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 = \frac{(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 38 + 18

Solution

Step 1:

Add 38 + 18

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 38 + 18 = (3+1)8 = 48

Step 2:

Reducing the fraction to lowest terms

48 = 12

So, 38 + 18 = 12

Problem 2

Subtract 56 16

Solution

Step 1:

Subtract 56 16

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 56 16 = (5−1)6 = 46

Step 2:

Simplifying to the lowest terms,

46 = 23

So, 56 16 = 23