Multiplying fractions review

CCSS Math: 5.NF.B.4
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
=56×57\phantom{=}\dfrac{5}{6} \times \dfrac{5}{7}
=5×56×7= \dfrac{5 \times 5}{6 \times 7}
=2542= \dfrac{25}{42}
Example 2: Mixed numbers
Before multiplying, we need to write the mixed numbers as improper fractions.
223×1352\dfrac{2}{3} \times 1\dfrac35
= 83×85 = ~\dfrac{8}3 \times \dfrac{8}5 \qquad
Here is how we rewrite 2232\dfrac23 as 83\dfrac{8}3 :
223=1+1+23\purple2\blue{\dfrac23} = \purple{1} +\purple{1} +\blue{\dfrac23}
223=33+33+23\phantom{2\dfrac23 }= \purple{\dfrac33} +\purple{\dfrac33} + \blue{\dfrac23}
223=3+3+23\phantom{2\dfrac23 }= \dfrac{\purple3 +\purple3 +\blue2}3
223=83\phantom{2\dfrac23 }= \dfrac{8}3
Here is how we rewrite 1351\dfrac35 as 85\dfrac{8}5 :
135=1+35\purple1\blue{\dfrac35} = \purple{1} +\blue{\dfrac35}
135=55+35\phantom{1\dfrac35 }= \purple{\dfrac55} + \blue{\dfrac35}
135=5+35\phantom{1\dfrac35 }= \dfrac{\purple5 +\blue3}5
135=85\phantom{1\dfrac35 }= \dfrac{8}5
=8×83×5=\dfrac{8\times 8}{3 \times5}
=6415=\dfrac{64}{15}
We can also write this as 44154\dfrac4{15} .
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
=310×16\phantom{=} \dfrac{3}{10} \times \dfrac16
=3×110×6=\dfrac{3\times1}{10\times6}
=31× 110×62=\dfrac{\stackrel{1}{\cancel{3}} \times ~1 }{ 10\times \underset{2}{\cancel{6}}} \qquad
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 33 in the numerator and the 66 in the denominator by their common factor of 3\pink3:
3÷31× 110×6÷32\dfrac{ \stackrel{1}{\cancel{3\pink{\div 3}}} \times ~1 }{ 10\times\underset{2}{\cancel{6\pink{\div3}}}}
=120=\dfrac{1}{20}
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
58×78\dfrac{5}{8} \times \dfrac{7}{8}
Want to try more problems like this? Check out these exercises:
Multiply fractions
Multiply mixed numbers