Fractions and Decimals: Multiplying and Dividing: Class 7 Study Guide
Fractions and decimals can be multiplied and divided using clear rules.
To multiply fractions, multiply the numerators and multiply the denominators: 2/3 × 3/4 = 6/12 = 1/2. To multiply a whole number by a fraction, write the whole number as a fraction: 4 × 2/5 = 8/5. 'Of' in a problem usually means multiply: 1/2 of 60 = 30.
To divide by a fraction, multiply by its reciprocal: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2.
Decimals
To multiply decimals, multiply as if they were whole numbers, then place the decimal point so that the answer has as many decimal places as both numbers together. 0.5 × 0.2 = 0.10 = 0.1. To divide by a decimal, make the divisor a whole number by multiplying both by 10, 100 and so on: 2.4 ÷ 0.6 = 24 ÷ 6 = 4. Multiplying by 10, 100 or 1000 shifts the decimal point right, and dividing shifts it left.
| Question | Answer |
|---|---|
| 2/5 × 5/6 | 1/3 |
| 7/8 ÷ 7/4 | 1/2 |
| 0.3 × 0.4 | 0.12 |
| 1.5 ÷ 0.3 | 5 |
| 4.56 × 100 | 456 |
Word problems
A packet holds 3/4 kg of rice. How much rice is in 6 packets? 6 × 3/4 = 18/4 = 4½ kg. A rope is 7.5 m long, and pieces of 1.5 m are cut. 7.5 ÷ 1.5 = 5 pieces.
What is asked?
'Of' means multiply.
Simplify at the end.
Does it make sense?
Simplify early
Cancel common factors before multiplying to keep numbers small: 4/9 × 3/8: cancel 4 with 8 and 3 with 9 to get 1/3 × 1/2 = 1/6.
Worked examples and common mistakes
Example: 2/3 of 15 = 10. Example: 0.2 × 0.3 = 0.06. Common mistakes: flipping the first fraction instead of the divisor, and putting the wrong number of decimal places. Remember: 0.2 × 0.3 has two decimal places, not one.
Check your understanding: model answers
1. 2/3. 2. 5. 3. 3 ÷ 1/4 = 12 bags.
✨ Key Takeaways
- Multiply tops and bottoms to multiply fractions.
- Divide by a fraction by multiplying by its reciprocal.
- Count decimal places when multiplying decimals.
- Simplify to lowest terms.
💬 Questions for Discussion & Reflection
- Find 3/5 × 10/9.
- Find 2.5 ÷ 0.5.
- How many 1/4 kg bags can be filled from 3 kg?
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