Multiplying & Dividing Fractions: Learn the Basics

Lesson Overview

• How to Multiply with Fractions
• Rules of Multiplication of Fraction
• How to Divide with Fractions
• Rules for Dividing Fractions
• Multiplying and Dividing Fractions Examples

Fractions are all around us, whether we're sharing a pizza or dividing a group of people. In this multiplying and dividing fractions lesson, learn how to multiply and divide fractions so that it's easy to understand and fun to do.

What Is Multiplying and Dividing Fractions?

Fractions are parts of a whole. When we multiply or divide fractions, we're figuring out how many parts of something we get when we combine or share those parts.

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How to Multiply with Fractions

When multiplying fractions, multiply the top and bottom numbers (numerators and denominators), and simplify if needed. Multiplying fractions is like stacking pieces together-easy and fun!

Rules of Multiplication of Fraction

Multiplying fractions might seem tricky at first, but it's actually quite simple and fun once you know the steps! Let's break it down into three easy rules.

Rule 1: Multiply the Numerators

The top number of a fraction is called the numerator. To multiply fractions, first multiply the numerators of both fractions.

Example:

Rule 2: Multiply the Denominators

The bottom number of a fraction is called the denominator. Multiply the denominators of both fractions.

Rule 3: Simplify if Possible

Check if the fraction can be simplified. Simplifying means making the fraction as small as possible while keeping its value the same.

Divide both the numerator and the denominator by their greatest common factor (GCF), which is 18:

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How to Divide with Fractions

To divide fractions, follow: Keep, Flip, Multiply! Keep the first fraction the same, flip the second fraction upside down, and then multiply the two fractions. Simplify your answer if needed, and you're done-it's that easy! 

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Rules for Dividing Fractions

Dividing fractions may sound tricky, but it's as easy as flipping and multiplying! Let's take a fun and simple approach to learning these steps.

Rule 1: Keep the First Fraction

When dividing fractions, leave the first fraction as it is. Don't change it!

Example:

Rule 2: Flip the Second Fraction

This step is called finding the reciprocal. To flip a fraction, just switch the numerator (top number) and denominator (bottom number).

Example: 

Rule 3: Multiply the Fractions

Now, multiply the first fraction by the flipped second fraction. Apply the rules for multiplying fractions: multiply the numerators, then multiply the denominators.

Rule 4: Simplify if Needed

Check if your answer can be simplified by dividing the numerator and denominator by their greatest common factor (GCF).

Multiplying and Dividing Fractions Examples

Example 1: Multiply Fractions

Multiply 2/3 by 4/5.

Step 1: Multiply the Numerators

The numerators are the numbers on top of the fractions. 

Multiply them: 2 × 4 = 8

Step 2: Multiply the Denominators

The denominators are the numbers at the bottom of the fractions. 

Multiply them: 3 × 5 = 15

Step 3: Write the Fraction

Put the numerator over the denominator: 8/15

Step 4: Simplify (if needed)

In this case, 8/15 is already in its simplest form.

Final Answer: 8/15

Example 2: Divide Fractions

Divide 3/4 by 2/5.

Step 1: Keep the First Fraction

Write the first fraction as it is: 3/4

Step 2: Flip the Second Fraction

Find the reciprocal of 2/5 by flipping it: 2/5 becomes 5/2.

Step 3: Multiply the Fractions

Now, multiply 3/4 by 5/2.

• Multiply the numerators: 3 × 5 = 15
• Multiply the denominators: 4 × 2 = 8

Step 4: Write the Fraction

Put the numerator over the denominator: 15/8

Step 5: Simplify (if needed)

Since 15/8 is an improper fraction, change it to a mixed number:

15 divided by 8 equals 1 with a remainder of 7.

So, 15/8 = 1 7/8.Final Answer: 1 7/8