Fractions

Division of a fraction by a whole number

Example 1: Divide \(1\over 2\) by 3

We have to divide \(1\over 2\) by 3

Let’s split \(1\over 2\) into 3 equal groups.

Each is now divided into 3 equal parts

Now, the total parts are 6 and one part out of 6 is \(1\over 6\)

So, \(1\over 2\) ÷3 =\(1\over 6\)

Which means if  \(1\over 2\) of a cake is divided into 3 children, each child will get \(1\over 6\) of the whole cake

Example 2: Divide \(1 \over 4\) by 2. 

\({1\over 4} \div 2={1\over 8} \)

We saw that:\({1\over 2} \div 3={1\over 6} \)

If you multiply  \({1\over 2} \) by  \(1\over 3\), you get \(1 \over 6\). This means dividing a number by another number is same as multiplying by the reciprocal of that number,

We can also say that multiplication is the inverse of division

Example 3: To divide \(1 \over 2\) by 3, we will take reciprocal of 3 and multiply the fractions.

Step 1: Take reciprocal of the whole number

Reciprocal of 3 is \(1\over 3\)

Step 2: Multiply the fraction with the reciprocal of the whole number.

\(\frac{1}{2} \div 3 = \frac{1}{2} \times \frac{1}{3} = \frac{{1 \times 1}}{{2 \times 3}} = \frac{1}{6}\)