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

Definition

To multiply fractions, multiply the numerators together and multiply the denominators together:
Example:
Multiplying fractions means finding a fraction of a fraction. When you calculate , you're finding half of one-third (or one-third of one-half).

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What is ?

Worked Examples

Calculate

1

Multiply the numerators

New numerator:

2

Multiply the denominators

New denominator:

3

Write the result

4

Simplify by dividing by GCF (2)

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. , not .

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.

Interactive Visual

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

Interactive Sandbox

Expression Calculator

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Practice Problems

15 problems
Problem 1 of 15
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What is ?

Why It Matters

Fraction multiplication is essential in everyday situations:
  • Cooking: If a recipe calls for cup of flour and you want to make half the recipe, you need cup
  • Sales and Discounts: A shirt is off, and you have a coupon for off the sale price
  • Time: If of the class finished a test, and 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 cup butter and you make half the batch: cup butter.

1Try It Yourself

A smoothie recipe calls for cup of yogurt. You want to make of the recipe.

How much yogurt do you need?

Step 1: Write the mathematical expression

Calculate:

Area Calculations

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

Example:

A garden plot is meter wide and meter long. Area = square meter.

2Try It Yourself

A picture frame is foot wide and foot tall.

What is the area of the picture frame?

Step 1: Write the mathematical expression

Calculate:

Key Takeaways

  • 1To multiply fractions, multiply numerators together and denominators together:
  • 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

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