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
$\phantom{=}\dfrac{5}{6} \times \dfrac{5}{7}$
$= \dfrac{5 \times 5}{6 \times 7}$
$= \dfrac{25}{42}$
Example 2: Mixed numbers
Before multiplying, we need to write the mixed numbers as improper fractions.
$2\dfrac{2}{3} \times 1\dfrac35$
$= ~\dfrac{8}3 \times \dfrac{8}5$ $\qquad$
Here is how we rewrite $2\dfrac23$ as $\dfrac{8}3$ :
$\purple2\blue{\dfrac23} = \purple{1} +\purple{1} +\blue{\dfrac23}$
$\phantom{2\dfrac23 }= \purple{\dfrac33} +\purple{\dfrac33} + \blue{\dfrac23}$
$\phantom{2\dfrac23 }= \dfrac{\purple3 +\purple3 +\blue2}3$
$\phantom{2\dfrac23 }= \dfrac{8}3$
Here is how we rewrite $1\dfrac35$ as $\dfrac{8}5$ :
$\purple1\blue{\dfrac35} = \purple{1} +\blue{\dfrac35}$
$\phantom{1\dfrac35 }= \purple{\dfrac55} + \blue{\dfrac35}$
$\phantom{1\dfrac35 }= \dfrac{\purple5 +\blue3}5$
$\phantom{1\dfrac35 }= \dfrac{8}5$
$=\dfrac{8\times 8}{3 \times5}$
$=\dfrac{64}{15}$
We can also write this as $4\dfrac4{15}$ .
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
$\phantom{=} \dfrac{3}{10} \times \dfrac16$
$=\dfrac{3\times1}{10\times6}$
$=\dfrac{\stackrel{1}{\cancel{3}} \times ~1 }{ 10\times \underset{2}{\cancel{6}}} \qquad$
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 $3$ in the numerator and the $6$ in the denominator by their common factor of $\pink3$:
$\dfrac{ \stackrel{1}{\cancel{3\pink{\div 3}}} \times ~1 }{ 10\times\underset{2}{\cancel{6\pink{\div3}}}}$
$=\dfrac{1}{20}$
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
$\dfrac{5}{8} \times \dfrac{7}{8}$
Want to try more problems like this? Check out these exercises:
Multiply fractions
Multiply mixed numbers