Division of Fractions
Division means sharing an item equally. We have learned about the division of whole numbers, now let us see how to divide fractions. A fraction has two parts  a numerator and a denominator. Dividing two fractions is almost the same as multiplying them. To divide two given fractions, we multiply the first fraction by the reciprocal (inverse) of the second fraction.
On this page, we will learn more about the division of fractions by fractions, by decimals, and with various other numbers.
1.  How to Divide Fractions? 
2.  Divide Fractions by Fractions 
3.  Dividing Fractions with Decimals 
4.  Divide Fractions with Mixed Numbers 
4.  FAQs on How to Divide Fractions 
How to Divide Fractions?
We know that division is a method of sharing equally and putting into equal groups. We divide a whole number by the divisor to get the quotient. Now, when we divide a fraction by another fraction, it is the same as multiplying the fraction by the reciprocal of the second fraction. The reciprocal of a fraction is a simple way of interchanging the fraction's numerator and denominator. Observe the following figure to learn a simple way of dividing fractions.
Divide Fractions by Fractions
We just learned how to divide fractions by taking the reciprocal. Let us see how to divide a fraction by another fraction with an example. Have a look at the formula given here in order to understand how to divide fractions by fractions.
\[\begin{align} \frac{{{\text{Fraction}}_1 }}{{{\text{Fraction}}_2 }} &= \frac{{\left[ {\frac{{{\text{Numerator}}_1 }\;\left(Nr_1\right)}{{{\text{Denominator}}_1 }\;\left(Dr_1\right)}} \right]}}{{\left[ {\frac{{{\text{Numerator}}_2 }\;\left(Nr_2\right)}{{{\text{Denominator}}_2 }\;\left(Dr_2\right)}} \right]}} \\\\ & = \frac{{{\text{Nr}}_1 }}{{{\text{Dr}}_1 }} \times \frac{{{\text{Dr}}_2 }}{{{\text{Nr}}_2 }} \\ \end{align}\]
Now, if we need to divide: 5/8 ÷ 15/16, we will substitute the values of the given numerators and denominators.
\[\begin{align} \frac{{{\text{Fraction}}_1 }}{{{\text{Fraction}}_2 }} &= \frac{{\left[ {\frac{{{\text{Numerator}}_1 }\;\left(5\right)}{{{\text{Denominator}}_1 }\;\left(8\right)}} \right]}}{{\left[ {\frac{{{\text{Numerator}}_2 }\;\left(15\right)}{{{\text{Denominator}}_2 }\;\left(16\right)}} \right]}} \\\\ & = \frac{{5 }}{{8 }} \times \frac{{16 }}{{15 }} \\ \end{align}\]
∴ The value of 5/8 ÷ 15/16 = 2/3
Dividing Fractions with Decimals
We know that decimal numbers themselves are a fraction to base 10. We can represent the decimal in the fractional form and then perform the division. Consider the example:
\[\begin{align} \frac{\frac{3}{4}}{0.5} &=\frac{ \frac{3}{4}}{\frac{5}{10}} \;( \because 0.5 \!=\!\frac{5}{10}) \\\\
&= \frac{3}{4} \times \frac{10}{5} \\\\
&=\frac{30}{20}\\\\
&=\frac{3}{2}
\end{align}\]
Divide Fractions with Mixed Numbers
We have learnt how to convert mixed fractions to improper fractions. To divide fractions with mixed form, we have to convert the mixed fraction to an improper fraction and then divide them. Consider the following example.
\(\begin{align}\frac{ \frac{3}{4}}{1\frac{1}{2}} \end{align}\)
This can be solved in the following way:
\[\begin{align} \frac{\frac{3}{4}}{1\frac{1}{2}} &=\frac{ \frac{3}{4}}{\frac{3}{2}} \;( \because 1\frac{1}{2}\!=\!\frac{(2\!\times\!1) \!+\! 1}{2} \!=\!\frac{3}{2} )\\\\
&= \frac{3}{4} \times \frac{2}{3} \\\\
&=\frac{1}{2}
\end{align}\]
Solved Examples on How to Divide Fractions

Example 1: Find the value of 3/16 ÷ 15/32.
Solution:
To divide 3/16 ÷ 15/32, we will change the second fraction to its reciprocal and then multiply the two fractions. 3/16 × 32/15. After simplifying, we get (3 × 32) / (16 × 15) = 2/5.
∴ The value of 3/16 ÷ 15/32 = 2/5

Example 2: Tim has \(1\frac{1}{2}\) litres of juice in a jug. He has to pour the juice into cups. Each cup can hold \(\frac{1}{4}\) litres of juice. How many cups will he need to pour all the juice?
Solution:
Number of cups needed = Total quantity of juice/ Capacity of 1 cup
\[\begin{align}
&= \frac{1\frac{1}{2}}{\frac{1}{4}} \\\\
&= \frac{\frac{3}{2}}{\frac{1}{4}} \;(\because 1\frac{1}{2} = \frac{3}{2})\\\\
&= \frac{3}{2} \times \frac{4}{1} \\\\
&= 6
\end{align}\]Therefore, the number of cups required to pour the juice is 6.
Practice Questions on How to Divide Fractions
FAQs on How to Divide Fractions
What are the Steps in Dividing Fractions?
The following steps show the way to divide fractions:
 Step 1: Take the reciprocal of the second fraction.
 Step 2: Multiply it with the first fraction.
 Step 3: Reduce the resultant fraction to its lowest terms.
How to Teach Dividing Fractions?
Division of fractions can be taught in many ways such as, by using models or applying the concept of multiplication of fractions. A simple way to explain how to divide fractions is :
 Flip the reciprocal of the divisor.
 Change the division sign into a multiplication sign.
 Multiply it with the dividend.
How to Divide a Number by a Fraction?
To divide a whole number by a fraction, we multiply the whole number with the reciprocal of the given fraction. To divide a fraction by a fraction, we multiply the reciprocal of the second fraction with the first fraction.
How to Divide Fractions With Whole Numbers?
Dividing fractions with whole numbers is a threestep process:
 Step 1: Keep the fraction as it is. For example, 3/4 ÷ 6.
 Step 2: Flip the whole number, which will make it a fraction of the format 1/a. In this case, 6 will become 1/6.
 Step 3: Change the sign into multiplication between the fractions, multiply and simplify them. This will be: 3/4 × 1/6 = 3/24 = 1/8.
How to Multiply Fractions?
The following steps are used to multiply fractions:
 Step 1: Multiply the numerators of both the fractions.
 Step 2: Multiply the denominators of both the fractions.
 Step 3: Simplify the fraction obtained after multiplication.
How to Divide Fractions With Mixed Numbers?
To divide fractions with mixed numbers, the following steps are used:
 Step 1: Keep the fraction as it is.
 Step 2: Convert the mixed number into a proper or improper fraction and flip the second fraction.
 Step 3: Change the sign into multiplication between the fractions, multiply and simplify them.