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:

\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}

Example:

\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

\frac{1}{2} \times \frac{1}{3}

, you're finding half of one-third (or one-third of one-half).

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What is

\frac{1}{2} \times \frac{1}{3}

Worked Examples

Calculate $\frac{2}{5} \times \frac{3}{4}$

Multiply the numerators

$2 \times 3 = 6$ → New numerator: $6$

Multiply the denominators

$5 \times 4 = 20$ → New denominator: $20$

Write the result

$\frac{6}{20}$

Simplify by dividing by GCF (2)

$\frac{6 \div 2}{20 \div 2} = \frac{3}{10}$

Answer: $\frac{2}{5} \times \frac{3}{4} = \frac{3}{10}$

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. $\frac{2}{3} \times \frac{1}{4} = \frac{2}{12}$ , not $\frac{3}{7}$ .

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

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2/3

(horizontal)

3/4

(vertical)

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Practice Problems

15 problems

Problem 1 of 15

Easy

What is $\frac{1}{2} \times \frac{1}{3}$ ?

Why It Matters

Fraction multiplication is essential in everyday situations:

Cooking: If a recipe calls for $\frac{2}{3}$ cup of flour and you want to make half the recipe, you need $\frac{1}{2} \times \frac{2}{3} = \frac{1}{3}$ cup
Sales and Discounts: A shirt is $\frac{1}{4}$ off, and you have a coupon for $\frac{1}{2}$ off the sale price
Time: If $\frac{3}{4}$ of the class finished a test, and $\frac{2}{3}$ 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 $\frac{3}{4}$ cup butter and you make half the batch: $\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}$ cup butter.

1Try It Yourself

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

How much yogurt do you need?

Step 1: Write the mathematical expression

Calculate: $\frac{3}{4} \times \frac{2}{3}$

Area Calculations

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

Example:

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

2Try It Yourself

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

What is the area of the picture frame?

Step 1: Write the mathematical expression

Calculate: $\frac{5}{6} \times \frac{4}{5}$

Key Takeaways

1To multiply fractions, multiply numerators together and denominators together: $\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$
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.

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