Fractions and Decimals: Class 5 Study Guide
Parts of a whole can be shown as fractions or as decimals. Both appear in everyday life, from recipes to rupees.
A fraction names equal parts of a whole. In 3/4, the numerator 3 is the number of parts taken and the denominator 4 is the number of equal parts in the whole. A proper fraction is less than one (3/4), an improper fraction is one or more (7/4) and a mixed number combines a whole and a fraction (1 3/4).
A decimal writes a fraction with a denominator of 10, 100 or 1000 using a decimal point. 0.5 is five tenths (5/10 or 1/2). 0.25 is twenty-five hundredths (25/100 or 1/4). Money in rupees and paise is a useful model: ₹2.50 is two rupees and fifty paise.
Equivalent fractions and comparing
Multiply or divide the numerator and denominator by the same number to get an equivalent fraction: 2/3 = 4/6 = 6/9. To compare fractions with unlike denominators, make the denominators the same. 3/4 and 5/6: the common denominator is 12, giving 9/12 and 10/12. So 5/6 > 3/4.
| Fraction | Decimal | Percent idea |
|---|---|---|
| 1/2 | 0.5 | 50 out of 100 |
| 1/4 | 0.25 | 25 out of 100 |
| 3/4 | 0.75 | 75 out of 100 |
| 1/10 | 0.1 | 10 out of 100 |
Adding and subtracting fractions
With the same denominator, add or subtract the numerators: 3/8 + 2/8 = 5/8. With different denominators, rewrite them first: 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Always simplify the answer, for example 4/8 = 1/2.
For 1/2 and 1/3, use 6.
3/6 and 2/6.
5/6.
5/6 is already simplest.
Decimals in everyday use
Line up the decimal points when adding or subtracting decimals. 12.50 + 3.75 = 16.25. A ₹5.75 pen and a ₹12.50 notebook cost ₹18.25 together. If you pay with ₹20, the change is ₹1.75. Compare decimals by place: 0.6 is greater than 0.45 because 0.60 > 0.45.
Worked examples and common mistakes
Example: Convert 7/4 to a mixed number: 7 ÷ 4 = 1 remainder 3, so 1 3/4. Common mistakes: adding denominators (1/4 + 1/4 is not 2/8), lining up decimals by the last digit instead of the point, and thinking 0.45 > 0.6 because 45 > 6. Always rewrite with the same number of decimal places.
Check your understanding: model answers
1. 4/10 + 1/10 = 5/10 = 1/2. 2. 0.75. 3. 7.75.
✨ Key Takeaways
- Equivalent fractions have the same value.
- Use a common denominator to add or compare.
- Decimals are fractions with denominators 10, 100, 1000.
- Line up the decimal points.
💬 Questions for Discussion & Reflection
- Add 2/5 + 1/10.
- Write 3/4 as a decimal.
- Find 15.60 − 7.85.
Print a fractions equivalence chart →