Add or Subtract Fractions With the Same Denominator and Simplification

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 = $\frac{a}{c}$ + $\frac{b}{c}$ = $\frac{(a + b)}{c}$, where a, b and c are any three real numbers.

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 = $\frac{a}{c}$ − $\frac{b}{c}$ = $\frac{(a − b)}{c}$, where a, b and c are any three real numbers.

Add $\frac{3}{8}$ + $\frac{1}{8}$

Solution

Step 1:

Add $\frac{3}{8}$ + $\frac{1}{8}$

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 $\frac{3}{8}$ + $\frac{1}{8}$ = $\frac{(3+1)}{8}$ = $\frac{4}{8}$

Step 2:

Reducing the fraction to lowest terms

$\frac{4}{8}$ = $\frac{1}{2}$

So, $\frac{3}{8}$ + $\frac{1}{8}$ = $\frac{1}{2}$

Subtract $\frac{5}{6}$ − $\frac{1}{6}$

Solution

Step 1:

Subtract $\frac{5}{6}$ − $\frac{1}{6}$

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 $\frac{5}{6}$ − $\frac{1}{6}$ = $\frac{(5-1)}{6}$ = $\frac{4}{6}$

Step 2:

Simplifying to the lowest terms,

$\frac{4}{6}$ = $\frac{2}{3}$

So, $\frac{5}{6}$ − $\frac{1}{6}$ = $\frac{2}{3}$