Add or Subtract Fractions With the Same Denominator and Simplification

Adding like fractions and simplification − Formula

If fractions with same denominators are to be added, we add the numerators only and keep the same denominator. If necessary, we simplify the resulting fraction to lowest terms.

• Sum of the fractions = ac�� + bc�� = (a+b)c(�+�)�, where a, b and c are any three real numbers.

Subtracting like fractions and simplification − Formula

If fractions with same denominators are to be subtracted, we subtract the numerators only and keep the same denominator. If necessary, we simplify the resulting fraction to lowest terms.

• Difference of the fractions = ac�� − bc�� = (a−b)c(�−�)�, where a, b and c are any three real numbers.

Problem 1:

Add 3838 + 1818

Solution

Step 1:

Add 3838 + 1818

Here, the denominators are the same 8. Since this is an addition operation,

We add the numerators 3 + 1 = 4 and put the result 4 over the common denominator to get the answer.

So 3838 + 1818 = (3+1)8(3+1)8 = 4848

Step 2:

Reducing the fraction to lowest terms

4848 = 1212

So, 3838 + 1818 = 1212Problem 2:

Subtract 5656 − 1616

Solution

Step 1:

Subtract 5656 − 1616

Here, the denominators are same 6. Since this is a subtraction operation, we subtract the numerators, 5 − 1 = 4 and put the result 4 over the common denominator 6.

So 5656 − 1616 = (5−1)6(5−1)6 = 4646

Step 2:

Simplifying to the lowest terms,

4646 = 2323

So, 5656 − 1616 = 23