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Multiplying whole number by a fraction
Lesson: Multiplying Whole Numbers by Fractions
Year 7 —how to multiply whole numbers by fractions with examples and practice.
1. Understanding the idea
Multiplying a whole number by a fraction means taking that fraction of the whole number.
Example: 1/3 of 12 means finding one third of 12 → 12 ÷ 3 = 4.
2. Rule for multiplying whole numbers by fractions
To multiply a whole number by a fraction:
- Write the whole number as a fraction (put it over 1).
- Multiply the numerators.
- Multiply the denominators.
- Simplify the answer if possible.
Example: 5 × 1/4
Write 5 as 5/1
Multiply: 5/1 × 1/4 = 5/4
Convert to mixed number: 5/4 = 1 1/4
3. Visual meaning
If you divide a whole number into equal parts, a fraction picks out some of those parts.
Example: 3 × 1/2 means “three halves”.
3 × 1/2 = 3/2 = 1 1/2
4. More worked examples
a) 7 × 2/3
Write as a fraction: 7/1 × 2/3 = 14/3 = 4 2/3
b) 9 × 3/5
9/1 × 3/5 = 27/5 = 5 2/5
c) 4 × 3/4
4/1 × 3/4 = 12/4 = 3
5. Common mistakes to avoid
- Multiplying whole number by denominator instead of numerator.
- Forgetting to simplify the final answer.
- Not converting improper fractions back to mixed numbers.
6. Practice
6 × 1/310 × 2/58 × 3/412 × 5/615 × 4/9
Answers (teacher)
6 × 1/3 = 6/3 = 210 × 2/5 = 20/5 = 48 × 3/4 = 24/4 = 612 × 5/6 = 60/6 = 1015 × 4/9 = 60/9 = 6 6/9 = 6 2/3