Multiplying Fractions

Learn how to multiply fractions by multiplying numerators and denominators, and understand what it means to take a fraction of a fraction.

Intermediate25 minLesson
Printable worksheet

Definition

To multiply fractions, multiply the numerators together and multiply the denominators together:
ab×cd=a×cb×d\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}
Example:
23×45=2×43×5=815\frac{2}{3} \times \frac{4}{5} = \frac{2 \times 4}{3 \times 5} = \frac{8}{15}
Multiplying fractions means finding a fraction of a fraction. When you calculate 12×13\frac{1}{2} \times \frac{1}{3}, you're finding half of one-third (or one-third of one-half).

Try it now

What is 12×13\frac{1}{2} \times \frac{1}{3}?

Worked Examples

Calculate 25×34\frac{2}{5} \times \frac{3}{4}
1

Multiply the numerators

2×3=62 \times 3 = 6 → New numerator: 66
2

Multiply the denominators

5×4=205 \times 4 = 20 → New denominator: 2020
3

Write the result

620\frac{6}{20}
4

Simplify by dividing by GCF (2)

6÷220÷2=310\frac{6 \div 2}{20 \div 2} = \frac{3}{10}

Common Mistakes

Adding numerators and denominators instead of multiplying

Why it's wrong: Students confuse fraction multiplication with addition rules. Addition needs common denominators, but multiplication does not.

Correct: Always multiply: numerator times numerator, denominator times denominator. 23×14=212\frac{2}{3} \times \frac{1}{4} = \frac{2}{12}, not 37\frac{3}{7}.

Finding common denominators before multiplying

Why it's wrong: This extra step comes from fraction addition. For multiplication, you don't need common denominators.

Correct: Just multiply straight across! No need to find common denominators when multiplying fractions.

Forgetting to simplify the final answer

Why it's wrong: The product of two fractions often needs to be reduced to lowest terms.

Correct: Always check if your answer can be simplified. Better yet, cross-cancel before multiplying to make the final answer easier.

Cross-canceling incorrectly (canceling horizontally)

Why it's wrong: Cross-canceling only works diagonally between a numerator and the opposite denominator.

Correct: You can only cancel a numerator with the other fraction's denominator, not with its own denominator.

Watch a video explanation

The same topic explained by another teacher, if a video helps you more.

How to Add, Subtract, Multiply, and Divide Fractions (Step-by-Step)

by Understand The Math

Watch on YouTube

Interactive Visual

2/5
(horizontal)
3/4
(vertical)

Interactive Sandbox

Expression Calculator

Try these:

History

No calculations yet

Practice Problems

15 problems
Problem 1 of 15
Easy
What is 12×13\frac{1}{2} \times \frac{1}{3}?

Why It Matters

Fraction multiplication is essential in everyday situations:
  • Cooking: If a recipe calls for 23\frac{2}{3} cup of flour and you want to make half the recipe, you need 12×23=13\frac{1}{2} \times \frac{2}{3} = \frac{1}{3} cup
  • Sales and Discounts: A shirt is 14\frac{1}{4} off, and you have a coupon for 12\frac{1}{2} off the sale price
  • Time: If 34\frac{3}{4} of the class finished a test, and 23\frac{2}{3} of those got an A, what fraction got an A?
  • Area: Finding the area of a rectangle with fractional dimensions
Unlike adding fractions (where you need common denominators), multiplying fractions is actually simpler!

Real World Applications

Cooking and Recipes

When you scale a recipe up or down, you multiply fractions to find the new ingredient amounts.

Example:

If a cookie recipe needs 34\frac{3}{4} cup butter and you make half the batch: 12×34=38\frac{1}{2} \times \frac{3}{4} = \frac{3}{8} cup butter.

1Try It Yourself

A smoothie recipe calls for 23\frac{2}{3} cup of yogurt. You want to make 34\frac{3}{4} of the recipe.

How much yogurt do you need?

Step 1: Write the mathematical expression

Calculate: 34×23\frac{3}{4} \times \frac{2}{3}

Area Calculations

Finding the area of rectangles with fractional dimensions requires multiplying fractions.

Example:

A garden plot is 34\frac{3}{4} meter wide and 25\frac{2}{5} meter long. Area = 34×25=620=310\frac{3}{4} \times \frac{2}{5} = \frac{6}{20} = \frac{3}{10} square meter.

2Try It Yourself

A picture frame is 56\frac{5}{6} foot wide and 45\frac{4}{5} foot tall.

What is the area of the picture frame?

Step 1: Write the mathematical expression

Calculate: 56×45\frac{5}{6} \times \frac{4}{5}

Key Takeaways

  • 1To multiply fractions, multiply numerators together and denominators together: ab×cd=a×cb×d\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}
  • 2The word 'of' in fraction problems usually means multiply
  • 3Cross-canceling (simplifying before multiplying) makes calculations easier
  • 4A whole number can be written as a fraction with denominator 1
  • 5Always simplify your final answer to lowest terms

Frequently Asked Questions

Common denominators are only needed for addition and subtraction (to combine like parts). Multiplication is about finding a 'fraction of a fraction,' which works by multiplying the parts directly.
Common denominators are only needed for addition and subtraction (to combine like parts). Multiplication is about finding a 'fraction of a fraction,' which works by multiplying the parts directly.
When you multiply two proper fractions (both less than 1), you're taking a part of a part, which is always smaller. For example, half of half is a quarter.
Cross-canceling is dividing a numerator and the opposite denominator by a common factor before multiplying. It simplifies the calculation and avoids large numbers. Always optional but recommended!

Glossary

Numerator
The top number of a fraction, showing how many parts you have
Denominator
The bottom number of a fraction, showing how many equal parts the whole is divided into
Cross-cancel
Simplifying before multiplying by dividing a numerator and the opposite denominator by their common factor
Product
The result of multiplying two or more numbers
Simplify
Reduce a fraction to its lowest terms by dividing numerator and denominator by their GCF
Today's challengeOne problem, three tries

More in This Topic

Adding Fractions with the Same Denominator

Elementary15 min

Adding Fractions with Different Denominators

Elementary25 min

Subtracting Fractions

Elementary25 min

Dividing Fractions

Intermediate25 min