Addition or Subtraction of Fractions With Different Denominators

Definition

When the denominators of any fractions are unequal or are different those fractions are called unlike fractions.

Operations like addition and subtraction cannot be done directly on unlike fractions.

These unlike fractions are first converted into like fractions by finding the least common denominator of these fractions and rewriting the fractions into equivalent fractions with same denominators (LCD)Adding unlike fractions − Formula

When fractions with different or unlike fractions are to be added, first the least common denominator of the fractions is found. The equivalent fractions of given fractions are found with LCD as the common denominator. The numerators are now added and the result is put over the LCD to get the sum of fractions.

• We find the least common denominator of all the fractions.
• We rewrite the fractions to have the denominators equal to the LCD obtained in first step .
• We add the numerators of all the fractions keeping the denominator value equal to the LCD obtained in first step.
• We then express the fraction in lowest terms.

Subtracting unlike fractions − Formula

When fractions with different or unlike fractions are to be subtracted, first the least common denominator of the fractions is found. The equivalent fractions of given fractions are found with LCD as the common denominator. The numerators are now subtracted and the result is put over the LCD to get the difference of the given fractions.

• We find the least common denominator of all the fractions.
• We rewrite the fractions to have the denominators equal to the LCD obtained in step 1.
• We subtract the numerators of all the fractions keeping the denominator value equal to the LCD obtained in step 1.
• We express the fraction in lowest terms.

Problem 1:

Add 1515 + 2727

Solution

Step 1:

Add 1515 + 2727

Here the denominators are different. As 5 and 7 are prime the LCD is their product 35.

Step 2:

Rewriting

1515 + 2727 = (1×7)(5×7)(1×7)(5×7) + (2×5)(7×5)(2×5)(7×5) = 735735 + 10351035

Step 3:

As the denominators have become equal

735735 + 10351035 = (7+10)35(7+10)35 = 17351735

Step 4:

So, 1515 + 2727 = 17351735Problem 2:

Subtract 215215 − 110110

Solution

Step 1:

Subtract 215215 − 110110

Here the denominators are different. The LCM of 10 and 15 is 30.

Step 2:

Rewriting

215215 − 110110 = (2×2)(15×2)(2×2)(15×2) − (1×3)(10×3)(1×3)(10×3) = 430430 − 330330

Step 3:

As the denominators have become equal

430430 − 330330 = (4−3)30(4−3)30 = 130130

Step 4:

So, 215215 − 110110 = 130