Add or Subtract Fractions With the Same Denominator and Simplification

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

Problem 1

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

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