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 space
[How do we write a mixed number as a fraction?]
Here is how we rewrite 2, start fraction, 2, divided by, 3, end fraction as start fraction, 8, divided by, 3, end fraction :
start color purple, 2, end color purple, start color blue, start fraction, 2, divided by, 3, end fraction, end color blue, equals, start color purple, 1, end color purple, plus, start color purple, 1, end color purple, plus, start color blue, start fraction, 2, divided by, 3, end fraction, end color blue
empty space, equals, start color purple, start fraction, 3, divided by, 3, end fraction, end color purple, plus, start color purple, start fraction, 3, divided by, 3, end fraction, end color purple, plus, start color blue, start fraction, 2, divided by, 3, end fraction, end color blue
empty space, equals, start fraction, start color purple, 3, end color purple, plus, start color purple, 3, end color purple, plus, start color blue, 2, end color blue, divided by, 3, end fraction
empty space, equals, start fraction, 8, divided by, 3, end fraction
Here is how we rewrite 1, start fraction, 3, divided by, 5, end fraction as start fraction, 8, divided by, 5, end fraction :
start color purple, 1, end color purple, start color blue, start fraction, 3, divided by, 5, end fraction, end color blue, equals, start color purple, 1, end color purple, plus, start color blue, start fraction, 3, divided by, 5, end fraction, end color blue
empty space, equals, start color purple, start fraction, 5, divided by, 5, end fraction, end color purple, plus, start color blue, start fraction, 3, divided by, 5, end fraction, end color blue
empty space, equals, start fraction, start color purple, 5, end color purple, plus, start color blue, 3, end color blue, divided by, 5, end fraction
empty space, equals, start fraction, 8, divided by, 5, end fraction
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 .
Want to learn more about multiplying fractions? Check out this video.

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
[Explain]
Instead of simplifying our answer at the end, we can divide the numerator and denominator by a common factor before multiplying. This makes multiplying easier!
We can divide the 3 in the numerator and the 6 in the denominator by their common factor of start color pink, 3, end color pink:
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
start fraction, 5, divided by, 8, end fraction, times, start fraction, 7, divided by, 8, end fraction
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, p, i or 2, slash, 3, space, p, i

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