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}
Read Solution\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
(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
(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
(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
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}