Add or Subtract Fractions With Different Denominators: Advanced

Introduction

When we have addition or subtraction of fractions with unlike denominators, we first find the Least Common Denominator (LCD) of the fractions. We then rewrite all fractions as equivalent fractions with LCD as the denominator. Now that all denominators are alike, we add or subtract the numerators and put the result over the common denominator to get the answer. If necessary, we express the fraction in lowest terms.Problem 1:

Add 3535 + 3838

Solution

Step 1:

Add 3535 + 3838

Here the denominators are different. The LCD is 40 (product of 5 and 8) as 5 and 8 are co-prime numbers.

Step 2:

Rewriting

3535 + 3838 = (3×8)(5×8)(3×8)(5×8) + (5×5)(8×5)(5×5)(8×5) = 24402440 + 25402540

As the denominators have become equal

24402440 + 25402540 = (24+25)40(24+25)40 = 49404940

Step 3:

So, 3535 + 3838 = 49404940Problem 2:

Subtract 5858 − 712712

Solution

Step 1:

5858 − 712712

Here the denominators are different. The LCD here is 24.

Step 2:

Rewriting

5858 − 712712 = (5×3)(8×3)(5×3)(8×3) − (7×2)(12×2)(7×2)(12×2) = 15241524 − 14241424

As the denominators have become equal

15241524 − 14241424 = (15−14)24(15−14)24 = 124124

Step 3:

So, 5858 − 712712 = 124