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Number - Equivalent fractions

Grade 3Cambridge (IGCSE)

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. For example, 12\frac{1}{2}, 24\frac{2}{4}, and 48\frac{4}{8} all represent the same value.

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

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To find an equivalent fraction with smaller numbers (simplifying), you can divide the numerator and the denominator by the same common factor.

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Visualizing equivalent fractions often involves looking at shapes. If you shade 13\frac{1}{3} of a circle and then divide every section into 22 equal parts, you will see that 26\frac{2}{6} of the circle is shaded, showing that 13=26\frac{1}{3} = \frac{2}{6}.

📐Formulae

ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n}

ab=a÷nb÷n\frac{a}{b} = \frac{a \div n}{b \div n}

💡Examples

Problem 1:

Find the missing number to make the fractions equivalent: 25=?15\frac{2}{5} = \frac{?}{15}

Solution:

2×35×3=615\frac{2 \times 3}{5 \times 3} = \frac{6}{15} The missing number is 66.

Explanation:

To get from the denominator 55 to 1515, we multiply by 33. To keep the fraction equivalent, we must also multiply the numerator 22 by 33. 2×3=62 \times 3 = 6.

Problem 2:

Write two equivalent fractions for 14\frac{1}{4}.

Solution:

1×24×2=28\frac{1 \times 2}{4 \times 2} = \frac{2}{8} 1×104×10=1040\frac{1 \times 10}{4 \times 10} = \frac{10}{40}

Explanation:

By multiplying both the top and bottom numbers by the same value (like 22 or 1010), we create new fractions that represent the same part of a whole.

Problem 3:

Is 39\frac{3}{9} equivalent to 13\frac{1}{3}?

Solution:

Yes, because 3÷39÷3=13\frac{3 \div 3}{9 \div 3} = \frac{1}{3}

Explanation:

If we divide both the numerator (33) and the denominator (99) by their common factor 33, we get 13\frac{1}{3}. Since they can be simplified to the same value, they are equivalent.

Equivalent fractions Grade 3 Notes & Examples