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## Arithmetic (all content)

### Course: Arithmetic (all content)>Unit 5

Lesson 21: Multiplying fractions

# Multiplying fractions review

Review the basics of multiplying fractions, and try some practice problems.

## Multiplying fractions

To multiply fractions, we multiply the numerators and then multiply the denominators.
Example 1: Fractions
empty space, start fraction, 5, divided by, 6, end fraction, times, start fraction, 5, divided by, 7, end fraction
equals, start fraction, 5, times, 5, divided by, 6, times, 7, end fraction
equals, start fraction, 25, divided by, 42, end fraction
Example 2: Mixed numbers
Before multiplying, we need to write the mixed numbers as improper fractions.
2, start fraction, 2, divided by, 3, end fraction, times, 1, start fraction, 3, divided by, 5, end fraction
equals, space, start fraction, 8, divided by, 3, end fraction, times, start fraction, 8, divided by, 5, end fraction $\qquad$
equals, start fraction, 8, times, 8, divided by, 3, times, 5, end fraction
equals, start fraction, 64, divided by, 15, end fraction
We can also write this as 4, start fraction, 4, divided by, 15, end fraction .

### Cross-reducing

Cross-reducing is a way to simplify before we multiply. This can save us from dealing with large numbers in our product.
Example
empty space, start fraction, 3, divided by, 10, end fraction, times, start fraction, 1, divided by, 6, end fraction
equals, start fraction, 3, times, 1, divided by, 10, times, 6, end fraction
equals, start fraction, start cancel, 3, end cancel, start superscript, 1, end superscript, times, space, 1, divided by, 10, times, start cancel, 6, end cancel, start subscript, 2, end subscript, end fraction
equals, start fraction, 1, divided by, 20, end fraction
Prefer a visual understanding of fraction multiplication? Check out one of these videos:
Multiplying 2 fractions: fraction model
Multiplying 2 fractions: number line

## Practice

Problem 1
• Current
start fraction, 5, divided by, 8, end fraction, times, start fraction, 7, divided by, 8, end fraction

Want to try more problems like this? Check out these exercises:
Multiply fractions
Multiply mixed numbers