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

Divide the numerator and the denominator by the common factor 2 and simplify
$\dfrac{ \cancel{2} \times 7}{3 \times \cancel{2}} = \dfrac{7}{3}$

Example 2
Multiply and simplfy, and express the final answer as a fraction.
$\dfrac{11}{9} \times \dfrac{12}{25}$ Solution to Example 2
Multiply numerators and denominators
$\dfrac{11}{9} \times \dfrac{12}{25} = \dfrac{11 \times 12}{9 \times 25}$

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

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

Example 3 (Multiply a fraction by an integer)
Multiply, simplfy and express the final answer as a fraction.
$\dfrac{2}{15} \times 5$ Solution to Example 3
Multiply numerator of first fraction by 5
$\dfrac{2}{15} \times 5 = \dfrac{2 \times 5}{15}$

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

Example 4 (Multiply a fraction by a decimal number)
Multiply, simplfy and express the final answer as a fraction.
$\dfrac{2}{15} \times 1.5$ Solution to Example 4
Rewrite the decimal number $1.5$ as a fraction
$1.5 = \dfrac{1.5}{1} = \dfrac{1.5 \times 10}{1 \times 10} = \dfrac{15}{10}$

Rewrite the given expression using fractions
$\dfrac{2}{15} \times 1.5 = \dfrac{2}{15} \times \dfrac{15}{10}$

Multiply numerators and denominators
$= \dfrac{2 \times 15}{15 \times 10}$

Divide numerator and denominator by $15$ and simplify
$= \dfrac{2}{10}$

Divide numerator and denominator by $2$ and simplify
$= \dfrac{1}{5}$

## Exercises with Answers: Multiply Fractions

Multiply, simplify and express as fractions.

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

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

3.     $5 \times \dfrac{2}{25}$

4.     $0.14 \times \dfrac{40}{21}$

1.     $\dfrac{7}{9}$

2.     $\dfrac{253}{250}$

3.     $\dfrac{2}{5}$

4.     $\dfrac{4}{15}$