# Product of a Unit Fraction and a Whole Number

A unit fraction is a fraction whose numerator is always 1 and whose denominator is a positive integer.

For example, following are some unit fractions $\frac{1}{2}$, $\frac{1}{9}$, $\frac{1}{16}$, $\frac{1}{47}$ and so on.

Rules to find the product of a unit fraction and a whole number

• We first write the whole number as a fraction, i.e., writing it divided by one; for example: 7 is written as $\frac{7}{1}$

• We then multiply the numerators

• We multiply the denominators

• If any simplification is required, it is done and then we write the final fraction.

What is $\frac{1}{2}$ of 6

### Solution

Step 1:

$\frac{1}{2}$ of 6 is $\frac{1}{2}$ × 6

Step 2:

First, we write the whole number 6 as a fraction $\frac{6}{1}$

$\frac{1}{2}$ × 6 = $\frac{1}{2}$ × $\frac{6}{1}$

Step 3:

As 2 and 6 are multiples of 2, cross cancelling 2 and 6, we get

$\frac{1}{2}$ × $\frac{6}{1}$ = $\frac{1}{1}$ × $\frac{3}{1}$

Step 4:

Multiply the numerators and denominators of both fractions as follows.

$\frac{1}{1}$ × $\frac{3}{1}$ = $\frac{(1 × 3)}{(1 × 1)}$ = $\frac{3}{1}$ = 3

Step 5:

So $\frac{1}{2}$ of 6 = 3

What is $\frac{1}{4}$ of 16

### Solution

Step 1:

$\frac{1}{4}$ of 16 is $\frac{1}{4}$ × 16

Step 2:

First, we write the whole number 16 as a fraction $\frac{16}{1}$

$\frac{1}{4}$ × 16 = $\frac{1}{4}$ × $\frac{16}{1}$

Step 3:

As 4 and 16 are multiples of 4, cross cancelling 4 and 16, we get

$\frac{1}{4}$ × $\frac{16}{1}$ = $\frac{1}{1}$ × $\frac{4}{1}$

Step 4:

Multiply the numerators and denominators of both fractions as follows.

$\frac{1}{1}$ × $\frac{4}{1}$ = $\frac{(1 × 4)}{(1 × 1)}$ = $\frac{4}{1}$ = 4

Step 5:

So $\frac{1}{4}$ of 16 = 4