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Fractions, Decimals, and Percentages - Equivalent fractions and simplifying

Grade 4IGCSE

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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You can find an equivalent fraction by multiplying the numerator and the denominator by the same non-zero number.

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Simplifying a fraction means dividing both the numerator and the denominator by their highest common factor (HCF) until they cannot be divided further.

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A fraction is in its 'simplest form' when the only number that divides both the numerator and denominator exactly is 1.

📐Formulae

ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n} (To find equivalent fractions)

ab=a÷nb÷n\frac{a}{b} = \frac{a \div n}{b \div n} (To simplify fractions)

Simplest Form⇒HCF(numerator, denominator)=1\text{Simplest Form} \Rightarrow \text{HCF}(\text{numerator, denominator}) = 1

💡Examples

Problem 1:

Find an equivalent fraction for 34\frac{3}{4} with a denominator of 12.

Solution:

912\frac{9}{12}

Explanation:

To change the denominator from 4 to 12, we multiply by 3 (4×3=124 \times 3 = 12). We must do the same to the numerator: 3×3=93 \times 3 = 9. Therefore, 34=912\frac{3}{4} = \frac{9}{12}.

Problem 2:

Simplify the fraction 820\frac{8}{20} to its simplest form.

Solution:

25\frac{2}{5}

Explanation:

Find a common factor for 8 and 20. Both can be divided by 4. 8÷4=28 \div 4 = 2 and 20÷4=520 \div 4 = 5. Since 2 and 5 have no more common factors, the simplest form is 25\frac{2}{5}.

Problem 3:

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

Solution:

Yes

Explanation:

If we multiply both the numerator and denominator of 23\frac{2}{3} by 5, we get 2×53×5=1015\frac{2 \times 5}{3 \times 5} = \frac{10}{15}. Since they represent the same value, they are equivalent.