- We have already learned about Fraction Definition, Comparing Fractions, How to add Fractions, How to Subtract Fractions,Comparison, Addition and Subtraction of Mixed Fractions,Multiplying fractions .
- In this we will learning How to divide the fractions, how to divide fractions with whole numbers and various other thing related to division

$1 \div \frac {1}{2}$

This can be understood as we have 1 full pizza and we divide into two equal piece. The above division can be understood as how many 1/2 part can be obtained from 1 whole. Obviously it is 2 ,So

$1 \div \frac {1}{2} = 2$

or

$1 \div \times \frac {2}{1} = 2$

The conversion of $\frac {1}{2}$ to $\frac {2}{1}$ is called reciprocal of fraction. $\frac {2}{1}$ is called the reciprocal of fraction $\frac {1}{2}$.

Few examples on reciprocal of fraction

1. $\frac {1}{2}$

Reciprocal Fraction = $\frac {2}{1}$

2. $\frac {2}{3}$

Reciprocal Fraction = $\frac {3}{2}$

3. $\frac {4}{9}$

Reciprocal Fraction = $\frac {9}{4}$

4. 4

Reciprocal Fraction = $\frac {1}{4}$

So steps for Division of Whole Number by a Fraction can be summarized as
Reciprocal Fraction = $\frac {2}{1}$

2. $\frac {2}{3}$

Reciprocal Fraction = $\frac {3}{2}$

3. $\frac {4}{9}$

Reciprocal Fraction = $\frac {9}{4}$

4. 4

Reciprocal Fraction = $\frac {1}{4}$

- if we have Mixed Fraction in the division, first convert into Improper Fraction
- Now obtain the reciprocal of the fraction part
- Now We can simplify multiply the whole number with reciprocal fractions .If the results is improper fraction, you can convert into mixed fraction if required.

$ 3 \div \frac {1}{5}=3 \times \frac {5}{1} =15$

$ 2 \div \frac {4}{5}=2 \times \frac {5}{4} = \frac {2 \times 5}{4}=\frac {10}{4} = \frac {5}{2} =2 \frac {1}{2}$

$ 2 \div 1\frac {1}{5}= 2 \div \frac {6}{5} = 2 \times \frac {5}{6}=\frac {10}{6} = \frac {5}{3}= 1 \frac {2}{3}$

$ 2 \div \frac {1}{8} =2 \times \frac {8}{1} =16 $

Division of a fraction by a whole number is done in the similar manner.

$ \frac {1}{8} \div 2 =\frac {1}{8} \times \frac {1}{2} =\frac {1}{16} $

Here are the steps

- if we have mixed fraction, first convert into improper fraction

- Now obtain the reciprocal of the whole number

- Now We can simplify multiply both the fractions .If the results is improper fraction, you can convert into mixed fraction if required.

$ \frac {1}{5} \div 20 = \frac {1}{5} \times \frac {1}{20}= \frac {1}{100}$

$\frac {2}{5} \div 10= \frac {2}{5} \times \frac {1}{10}=\frac {2}{50} =\frac {1}{25} $

$1\frac {1}{5} \div 3= \frac {6}{5} \div 3= \frac {6}{5} \times \frac {1}{3}=\frac {6}{15} =\frac {2}{5} $

$ \frac {1}{5} \div \frac {5}{6}= \frac {1}{5} \times \frac {6}{5} = \frac {6}{25}$

Here we can see that dividing fraction is simply acheived by .This same steps applies for how to divide mixed fractions

- if we have mixed fraction, first convert into improper fraction

- Now obtain the reciprocal of the fraction which is the divisor

- Now We can simplify multiply both the fractions .If the results is improper fraction, you can convert into mixed fraction if required.

$ \frac {3}{4} \div \frac {1}{2} =\frac {3}{4} \times \frac {2}{1}= \frac {3 \times 2}{4}= \frac {6}{4}=\frac {3}{1}=1\frac {1}{2} $

$ \frac {1}{7} \div \frac {4}{9}=\frac {1}{7} \times \frac {9}{4} = \frac {9}{28} $

$ \frac {3}{7} \div 2\frac {1}{5} =\frac {3}{7} \div \frac {11}{5} = \frac {3}{7} \times \frac {5}{11}=\frac {15}{77} $

$ 2\frac {1}{5} \div 1\frac {1}{2} =\frac {11}{5} \div 1\frac {3}{2} =\frac {11}{5} \times \frac {2}{3} = \frac {22}{15} = 1 \frac {7}{15}$

**Notes****Assignments**

Given below are the links of some of the reference books for class 7 math.

- Mathematics for class 7 by R S Aggarwal
- Mathematics for Class 7 by R D Sharma
- Mathematics Foundation Course For JEE/IMO/Olympiad - Class 7
- IIT Foundation Physics, Chemistry & Maths for Class 7

You can use above books for extra knowledge and practicing different questions.

Class 7 Maths Class 7 Science

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