Number - Fractions, decimals and percentages

Grade 7IGCSE

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

🔑Concepts

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Equivalent Fractions: Fractions that represent the same value by multiplying or dividing the numerator and denominator by the same non-zero number.

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Mixed Numbers and Improper Fractions: Converting between numbers with a whole part (e.g., 1 1/2) and fractions where the numerator is larger than the denominator (e.g., 3/2).

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FDP Conversion: Understanding how to move between Fractions, Decimals, and Percentages (e.g., 1/2 = 0.5 = 50%).

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Decimal Place Value: Identifying tenths, hundredths, and thousandths to perform accurate addition and subtraction.

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Percentage of a Quantity: Calculating a specific portion of a total value using multiplication.

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Common Denominators: Finding a shared multiple to add or subtract fractions with different denominators.

📐Formulae

\text{Percentage to Fraction} = \frac{\text{Percentage Value}}{100}

\text{Fraction to Percentage} = \frac{\text{Numerator}}{\text{Denominator}} \times 100

\text{Percentage of Amount} = \frac{\text{Percentage}}{100} \times \text{Total Amount}

\text{Percentage Change} = \frac{\text{Change}}{\text{Original Value}} \times 100

💡Examples

Problem 1:

\frac{3}{4} + \frac{1}{6}

Solution:

11/12

Explanation:

Find the lowest common multiple (LCM) of 4 and 6, which is 12. Convert fractions: (3/4 = 9/12) and (1/6 = 2/12). Add the numerators: 9 + 2 = 11. The result is 11/12.

Problem 2:

Convert 0.85 into a fraction in its simplest form.

Solution:

17/20

Explanation:

0.85 is 85 hundredths, written as 85/100. Divide both the numerator and the denominator by their highest common factor, 5. 85 \div 5 = 17 and 100 \div 5 = 20.

Problem 3:

A coat usually costs $120. In a sale, it is reduced by 15%. Work out the sale price.

Solution:

$102

Explanation:

First find 15% of $120: (15/100) \times 120 = 18. Subtract the discount from the original price: 120 - 18 = 102.

Problem 4:

\frac{2}{3}

Solution:

5/6

Explanation:

Use the 'Keep-Change-Flip' rule. Keep 2/3, change division to multiplication, and flip 4/5 to 5/4. (2/3) \times (5/4) = 10/12. Simplify by dividing by 2 to get 5/6.