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How to Divide fractions | dividing mixed fractions



Introduction

Division of Whole Number by a Fraction

Division of Whole Number by a Fraction can be understood by below example
$1 \div \frac {1}{2}$
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 How to divide whole Number by a fraction
  • 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.

how to divide whole Number by a fraction
Solved Examples
Question 1. $ 3 \div \frac {1}{5}$
Answer
$ 3 \div \frac {1}{5}=3 \times \frac {5}{1} =15$

Question 2. $ 2 \div \frac {4}{5}$
Answer
$ 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}$

Question 3. $ 2 \div 1\frac {1}{5}$
Answer
$ 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}$

Question 4. $ 2 \div \frac {1}{8}$
Answer
$ 2 \div \frac {1}{8} =2 \times \frac {8}{1} =16 $

Division of a Fraction by a Whole Number


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.

how to divide fraction by whole number

Solved Examples
Question 1. $ \frac {1}{5} \div 20$
Answer
$ \frac {1}{5} \div 20 = \frac {1}{5} \times \frac {1}{20}= \frac {1}{100}$

Question 2. $ \frac {2}{5} \div 10$
Answer
$\frac {2}{5} \div 10= \frac {2}{5} \times \frac {1}{10}=\frac {2}{50} =\frac {1}{25} $
Question 3. $ 1\frac {1}{5} \div 3$
Answer
$1\frac {1}{5} \div 3= \frac {6}{5} \div 3= \frac {6}{5} \times \frac {1}{3}=\frac {6}{15} =\frac {2}{5} $

How to divide fraction by a fraction

we have already see the division of fraction by whole number.Let us understand How to divide fraction by a fraction.
$ \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.

How to divide fraction by a fraction
Solved Examples
Question 1. $ \frac {3}{4} \div \frac {1}{2}$
Answer
$ \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} $

Question 2. $ \frac {1}{7} \div \frac {4}{9}$
Answer
$ \frac {1}{7} \div \frac {4}{9}=\frac {1}{7} \times \frac {9}{4} = \frac {9}{28} $

Question 3. $ \frac {3}{7} \div 2\frac {1}{5}$
Answer
$ \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} $

Question 4. $ 2\frac {1}{5} \div 1\frac {1}{2}$
Answer
$ 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}$
Checkout Dividing Fractions calculator

Quiz Time

Question 1$ 3 \div \frac {1}{2} $?
A) $6$
B)$\frac {1}{6}$
C)$\frac {2}{3}$
D)$\frac {3}{2}$
Question 2 $ \frac {1}{12} \div 3 $?
A)$\frac {1}{48}$
B)$\frac {1}{36}$
C) $\frac {1}{4}$
D)None of these
Question 3 $\frac {1}{2} \div \frac {4}{3}$
A)$\frac {3}{2}$
B)$\frac {2}{3}$
C)$\frac {1}{3}$
D)$1\frac {1}{2}$
Question 4 $\frac {2}{9} \div \frac {1}{9}$
A)$2$
B) $\frac {2}{81}$
C) $\frac {81}{2}$
D) $81$
Question 5 The reciprocal of fraction $1 \frac {2}{3}$?
A)$\frac {2}{5}$
B)$\frac {5}{3}$
C)$\frac {3}{2}$
D)$\frac {3}{5}$

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