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Multiply Fractions

Examples of fractions multiplication are presented along with detailed solutions and exercises with answers on are presented. A calculator to multiply fractions is included in this website.

How to Multiply Fractions? Rule

To multiply two fractions, we multiply the numerators together and the denominators together. Hence

$\dfrac{a}{b} \times \dfrac{c}{d} = \dfrac{a \times c}{b \times d}$

Multiply Fractions: Examples with Detailed Solutions

Example 1
Multiply and simplfy, and express the final answer as a fraction.
$\frac{2}{3} \times \frac{7}{2}$

$\dfrac{2}{3} \times \dfrac{7}{2}$ Solution to Example 1
To multiply fractions you multiply numerators and denominators

\frac{2}{3} \times \frac{7}{2} = \frac{2 \times 7}{3 \times 2}

$\dfrac{2}{3} \times \dfrac{7}{2} = \dfrac{2 \times 7}{3 \times 2}$

Divide the numerator and the denominator by the common factor 2 and simplify

\frac{\cancel 2 \times 7}{3 \times \cancel 2} = \frac{7}{3}

$\dfrac{ \cancel{2} \times 7}{3 \times \cancel{2}} = \dfrac{7}{3}$

Example 2
Multiply and simplfy, and express the final answer as a fraction.
$\frac{11}{9} \times \frac{12}{25}$

$\dfrac{11}{9} \times \dfrac{12}{25}$ Solution to Example 2
Multiply numerators and denominators

\frac{11}{9} \times \frac{12}{25} = \frac{11 \times 12}{9 \times 25}

$\dfrac{11}{9} \times \dfrac{12}{25} = \dfrac{11 \times 12}{9 \times 25}$

12 in the numeartor and 9 in the denominator have the greatest common factor equal to 3, hence divide 12 in numerator and 9 denominator by 3.

= \frac{11 \times (12 \div 3)}{(9 \div 3) \times 25}

$= \dfrac{11 \times (12\div 3)}{(9\div 3) \times 25}$

and simplify

\frac{11 \times 4}{3 \times 25} = \frac{44}{75}

$\dfrac{11 \times 4}{3 \times 25} = \dfrac{44}{75}$

Example 3 (Multiply a fraction by an integer)
Multiply, simplfy and express the final answer as a fraction.
$\frac{2}{15} \times 5$

$\dfrac{2}{15} \times 5$ Solution to Example 3
Multiply numerator of first fraction by 5

\frac{2}{15} \times 5 = \frac{2 \times 5}{15}

$\dfrac{2}{15} \times 5 = \dfrac{2 \times 5}{15}$

5 in the numerator and 15 in the denominator have the greatest common factor equal to 5, hence divide 5 in the numerator and 15 in the denominator by

5

$5$ to simplify

\frac{2 \times (5 \div 5)}{15 \div 5} = \frac{2}{3}

$\dfrac{2 \times (5 \div 5)}{15 \div 5} = \dfrac{2}{3}$

Example 4 (Multiply a fraction by a decimal number)
Multiply, simplfy and express the final answer as a fraction.
$\frac{2}{15} \times 1.5$

$\dfrac{2}{15} \times 1.5$ Solution to Example 4
Rewrite the decimal number

1.5

$1.5$ as a fraction

1.5 = \frac{1.5}{1} = \frac{1.5 \times 10}{1 \times 10} = \frac{15}{10}

$1.5 = \dfrac{1.5}{1} = \dfrac{1.5 \times 10}{1 \times 10} = \dfrac{15}{10}$

Rewrite the given expression using fractions

\frac{2}{15} \times 1.5 = \frac{2}{15} \times \frac{15}{10}

$\dfrac{2}{15} \times 1.5 = \dfrac{2}{15} \times \dfrac{15}{10}$

Multiply numerators and denominators

= \frac{2 \times 15}{15 \times 10}

$= \dfrac{2 \times 15}{15 \times 10}$

Divide numerator and denominator by

15

$15$ and simplify

= \frac{2}{10}

$= \dfrac{2}{10}$

Divide numerator and denominator by

2

$2$ and simplify

= \frac{1}{5}

$= \dfrac{1}{5}$

Exercises with Answers: Multiply Fractions

Multiply, simplify and express as fractions.

1.

\frac{2}{3} \times \frac{7}{6}

$\dfrac{2}{3} \times \dfrac{7}{6}$

2.

\frac{23}{30} \times \frac{33}{25}

$\dfrac{23}{30} \times \dfrac{33}{25}$

3.

5 \times \frac{2}{25}

$5 \times \dfrac{2}{25}$

4.

0.14 \times \frac{40}{21}

$0.14 \times \dfrac{40}{21}$

Answers to Above Exercises:.

1. $\dfrac{7}{9}$

2. $\dfrac{253}{250}$

3. $\dfrac{2}{5}$

4. $\dfrac{4}{15}$

Multiply Fractions

How to Multiply Fractions? Rule

Multiply Fractions: Examples with Detailed Solutions

Exercises with Answers: Multiply Fractions

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