Unit Fractions with Examples and FAQ

How can you say that a fraction is a unit fraction or not?

Any fraction with 1 as its numerator and a natural number in the denominator is called a unit fraction.

For example: \frac{2}{3}, \frac{1}{5}, \frac{8}{13}, \frac{1}{15} are some fractions out of which only \frac{1}{5} \text { and } \frac{1}{15} are unit fractions. The other two are not. 

Therefore, the general form of a unit fraction is \frac{1}{x}, where x is a natural number.

The images show unit fractions \frac{1}{4} \text { and } \frac{1}{8}.

Examples

Example 1: Select the unit fractions among the given fraction \frac{1}{4}, \frac{2}{6}, \frac{5}{15}, \frac{4}{9}, \frac{3}{4}, \frac{1}{6}.

Solution: 

From the given set of fractions, we can see that \frac{1}{4} \text { and } \frac{1}{6} are clearly unit fractions.

\frac{2}{6}=\frac{1}{3} \text { and } \frac{5}{15}=\frac{1}{3} can also be represented as unit fractions. 

\frac{4}{9} \text { and } \frac{3}{4} can not be reduced to unit fractions.

Hence from the given set of fractions \frac{1}{4}, \frac{2}{6}, \frac{5}{15} \text { and } \frac{1}{6}are unit fractions.

Example 2: Add the unit fractions,\frac{1}{4} \text { and } \frac{1}{6}.

Solution: 

To add the two unit fractions at first, we must change them to like fractions.

Since the denominators in the given fractions are different, we find the LCM of 4 and 6 to make the same.

LCM of 4 and 6 = 12.

\text { Now, multiply } \frac{1}{4} \text { with } \frac{3}{3} \Rightarrow \frac{1}{4} \times \frac{3}{3}=\frac{3}{12} \text {. }

\text { Similarly multiplying } \frac{1}{6} \text { with } \frac{2}{2} \Rightarrow \frac{1}{6} \times \frac{2}{2}=\frac{2}{12}

Hence we have got like fractions which makes the addition simple.

\therefore \frac{1}{4}+\frac{1}{6}=\frac{3}{12}+\frac{2}{12}=\frac{3+2}{12}=\frac{5}{12}

\text { Hence, } \frac{1}{4}+\frac{1}{6}=\frac{5}{12} \text {. }