Fractions, Decimals, and Percentages - Multiplying fractions by whole numbers

Grade 5IGCSE

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

🔑Concepts

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Repeated Addition: Multiplying a fraction by a whole number is the same as adding the fraction to itself multiple times (e.g., 3 x 1/4 = 1/4 + 1/4 + 1/4).

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Numerator Multiplication: To multiply, you only multiply the whole number by the numerator; the denominator remains the same.

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Simplification: If the resulting fraction is improper (numerator is larger than the denominator), it should be converted into a mixed number.

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The 'Of' Rule: In word problems, the word 'of' usually indicates multiplication (e.g., '1/2 of 20' means 1/2 x 20).

📐Formulae

W \times \frac{a}{b} = \frac{W \times a}{b}

\frac{a}{b} \times W = \frac{a \times W}{b}

💡Examples

Problem 1:

4 \times \frac{2}{9}

Solution:

\frac{8}{9}

Explanation:

Multiply the whole number 4 by the numerator 2 to get 8. Keep the denominator 9 the same. The result is 8/9, which is a proper fraction and cannot be simplified further.

Problem 2:

5 \times \frac{3}{4}

Solution:

3 \frac{3}{4}

Explanation:

First, multiply 5 by 3 to get 15, keeping the denominator as 4, resulting in 15/4. To convert to a mixed number, divide 15 by 4. 4 goes into 15 three times (12) with a remainder of 3. So, the answer is 3 3/4.

Problem 3:

\frac{2}{3}

Solution:

4 cups

Explanation:

6 \times \frac{2}{3} = \frac{12}{3}