Addition or Subtraction of Unit Fractions

A unit fraction is a fraction where the numerator is always one and the denominator is a positive integer. Addition or subtraction of unit fractions can be of two types; one, where the denominators are same; two, where the denominators are different.

• When the unit fractions have like denominators, we add the numerators and put the result over the common denominator to get the answer.

• When the unit fractions have unlike or different denominators, we first find the LCD of the fractions. Then we rewrite all unit fractions to equivalent fractions using the LCD as the denominator. Now that all denominators are alike, we add the numerators and put the result over the common denominator to get the answer.

• When the unit fractions have like denominators, we subtract the numerators and put the result over the common denominator to get the answer.

• When the unit fractions have unlike or different denominators, we first find the LCD of the fractions. Then we rewrite all unit fractions to equivalent fractions using the LCD as the denominator. Now that all denominators are alike, we subtract the numerators and put the result over the common denominator to get the answer.

Add $\frac{1}{3}$ + $\frac{1}{9}$

Solution

Step 1:

Add $\frac{1}{3}$ + $\frac{1}{9}$

Here the denominators are different. As 9 is a multiple of 3, the LCD is 9 itself.

Step 2:

Rewriting

$\frac{1}{3}$ + $\frac{1}{9}$ = $\frac{(1×3)}{(3×3)}$ + $\frac{1}{9}$ = $\frac{3}{9}$ + $\frac{1}{9}$

Step 3:

As the denominators have become equal

$\frac{3}{9}$ + $\frac{1}{9}$ = $\frac{(3+1)}{9}$ = $\frac{4}{9}$

Step 4:

So, $\frac{1}{3}$ + $\frac{1}{9}$ = $\frac{4}{9}$

Subtract $\frac{1}{9}$ − $\frac{1}{12}$

Solution

Step 1:

Subtract $\frac{1}{9}$ − $\frac{1}{12}$

Here the denominators are different. The LCD of the fractions is 36.

Step 2:

Rewriting

$\frac{1}{9}$ − $\frac{1}{12}$ = $\frac{(1×4)}{(9×4)}$ − $\frac{(1×3)}{(12×3)}$ = $\frac{4}{36}$ − $\frac{3}{36}$

Step 3:

As the denominators have become equal

$\frac{4}{36}$ − $\frac{3}{36}$ = $\frac{(4−3)}{36}$ = $\frac{1}{36}$

Step 4:

So, $\frac{1}{9}$ − $\frac{1}{12}$ = $\frac{1}{36}$