Introduction

To multiply fractions, we multiply the numerators, multiply the denominators, and simplify (if necessary).

For example, to multiply \dfrac 1 {2} \times \dfrac 1 {3}, we multiply the numerators and we multiply the denominators:

\dfrac{\color{blue}1}{\color{red}2} \times \dfrac{\color{blue}1}{\color{red}3} = \dfrac {{\color{blue}1}\times {\color{blue}1}} {{\color{red}2}\times {\color{red}3}} = \dfrac{1}{6}

Notice that we get the same answer when we use a fraction model.


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Example: Multiplying Fractions by Unit Fractions

Find the value of \dfrac 3 {7} \times \dfrac 1 {4}.

EXPLANATION

To multiply two fractions, we multiply the numerators, and we multiply the denominators:

\dfrac 3 {7} \times \dfrac 1 {4} = \dfrac {3\times 1} {7\times 4} = \dfrac{3}{28}

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Practice: Multiplying Fractions by Unit Fractions

$\dfrac 1 {4} \times \dfrac 1 {5} =$

a
 $\dfrac 1 {9}$
b
 $\dfrac 1 {45}$
c
 $\dfrac 4 {5}$
d
 $\dfrac 2 {5}$
e
 $\dfrac 1 {20}$
Practice: Multiplying Fractions by Unit Fractions

$\dfrac{4}{7} \times \dfrac{1}{9} = $

a
 $\dfrac{5}{16}$
b
 $\dfrac{2}{9}$
c
 $\dfrac{4}{21}$
d
 $\dfrac{2}{31}$
e
 $\dfrac{4}{63}$
Example: Multiplying Fractions

Multiply \dfrac 2 {9} \times \dfrac 4 {5}.

EXPLANATION

To multiply two fractions, we multiply the numerators, and we multiply the denominators:

\dfrac 2 {9} \times \dfrac 4 {5} = \dfrac {2\times 4} {9\times 5} = \dfrac{8}{45}

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Practice: Multiplying Fractions

$\dfrac 4 {5} \times \dfrac 3 {7}=$

a
 $ \dfrac{5}{12}$
b
 $ \dfrac{12}{35}$
c
 $ \dfrac{7}{35}$
d
 $ \dfrac{15}{28}$
e
 $ \dfrac{7}{12}$
Practice: Multiplying Fractions

$\dfrac{7}{2} \times \dfrac{9}{4} =$

a
 $\dfrac{63}{8}$
b
 $\dfrac{17}{6}$
c
 $\dfrac{54}{7}$
d
 $\dfrac{24}{9}$
e
 $\dfrac{8}{3}$
Example: Multiplying Fractions When Simplification is Needed

Multiply \dfrac 5 {6} \times \dfrac 3 {4}.

EXPLANATION

To multiply two fractions, we multiply the numerators, and we multiply the denominators:

\dfrac 5 {6} \times \dfrac 3 {4} = \dfrac {5\times 3} {6\times 4} = \dfrac{15}{24}

We reduce this fraction to its simplest form by dividing the numerator and denominator by 3\mathbin{:}

\dfrac {15} {24} = \dfrac {15\div 3} {24\div 3} = \dfrac{5}{8}

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Practice: Multiplying Fractions When Simplification is Needed

$\dfrac{1}{2} \times \dfrac{4}{5} =$

a
 $\dfrac{6}{7}$
b
 $\dfrac{5}{6}$
c
 $\dfrac{2}{5}$
d
 $\dfrac{3}{8}$
e
 $\dfrac{1}{5}$
Practice: Multiplying Fractions When Simplification is Needed

$\dfrac{1}{3} \times \dfrac{6}{7} = $

a
 $\dfrac{1}{3}$
b
 $\dfrac{3}{7}$
c
 $\dfrac{2}{7}$
d
 $\dfrac{2}{3}$
e
 $\dfrac{7}{3}$
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