# How to multiply fractions

In this post we will learn methods for multiplying fractions.

First we will review the concept of fractions, then will understand the techniques to multiply fractions and finally move on to solve worksheets related to the concept

## Understanding Fraction Multiplication

Consider the below box as whole number 1

Multiplication with fraction (1/2)

The expression \Longrightarrow 1\times \frac{1}{2}\ means that the whole figure is divided into two equal halves.

This multiplication can be expressed as:
\Longrightarrow \ 1\ \times \frac{1}{2}\\\ \\ \Longrightarrow \frac{1}{2}

Hence only one half of the figure is selected as result

Further multiplication with fraction 1/3

Now we multiply \Longrightarrow \ \frac{1}{2} \times \frac{1}{3}\

It means that the half portion is divided into three equal parts

The multiplication can be expressed as:

\Longrightarrow \ \frac{1}{2} \times \frac{1}{3}\\\ \\ \Longrightarrow \ \frac{1}{6}\\\ \\

Hence \frac{1}{3} \ of \ \frac{1}{2} \ results \ in \ \frac{1}{6}

It means that final answer is \frac{1}{6} of the whole figure

The result is shown by following image:

Now we have understood the concept of fraction multiplication.
Let us now understand the method to multiply the fractions.

## How to multiply the fractions

The method is simple and straight forward.

Suppose two fractions are given:

You can do multiplication by following below steps

Step 01
Multiply the numerators (top numbers) of Fraction

Step 02
Multiply the denominators (bottom numbers) of fraction

Step 03
Simplify the result (if required)
Reduce the numerator and denominator to its lowest terms

Let us understand the method with the help of examples

Example 01
Multiply the below fractions
\Longrightarrow \frac{7}{3} \times \frac{4}{5}\

(a) Rearranging numbers
\Longrightarrow \ \frac{7\ \times 4}{3\times 5}\

(b) Multiplying numerator and denominator separately
\Longrightarrow \ \frac{28}{15}

(c) Simplify Number
Further simplification is not possible

Hence, \frac{28}{15} \ is the solution

Example 02
Multiply the below fraction
\Longrightarrow \frac{5}{6} \times \frac{8}{9}\

(a) Rearranging numbers
\Longrightarrow \ \frac{5\ \times 8}{6\times 9}\

(b) Multiplying numerator and denominator separately
\Longrightarrow \ \frac{40}{54}

(c) Simplify Number
Divide numerator and denominator by 2

Hence, \frac{20}{27} \ is the solution

## Multiplying Fractions Worksheet

Below is the collection of Fraction Multiplication for Grade 5.

All the questions have been provided with detailed solution.

Please take out pen and paper and try to solve each ofthe question

### Multiply the given fractions step by step

(a) \frac{6}{12} \ \times \frac{2}{10}

\Longrightarrow \ \frac{6}{12} \ \times \frac{2}{10}\\\ \\ \Longrightarrow \ \frac{6\ \times \ 2}{12\times 10}\\\ \\ \Longrightarrow \ \frac{12}{120}\\\ \\

Divide numerator and denominator by 12

Hence \frac{1}{10} is the solution

(b) \frac{11}{20} \ \times \frac{4}{14} \\\ \\ Read Solution

\Longrightarrow \ \frac{11}{20} \ \times \frac{4}{14}\\\ \\ \Longrightarrow \ \frac{11\ \times \ 4}{20\times 14}\\\ \\ \Longrightarrow \ \frac{44}{280}\\\ \\

Divide numerator and denominator by 4

Hence \frac{11}{70} is the solution

(c) \frac{7}{3} \ \times \frac{2}{5} \\\ \\ Read Solution

\Longrightarrow \ \frac{7}{3} \ \times \frac{2}{5}\\\ \\ \Longrightarrow \ \frac{7\ \times \ 2}{3\times 5}\\\ \\ \Longrightarrow \ \frac{14}{15}\\\ \\ \frac{14}{15} is the solution

(d) \frac{5}{7} \ \times \frac{15}{16} \\\ \\ Read Solution

\Longrightarrow \ \frac{5}{7} \ \times \frac{15}{16}\\\ \\ \Longrightarrow \ \frac{5\ \times \ 15}{7\times 16}\\\ \\ \Longrightarrow \ \frac{75}{112}\\\ \\ \frac{75}{112} is the solution

(e) \frac{11}{7} \ \times \frac{3}{4} \\\ \\ Read Solution

\Longrightarrow \ \frac{11}{7} \ \times \frac{3}{4}\\\ \\ \Longrightarrow \ \frac{11\ \times \ 3}{7 \times 4}\\\ \\ \Longrightarrow \ \frac{33}{28}\\\ \\ \frac{33}{28} is the solution

(f) \frac{13}{2} \ \times \frac{4}{3} \\\ \\ Read Solution

\Longrightarrow \ \frac{13}{2} \ \times \frac{4}{3}\\\ \\ \Longrightarrow \ \frac{13\ \times \ 4}{2\times 3}\\\ \\ \Longrightarrow \ \frac{52}{6}\\\ \\

Divide numerator and denominator by 2

\frac{27}{3} is the solution

(g) \frac{8}{9} \ \times \frac{1}{2} \\\ \\ Read Solution

\Longrightarrow \ \frac{8}{9} \ \times \frac{1}{2}\\\ \\ \Longrightarrow \ \frac{8\ \times \ 1}{9\times 2}\\\ \\ \Longrightarrow \ \frac{8}{18}\\\ \\

Divide numerator and denominator by 2

\frac{4}{9} is the solution

(h) \frac{20}{11} \ \times \frac{10}{7} \\\ \\ Read Solution

\Longrightarrow \ \frac{20}{11} \ \times \frac{10}{7}\\\ \\ \Longrightarrow \ \frac{20\ \times \ 10}{11\times 7}\\\ \\ \Longrightarrow \ \frac{200}{77}\\\ \\ \frac{200}{77} is the solution

(i) \frac{1}{3} \ \times \frac{2}{9}\\\ \\ Read Solution

\Longrightarrow \ \frac{1}{3} \ \times \frac{2}{9}\\\ \\ \Longrightarrow \ \frac{1\ \times \ 2}{3\times 9}\\\ \\ \Longrightarrow \ \frac{2}{27}\\\ \\ \frac{2}{27} is the solution

(j) \frac{0}{5} \ \times \frac{12}{6} \\\ \\ Read Solution

\Longrightarrow \ \frac{0}{5} \ \times \frac{12}{6}\\\ \\ \Longrightarrow \ \frac{0\ \times \ 12}{5\times 6}\\\ \\ \Longrightarrow \ \frac{0}{30}\\\ \\

0 is the solution

(k) \frac{2}{13} \ \times \frac{5}{4} \\\ \\ Read Solution

\Longrightarrow \ \frac{2}{13} \ \times \frac{5}{4}\\\ \\ \Longrightarrow \ \frac{2\ \times \ 5}{13\times 4}\\\ \\ \Longrightarrow \ \frac{10}{52}\\\ \\

Divide numerator and denominator by 2

\frac{5}{26} is the solution

(l) \frac{5}{14} \ \times \frac{17}{2} \\\ \\ Read Solution

\Longrightarrow \ \frac{5}{14} \ \times \frac{17}{2}\\\ \\ \Longrightarrow \ \frac{5\ \times \ 17}{14\times 2}\\\ \\ \Longrightarrow \ \frac{85}{28}\\\ \\ \frac{85}{28} is the solution

(m) \frac{1}{2} \ \times \frac{2}{1} \\\ \\ Read Solution

\Longrightarrow \ \frac{1}{2} \ \times \frac{2}{1}\\\ \\ \Longrightarrow \ \frac{1\ \times \ 2}{2\times 1}\\\ \\ \Longrightarrow \ \frac{2}{2}\\\ \\

Divide numerator and denominator by 2

1 is the solution

(n) \frac{17}{4} \ \times \frac{5}{11} \\\ \\ Read Solution

\Longrightarrow \ \frac{17}{4} \ \times \frac{5}{11}\\\ \\ \Longrightarrow \ \frac{17\ \times \ 5}{4\times 11}\\\ \\ \Longrightarrow \ \frac{85}{44}\\\ \\ \frac{85}{44} is the solution

(o) \frac{5}{9} \ \times \frac{12}{6} \\\ \\ Read Solution

\Longrightarrow \ \frac{5}{9} \ \times \frac{12}{6}\\\ \\ \Longrightarrow \ \frac{5\ \times \ 12}{9\times 6}\\\ \\ \Longrightarrow \ \frac{60}{54}\\\ \\

Divide Numerator and Denominator by 6

\frac{10}{9} is the solution

### Multiply three or more fractions

This section is more difficult to solve. Here we involve three sets of number for multiplication.

The process for multiplication is same:
(a) Multiply numerators and denominators separately
(b) simplify the result by lowering the numerator and denominator to its lowest terms

(a) \frac{2}{3} \ \times \frac{3}{2} \ \times \frac{4}{6} \\\ \\ Read Solution

\Longrightarrow \ \frac{2}{3} \times \frac{3}{2} \times \frac{4}{6}\\\ \\ \Longrightarrow \ \frac{2\times 3\times 4}{3\times 2\times 6}\\\ \\ \Longrightarrow \ \frac{24}{36}

(b) \frac{1}{7} \ \times \frac{3}{5} \ \times \frac{6}{1} \\\ \\ Read Solution

\Longrightarrow \ \frac{1}{7} \times \frac{3}{5} \times \frac{6}{1}\\\ \\ \Longrightarrow \ \frac{1\times 3\times 6}{7\times 5\times 1}\\\ \\ \Longrightarrow \ \frac{18}{35}

(c) \frac{1}{3} \ \times \frac{2}{3} \ \times \frac{1}{2} \\\ \\ Read Solution

\Longrightarrow \ \frac{1}{3} \times \frac{2}{3} \times \frac{1}{2}\\\ \\ \Longrightarrow \ \frac{1\times 2\times 1}{3\times 3\times 2}\\\ \\ \Longrightarrow \ \frac{2}{18}

(d) \frac{1}{5} \ \times \frac{0}{7} \ \times \frac{6}{1} \\\ \\ Read Solution

\Longrightarrow \ \frac{1}{5} \times \frac{0}{7} \times \frac{6}{1}\\\ \\ \Longrightarrow \ \frac{1\times 0\times 6}{5\times 7\times 1}\\\ \\ \Longrightarrow \ \frac{0}{35}

(e) \frac{2}{6} \ \times \frac{4}{3} \ \times \frac{3}{2} \\\ \\ Read Solution

\Longrightarrow \ \frac{2}{6} \times \frac{4}{3} \times \frac{3}{2}\\\ \\ \Longrightarrow \ \frac{2\times 4\times 3}{6\times 3\times 2}\\\ \\ \Longrightarrow \ \frac{24}{36}

(f) \frac{7}{3} \ \times \frac{2}{1} \ \times \frac{9}{11} \\\ \\ Read Solution

\Longrightarrow \ \frac{7}{3} \times \frac{2}{1} \times \frac{9}{11}\\\ \\ \Longrightarrow \ \frac{7\times 2\times 9}{3\times 1\times 11}\\\ \\ \Longrightarrow \ \frac{126}{33}

(g) \frac{2}{4} \ \times \frac{8}{5} \ \times \frac{2}{3} \\\ \\ Read Solution

\Longrightarrow \ \frac{2}{4} \times \frac{8}{5} \times \frac{2}{3}\\\ \\ \Longrightarrow \ \frac{2\times 8\times 2}{4\times 5\times 3}\\\ \\ \Longrightarrow \ \frac{32}{60}

(h) \frac{1}{2} \ \times \frac{1}{2} \ \times \frac{1}{3} \\\ \\ Read Solution

\Longrightarrow \ \frac{1}{2} \times \frac{1}{2} \times \frac{1}{3}\\\ \\ \Longrightarrow \ \frac{1\times 1\times 1}{2\times 2\times 3}\\\ \\ \Longrightarrow \ \frac{1}{12}