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# Division and multiplication of fractions.

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Division simply means sharing. When it comes to the division of fractions we do have to apply the knowledge of multiplication of fractions in working it. So before we look at the division of fractions let’s see how the multiplication of fractions is solved.

## Multiplication of fractions

To multiply fractions, multiply the top numbers together and the bottom numbers together and then do cancellation if there is any. But before multiplying fractions check to see if there are mixed numbers there. If the fraction contains mixed numbers, change them to improper fraction before solving it. Let’s see an examples

Example1. Multiply $\frac{4}{7} × \frac{6}{9}$

Solution

To solve this multiply the top numbers together and bottom numbers together.
$\frac{4}{7} × \frac{6}{9} = \frac{4 × 6}{7 × 9} = \frac{24}{63} = \frac{8}{21}$ since 3 can enter into 24, 8 and go into 63, 21 times

Example2. Find the product of $2\frac{3}{7}$ and $4\frac{6}{11}$

Solution

This example is different from the first one because the fraction contain whole numbers and to solve this, first change the whole numbers to improper fraction and then do the multiplication.
= $2\frac{3}{7} × 4\frac{6}{11} = \frac{(2×7) + 3}{7} × \frac{(4×11) + 4}{11} = \frac{14+3}{7} × \frac{44+4}{11}$

= $\frac{17}{7} × \frac{48}{11} = \frac{17 × 48}{7 × 11} = \frac{816}{77} = 10\frac{46}{77}$

## Division of fractions

To divide fractions there are some basic rules that need to be followed. let’s go ahead and discuss that rules.

Rule 1. When dividing a whole number with a fraction, multiply the whole number with the reciprocal of the fraction. For instance $2 \div \frac{3}{7} = 2 \times \frac{7}{3} = \frac{14}{3} = 4\frac{2}{3}$

Rule 2. When dividing a fraction with a whole number, change the whole number to a fraction because every whole number is over 1 and then multiply the first fraction with the reciprocal of the second fraction. for example,

$\frac{3}{5} \div4 = \frac{3}{5} \div \frac{4}{1}=\frac{3}{5} \times \frac{1}{4} = \frac{3 \times 1}{5 \times 4} = \frac{3}{20}$

rule 3. when multiplying a fraction with another fraction, multiply the first fraction with the reciprocal of the second fraction. let’s see an example.

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$\frac{3}{7} \div \frac{4}{11} = \frac{3}{7} \times \frac{11}{4} = \frac{3 \times 11}{7 \times 4} = \frac{33}{28} = 1\frac{3}{28}$

note: always check the given fraction to see if they contain whole numbers. if there is any, change the mixed numbers to an improper fraction and then solve it. for example

$7\frac{4}{6} \div 3\frac{2}{9} = \frac{(7 \times 6) + 4}{6} \div \frac{(3 \times 9) + 2}{9}$ = $\frac{46}{6} \div \frac{29}{9} = \frac{46}{6} \times \frac{9}{29} = \frac{46 \times 9}{6 \times 29} = \frac{414}{174} = 2\frac{66}{174}$

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