# How do you divide fractions

In his post we will learn dividing fractions by fractions.

First we will learn step by step process to divide the two fractions. After than we will move on to solve some related questions.

## Steps to divide fractions

Suppose two fractions are given to you.
And you have to divide the 1st fraction by 2nd fraction

You can easily divide the two fraction by following the below steps:

Step 01
Convert the division into multiplication by inversing the right fraction

Step 02
Multiply the numerator of both fraction

Step 03
Multiply the denominator of both the fraction

Step 04
Reduce the numerator and denominator to lowest terms (if possible)

This is how you divide fraction with fraction.
Let us study some example to understand the process fully

Example 01
Divide the below fractions

Do the following steps

Step 01
Convert the division into multiplication by inversing fraction on right

Step 02
Multiply the numerator and denominator separately

Step 03
Reduce the fraction to its lowest terms

Divide both numerator and denominator by 12

Hence 1 is the solution of given problem

Example 02
Divide the below fractions

Step 01
Convert the multiplication into division by inverting the right fraction

Step 02
Multiply the numerator and denominator separately

Step 03
Reduce the fraction to lowest order

Divide both numerator and denominator by 30

Here 1 is the solution of given problem

Example 03
Calculate the division of two fraction

Do the following steps

Step 01
Convert the division into multiplication by inverting right fraction

Step 02
Multiply the numerator and denominator separately

Step 03
Reduce the fraction to its lowest terms

Divide both numerator and denominator by 2

Hence 14/3 is the solution

## Division of Fractions Questions

Below is the collection of dividing fraction questions.
Your job is to read the question and solve the division step by step.

All the questions are to the standard of Grade 5.
Each question is provided with solution for your reference.

### Divide the given fractions

Two fractions are given in the questions.
Divide them and find the right answer

(a) \frac{6}{5} \ \div \ \frac{6}{7}\\\ \\ Read Solution

Step 01
Convert division into multiplication by inverting the right side fraction
\Longrightarrow \ \frac{6}{5} \ \times \ \frac{7}{6}

Step 02
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{6\times 7}{5\times 6}\\\ \\ \Longrightarrow \frac{42}{30}

Step 03
If possible, simplify the fraction

Divide both numerator and denominator by 6

Hence, \frac{7}{5} is the solution

(b) \frac{4}{9} \ \div \ \frac{2}{11} \\\ \\ Read Solution

Step 01
Convert division into multiplication by inverting the right side fraction
\Longrightarrow \ \frac{4}{9} \ \times \ \frac{11}{2}

Step 02
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{4\times 11}{9\times 2}\\\ \\ \Longrightarrow \frac{44}{18}

Step 03
If possible, simplify the fraction

Divide both numerator and denominator by 2

Hence, \frac{22}{9} is the solution

(c) \frac{5}{3} \ \div \ \frac{9}{2} \\\ \\ Read Solution

Step 01
Convert division into multiplication by inverting the right side fraction
\Longrightarrow \ \frac{5}{3} \ \times \ \frac{2}{9}

Step 02
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{5\times 2}{3\times 9}\\\ \\ \Longrightarrow \frac{10}{27}

Step 03
If possible, simplify the fraction

Further simplification is not possible
Hence, \frac{10}{27} is the solution

(d) \frac{13}{2} \ \div \ \frac{9}{1} \\\ \\ Read Solution

Step 01
Convert division into multiplication by inverting the right side fraction
\Longrightarrow \ \frac{13}{2} \ \times \ \frac{1}{9}

Step 02
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{13\times 1}{2\times 9}\\\ \\ \Longrightarrow \frac{13}{18}

Step 03
If possible, simplify the fraction

Further simplification is not possible
Hence, \frac{13}{18} is the solution

(e) \frac{5}{3} \ \div \ \frac{20}{5} \\\ \\ Read Solution

Step 01
Convert division into multiplication by inverting the right side fraction
\Longrightarrow \ \frac{5}{3} \ \times \ \frac{5}{20}

Step 02
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{5\times 5}{3\times 20}\\\ \\ \Longrightarrow \frac{25}{60}

Step 03
If possible, simplify the fraction

Divide numerator and denominator by 5

Hence, \frac{5}{12} is the solution

(f) \frac{1}{9} \ \div \ \frac{9}{1} \\\ \\ Read Solution

Step 01
Convert division into multiplication by inverting the right side fraction
\Longrightarrow \ \frac{1}{9} \ \times \ \frac{1}{9}

Step 02
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{1\times 1}{9\times 9}\\\ \\ \Longrightarrow \frac{1}{81}

Step 03
If possible, simplify the fraction

Further simplification is not possible
Hence, \frac{1}{81} is the solution

(g) \frac{12}{4} \ \div \ \frac{5}{16} \\\ \\ Read Solution

Step 01
Convert division into multiplication by inverting the right side fraction
\Longrightarrow \ \frac{12}{4} \ \times \ \frac{16}{5}

Step 02
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{12\times 16}{4\times 5}\\\ \\ \Longrightarrow \frac{192}{20}

Step 03
If possible, simplify the fraction

Divide numerator and denominator by 4

Hence, \frac{48}{5} is the solution

(h) \frac{3}{7} \ \div \ \frac{9}{7} \\\ \\ Read Solution

Step 01
Convert division into multiplication by inverting the right side fraction
\Longrightarrow \ \frac{3}{7} \ \times \ \frac{7}{9}

Step 02
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{3\times 7}{7\times 9}\\\ \\ \Longrightarrow \frac{21}{63}

Step 03
If possible, simplify the fraction

Divide numerator and denominator by 21

Hence, \frac{1}{3} is the solution

(h) \frac{5}{10} \ \div \ \frac{6}{12} \\\ \\ Read Solution

Step 01
Convert division into multiplication by inverting the right side fraction
\Longrightarrow \ \frac{5}{10} \ \times \ \frac{12}{6}

Step 02
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{5\times 12}{10\times 6}\\\ \\ \Longrightarrow \frac{60}{60}

Step 03
If possible, simplify the fraction

Divide numerator and denominator by 60

Hence, 1 is the solution

(i) \frac{7}{11} \ \div \ \frac{1}{6}\\\ \\ Read Solution

Step 01
Convert division into multiplication by inverting the right side fraction
\Longrightarrow \ \frac{7}{11} \ \times \ \frac{6}{1}

Step 02
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{7\times 6}{11\times 1}\\\ \\ \Longrightarrow \frac{42}{11}

Step 03
If possible, simplify the fraction

Further simplification is not possible
Hence, \frac{42}{11} is the solution

(j) \frac{5}{9} \ \div \ \frac{1}{2} \\\ \\ Read Solution

Step 01
Convert division into multiplication by inverting the right side fraction
\Longrightarrow \ \frac{5}{9} \ \times \ \frac{2}{1}

Step 02
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{5\times 2}{9\times 1}\\\ \\ \Longrightarrow \frac{10}{9}

Step 03
If possible, simplify the fraction

Further simplification is not possible
Hence, \frac{10}{9} is the solution

(k) \frac{4}{8} \ \div \ \frac{2}{6} \\\ \\ Read Solution

Step 01
Convert division into multiplication by inverting the right side fraction
\Longrightarrow \ \frac{4}{8} \ \times \ \frac{6}{2}

Step 02
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{4\times 6}{8\times 2}\\\ \\ \Longrightarrow \frac{24}{16}

Step 03
If possible, simplify the fraction

Divide both numerator and denominator by 8

Hence, \frac{3}{2} is the solution

(l) \frac{1}{6} \ \div \ \frac{3}{5} \\\ \\ Read Solution

Step 01
Convert division into multiplication by inverting the right side fraction
\Longrightarrow \ \frac{1}{6} \ \times \ \frac{5}{3}

Step 02
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{1\times 5}{6\times 3}\\\ \\ \Longrightarrow \frac{5}{18}

Step 03
If possible, simplify the fraction

Further simplification is not possible

Hence, \frac{5}{18} is the solution

(m) \frac{0}{6} \ \div \ \frac{1}{8} \\\ \\ Read Solution

Step 01
Convert division into multiplication by inverting the right side fraction
\Longrightarrow \ \frac{0}{6} \ \times \ \frac{8}{1}

Step 02
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{0\times 8}{6\times 1}\\\ \\ \Longrightarrow \frac{0}{6}

Hence 0 is the solution of the given problem

(n) \frac{10}{5} \ \div \ \frac{5}{15} \\\ \\ Read Solution

Step 01
Convert division into multiplication by inverting the right side fraction
\Longrightarrow \ \frac{10}{5} \ \times \ \frac{15}{5}

Step 02
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{10\times 15}{5\times 5}\\\ \\ \Longrightarrow \frac{150}{25}

Step 03
If possible, simplify the fraction

Divide numerator and denominator by 25

Hence, 5 is the solution

(o) \frac{7}{21} \ \div \ \frac{14}{7} \\\ \\ Read Solution

Step 01
Convert division into multiplication by inverting the right side fraction
\Longrightarrow \ \frac{7}{21} \ \times \ \frac{7}{14}

Step 02
Multiply the numerator and denominator separately
\Longrightarrow \ \frac{7\times 7}{21\times 14}\\\ \\ \Longrightarrow \frac{49}{294}

Step 03
If possible, simplify the fraction

Divide numerator and denominator by 49

Hence, \frac{1}{6} is the solution