How to Multiply Fractions

Multiplying fractions is usually simpler than adding or subtracting them because you do not need a common denominator.

Quick idea

Multiply numerator by numerator and denominator by denominator. Then reduce the answer if possible.

Steps

1. Multiply the top numbers.
2. Multiply the bottom numbers.
3. Simplify the fraction by dividing by any common factor.
4. For mixed numbers, convert to improper fractions before multiplying.

Worked example

Multiply two thirds by four fifths.

Full solution

Step-by-step walkthrough

Step 1

Multiply the numerators: 2 times 4 equals 8.

Step 2

Multiply the denominators: 3 times 5 equals 15.

Step 3

The fraction 8 fifteenths is already simplified.

Common mistake

Do not look for a common denominator when multiplying fractions. That step belongs to addition and subtraction.

Practice problems

1. Multiply 1/2 x 3/5.
2. Multiply 2/7 x 4/3.
3. Multiply 5/6 x 2/5.

Answers

1. 3/10
2. 8/21
3. 1/3

Ask Pennpaper to explain it live

If the steps make sense but you still feel stuck, start a Pennpaper lesson and ask the tutor to draw the problem on the whiteboard. Seeing the symbols move step by step is often what makes the concept click.

Related guides

• How to Divide Fractions: Keep, Change, Flip
• How to Add Fractions With Unlike Denominators
• How to Solve Fraction Word Problems