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Fractions, Decimals, and Percentages - Adding and subtracting fractions with the same denominator

Grade 4IGCSE

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

🔑Concepts

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A fraction consists of a numerator (top number) and a denominator (bottom number).

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The denominator tells us how many equal parts make up one whole.

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Fractions with the same denominator are called 'like fractions'.

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When adding or subtracting like fractions, only the numerators are changed; the denominator stays the same.

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If the numerator becomes equal to the denominator (e.g., 4/4), it is equal to 1 whole.

📐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:

Calculate 27+37\frac{2}{7} + \frac{3}{7}.

Solution:

57\frac{5}{7}

Explanation:

Since the denominators are the same (7), we simply add the numerators: 2 + 3 = 5. The denominator remains 7.

Problem 2:

Subtract 49\frac{4}{9} from 89\frac{8}{9}.

Solution:

49\frac{4}{9}

Explanation:

We subtract the numerators: 8 - 4 = 4. The denominator stays as 9.

Problem 3:

Sarah ate 14\frac{1}{4} of a pizza and Tom ate 34\frac{3}{4} of the same pizza. How much did they eat in total?

Solution:

11 (or 44\frac{4}{4})

Explanation:

Add the numerators: 1 + 3 = 4. This gives 44\frac{4}{4}. Since the numerator and denominator are the same, it represents 1 whole pizza.