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Fractions, Decimals, and Percentages - Simplifying and comparing fractions

Grade 6IGCSE

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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Simplest Form: A fraction is in its lowest terms when the only common factor between the numerator and the denominator is 1.

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Highest Common Factor (HCF): Used to simplify fractions by dividing both the top and bottom numbers by the largest number that goes into both.

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Common Denominators: To compare or order fractions, they must be converted to have the same denominator using the Least Common Multiple (LCM).

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Cross-Multiplication: A technique used to quickly compare two fractions to see which is larger.

📐Formulae

Simplifying: a÷HCF(a,b)b÷HCF(a,b)\text{Simplifying: } \frac{a \div HCF(a,b)}{b \div HCF(a,b)}

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

Comparing: ab vs cd⇒compare (a×d) and (b×c)\text{Comparing: } \frac{a}{b} \text{ vs } \frac{c}{d} \Rightarrow \text{compare } (a \times d) \text{ and } (b \times c)

💡Examples

Problem 1:

Simplify the fraction 2436\frac{24}{36} to its simplest form.

Solution:

23\frac{2}{3}

Explanation:

Find the HCF of 24 and 36. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The HCF is 12. Divide both the numerator and denominator by 12: 24÷12=224 \div 12 = 2 and 36÷12=336 \div 12 = 3. Therefore, the simplest form is 23\frac{2}{3}.

Problem 2:

Which fraction is larger: 35\frac{3}{5} or 58\frac{5}{8}?

Solution:

58\frac{5}{8} is larger.

Explanation:

To compare, find a common denominator. The LCM of 5 and 8 is 40. Convert both fractions: 3×85×8=2440\frac{3 \times 8}{5 \times 8} = \frac{24}{40} and 5×58×5=2540\frac{5 \times 5}{8 \times 5} = \frac{25}{40}. Since 25>2425 > 24, then 58>35\frac{5}{8} > \frac{3}{5}. Alternatively, use cross-multiplication: 3×8=243 \times 8 = 24 and 5×5=255 \times 5 = 25. Since 2525 is greater, the second fraction is larger.

Problem 3:

Arrange the following fractions in ascending order: 12,34,25\frac{1}{2}, \frac{3}{4}, \frac{2}{5}.

Solution:

25,12,34\frac{2}{5}, \frac{1}{2}, \frac{3}{4}

Explanation:

Find the LCM of the denominators (2, 4, and 5), which is 20. Convert each fraction: 12=1020\frac{1}{2} = \frac{10}{20}, 34=1520\frac{3}{4} = \frac{15}{20}, and 25=820\frac{2}{5} = \frac{8}{20}. Comparing the numerators (8, 10, 15), the order is 820<1020<1520\frac{8}{20} < \frac{10}{20} < \frac{15}{20}, which corresponds to 25,12,34\frac{2}{5}, \frac{1}{2}, \frac{3}{4}.