Add or Subtract Fractions With the Same Denominator


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Fractions that have exact same denominators are called like fractions.

Fractions such as $\frac{1}{5}$ and $\frac{4}{5}$ are like fractions because they have a common denominator 5.

In other words, fractions with like denominators are categorized as like fractions. Performing any mathematical operations on like fractions is comparatively easier as we can make use of the common denominator for fraction operations like addition and subtraction.

If fractions with same denominators are to be added, we need to add the numerators only and keep the same denominator.

  • We add the numerators.
  • We keep the common denominator.
  • Then the Sum of the fractions = $\frac{(Sum-of-the- Numerators)}{(Common-Denominator)}$
  • 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 need to subtract the numerators only and keep the same denominator.

  • We subtract the numerators.
  • We keep the common denominator.
  • Then the Difference of the fractions = $\frac{(Difference-of-the- Numerators)}{(Common-Denominator)}$

  • 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 $\frac{3}{7}$ + $\frac{2}{7}$

Solution

Step 1:

Here, the denominators are the same 7. We add the numerators 3 + 2 = 5 and put the result 5 over the common denominator 7 to get the answer.

$\frac{3}{7}$ + $\frac{2}{7}$ = $\frac{(3+2)}{7}$ = $\frac{5}{7}$

Step 2:

So, $\frac{3}{7}$ + $\frac{2}{7}$ = $\frac{5}{7}$

Subtract $\frac{5}{6}$$\frac{4}{6}$

Solution

Step 1:

Here, the denominators are the same 6. We subtract the numerators; 5 − 4 = 1 and put the result 1 over the common denominator to get the answer.

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

Step 2:

So, $\frac{5}{6}$$\frac{4}{6}$ = $\frac{1}{6}$

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