# Division of fractions with solved examples

In mathematics division means sharing but when is comes to division of fractions there are some simple rules one needs to follow to divide a given fractions.

Rules Governing Division of fractions

There are rules that one needs to follow when dividing fractions. Below are some of the rules Governing Division of fractions.

Rule 1: Whole number ÷ fraction = whole number × reciprocal of the fraction. What this actually means is that when dividing a whole number with a fraction, the best thing to do is turn upside down the fraction (reciprocate of the fraction) and Multiply it with the whole number. Let’s look at an example

\text{Example: divide} \space3÷\frac{5}{6}\\
Answer: 3÷\frac{5}{6}=3×\frac{6}{5}=\frac{(3×6)}{5}=\frac{18}{5}=3\frac{3}{5}

Rule 2: Dividing a fraction by a whole number. To perform the operation of division of fractions on a whole number. Fraction ÷ whole number = fraction × reciprocal of the whole number. This means that in dividing a fraction with a whole number, reciprocate the whole number and then Multiply fractions with the reciprocal of the whole number. Let’s look at an example below

\text{Example: divide} \frac{6}{5}÷3\\
\frac{6}{5}÷3=\frac{6}{5}×\frac{1}{3}=\frac{6×1}{5×3}=\frac{6}{18}=\frac{1}{3}\\
\text{since the reciprocal of }\space4=\frac{1}{4}\\
Note : \text{every whole number is over 1} 

Rule 3: Dividing a fraction by a fraction. To divide a fraction with another fraction. Let’s say fraction 1 ÷ fraction 2. The rule is that Multiply the first fraction by the reciprocal of the second fraction. Hence fraction 1 ÷ fraction 2 = fraction 1 × reciprocal of fraction 2. Let’s look at the example below

\text{Example: Divide }\space\frac{2}{3}÷\frac{4}{5}\\
Answer: \text{the reciprocal of the second fraction }\space\frac{4}{5}=\frac{5}{4}\\
\frac{2}{3}÷\frac{4}{5}=\frac{2}{3}×\frac{5}{4}=\frac{2×5}{3×4}=\frac{10}{12}=\frac{5}{6}

Note that when dividing fractions that involves mixed numbers, first convert the mixed numbers to improper fractions before following the above rules and after simplifying your fractions to get the answer.

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