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Fractions, Decimals, and Percentages - Equivalent fractions and simplifying

Grade 5IGCSE

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

🔑Concepts

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Equivalent fractions are different fractions that name the same amount or part of a whole.

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To find an equivalent fraction, multiply or divide both the numerator (top) and the denominator (bottom) by the same non-zero number.

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Simplifying (or reducing) a fraction means rewriting it so that the numerator and denominator are as small as possible.

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A fraction is in its simplest form when the only common factor of the numerator and the denominator is 1.

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The Highest Common Factor (HCF) is used to simplify a fraction to its lowest terms in a single step.

📐Formulae

ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n} (where n≠0n \neq 0)

ab=a÷nb÷n\frac{a}{b} = \frac{a \div n}{b \div n} (where nn is a common factor)

Simplest Form  ⟹  HCF(numerator, denominator)=1\text{Simplest Form} \implies \text{HCF}(\text{numerator, denominator}) = 1

💡Examples

Problem 1:

Find an equivalent fraction for 35\frac{3}{5} with a denominator of 20.

Solution:

1220\frac{12}{20}

Explanation:

To change the denominator from 5 to 20, we must multiply by 4 (5×4=205 \times 4 = 20). To keep the fraction equivalent, we must also multiply the numerator by 4 (3×4=123 \times 4 = 12).

Problem 2:

Simplify the fraction 1824\frac{18}{24} to its simplest form.

Solution:

34\frac{3}{4}

Explanation:

Find the Highest Common Factor (HCF) of 18 and 24, which is 6. Divide both the numerator and the denominator by 6: 18÷6=318 \div 6 = 3 and 24÷6=424 \div 6 = 4.

Problem 3:

Are 23\frac{2}{3} and 1015\frac{10}{15} equivalent fractions?

Solution:

Yes

Explanation:

If we multiply the numerator and denominator of 23\frac{2}{3} by 5, we get 2×5=102 \times 5 = 10 and 3×5=153 \times 5 = 15. Since both parts were multiplied by the same number, they are equivalent.