Fractions and Decimals: Operations and Word Problems: Class 6 Study Guide
Class 6 builds fluency with fractions and decimals and uses them in everyday contexts.
A fraction a/b shows a parts out of b equal parts. Like fractions have the same denominator; unlike fractions do not. To compare or add unlike fractions, convert them to equivalent fractions with a common denominator, usually the LCM of the denominators.
Decimals extend the place value system to tenths, hundredths and thousandths. Money (₹12.50) and measurements (3.45 m) use them every day. Fractions and decimals can be converted into each other: 3/4 = 0.75, and 0.6 = 6/10 = 3/5.
Operations on fractions
To add or subtract: use a common denominator. 2/3 + 3/4 = 8/12 + 9/12 = 17/12 = 1 5/12. To multiply: multiply numerators and denominators. 2/5 × 3/4 = 6/20 = 3/10. To divide: multiply by the reciprocal. 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8 = 1 7/8. The reciprocal of a/b is b/a.
| Operation | Rule | Example |
|---|---|---|
| Add | common denominator | 1/2 + 1/3 = 5/6 |
| Subtract | common denominator | 3/4 − 1/6 = 7/12 |
| Multiply | top × top, bottom × bottom | 2/3 × 3/5 = 2/5 |
| Divide | multiply by reciprocal | 1/2 ÷ 1/4 = 2 |
Operations on decimals
Add and subtract by lining up the decimal points. To multiply 2.5 × 0.4, multiply 25 × 4 = 100, then place the point so that there are as many decimal places as in both numbers together (two): 1.00 = 1. To divide a decimal by a decimal, multiply both numbers by a power of 10 until the divisor is whole: 4.5 ÷ 0.9 = 45 ÷ 9 = 5.
Make the divisor whole.
Ignore the points.
Count decimal places.
Does 2.5 × 0.4 ≈ 1 make sense?
Word problems
A recipe needs 3/4 cup of flour for 12 biscuits. For 18 biscuits you need 3/4 × 18/12 = 9/8 = 1 1/8 cups. Rohit bought 2.5 kg of rice at ₹48.50 per kg: 2.5 × 48.50 = ₹121.25. Draw a bar model or write the numbers in order to decide which operation to use.
Worked examples and common mistakes
Example: Which is greater, 5/6 or 7/9? The LCM of 6 and 9 is 18: 15/18 and 14/18, so 5/6 is greater. Common mistakes: adding denominators, forgetting to flip the second fraction when dividing, and losing the decimal point. Always simplify the answer.
Check your understanding: model answers
1. 12/20 + 5/20 = 17/20. 2. 3/8 × 2 = 3/4. 3. 48 ÷ 6 = 8.
✨ Key Takeaways
- Use a common denominator to add, subtract or compare.
- Divide by multiplying by the reciprocal.
- Line up decimal points to add or subtract.
- Estimate to check.
💬 Questions for Discussion & Reflection
- Find 3/5 + 1/4.
- Find 3/8 ÷ 1/2.
- Find 4.8 ÷ 0.6.
Print a fractions equivalence chart →