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Fractions, Decimals, and Percentages - Comparing and ordering fractions

Grade 5IGCSE

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

🔑Concepts

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Equivalent Fractions: Fractions that represent the same value even though they have different numerators and denominators.

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Common Denominator: A shared multiple of the denominators of two or more fractions, used to make comparison possible.

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Same Denominator Comparison: If two fractions have the same denominator, the one with the larger numerator is greater.

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Same Numerator Comparison: If two fractions have the same numerator, the one with the smaller denominator is greater because the 'parts' are larger.

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Ordering: Arranging fractions in Ascending order (smallest to largest) or Descending order (largest to smallest).

📐Formulae

Equivalent Fraction Rule: ab=a×nb×n\frac{a}{b} = \frac{a \times n}{b \times n}

Comparison (Same Denominator): If a>ca > c, then ab>cb\frac{a}{b} > \frac{c}{b}

Comparison (Same Numerator): If b<db < d, then ab>ad\frac{a}{b} > \frac{a}{d}

💡Examples

Problem 1:

Which is greater: 35\frac{3}{5} or 710\frac{7}{10}?

Solution:

710\frac{7}{10} is greater.

Explanation:

To compare, find a common denominator. The Least Common Multiple of 5 and 10 is 10. Convert 35\frac{3}{5} to tenths: 3×25×2=610\frac{3 \times 2}{5 \times 2} = \frac{6}{10}. Now compare 610\frac{6}{10} and 710\frac{7}{10}. Since 7>67 > 6, 710\frac{7}{10} is larger.

Problem 2:

Order the following fractions from smallest to largest: 12,14,38\frac{1}{2}, \frac{1}{4}, \frac{3}{8}.

Solution:

14,38,12\frac{1}{4}, \frac{3}{8}, \frac{1}{2}

Explanation:

Find a common denominator for 2, 4, and 8, which is 8. Convert all fractions: 12=48\frac{1}{2} = \frac{4}{8}, 14=28\frac{1}{4} = \frac{2}{8}, and 38\frac{3}{8} stays the same. Comparing the numerators (2, 3, and 4), the order is 28<38<48\frac{2}{8} < \frac{3}{8} < \frac{4}{8}.

Problem 3:

Compare 23\frac{2}{3} and 25\frac{2}{5} using the same numerator rule.

Solution:

23>25\frac{2}{3} > \frac{2}{5}

Explanation:

Since both fractions have the same numerator (2), we look at the denominators. A denominator of 3 means the whole is divided into 3 large pieces, while a denominator of 5 means it is divided into 5 smaller pieces. Therefore, 2 large pieces (23\frac{2}{3}) are greater than 2 small pieces (25\frac{2}{5}).