Addition or Subtraction of Unit Fractions

Definition

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.

Rules for Addition of unit fractions

• 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.

Rules for Subtraction of unit fractions

• 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.

Problem 1

Add 13 + 19

Solution

Step 1:

Add 13 + 19

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

Step 2:

Rewriting

13 + 19 = (1×3)(3×3) + 19 = 39 + 19

Step 3:

As the denominators have become equal

39 + 19 = (3+1)9 = 49

Step 4:

So, 13 + 19 = 49

Problem 2

Subtract 19 − 112

Solution

Step 1:

Subtract 19 − 112

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

Step 2:

Rewriting

19 − 112 = (1×4)(9×4) − (1×3)(12×3) = 436 − 336

Step 3:

As the denominators have become equal

436 − 336 = (4−3)36 = 136

Step 4:

So, 19 − 112 = 136