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Number - Adding and subtracting fractions with the same denominator

Grade 3Cambridge (IGCSE)

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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A fraction represents part of a whole. The top number is the numerator (how many parts we have) and the bottom number is the denominator (the total number of equal parts in the whole).

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Fractions with the same denominator are called like fractions.

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When adding fractions with the same denominator, add only the numerators and keep the denominator exactly the same.

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When subtracting fractions with the same denominator, subtract the numerators and keep the denominator exactly the same.

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Never add or subtract the denominators.

📐Formulae

ac+bc=a+bc\frac{a}{c} + \frac{b}{c} = \frac{a + b}{c}

ac−bc=a−bc\frac{a}{c} - \frac{b}{c} = \frac{a - b}{c}

💡Examples

Problem 1:

Find the sum of 26\frac{2}{6} and 36\frac{3}{6}.

Solution:

26+36=2+36=56\frac{2}{6} + \frac{3}{6} = \frac{2 + 3}{6} = \frac{5}{6}

Explanation:

Since the denominators are the same (66), we add the numerators 22 and 33 to get 55. The denominator remains 66.

Problem 2:

Subtract 29\frac{2}{9} from 79\frac{7}{9}.

Solution:

79−29=7−29=59\frac{7}{9} - \frac{2}{9} = \frac{7 - 2}{9} = \frac{5}{9}

Explanation:

Both fractions have the same denominator (99). We subtract the numerator 22 from 77 to get 55. The denominator does not change.

Problem 3:

Sarah ate 14\frac{1}{4} of a pizza in the afternoon and 24\frac{2}{4} of the pizza for dinner. How much pizza did she eat in total?

Solution:

14+24=1+24=34\frac{1}{4} + \frac{2}{4} = \frac{1 + 2}{4} = \frac{3}{4}

Explanation:

To find the total, we add the two parts. Because both fractions are fourths, we add the numerators 11 and 22 to get 33. Sarah ate 34\frac{3}{4} of the pizza.