This is your answer! You have to clean at least 1/3 of the entire room before you can go outside!

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