📚 Class 7 CBSE – Mathematics
Topic: Comparing Quantities
Why do we compare?
Just like we decide who has more candies, we compare numbers to see which one is bigger, smaller, or the same.
1. Basic Idea
| Symbol | Meaning | Everyday Analogy |
|---|---|---|
> |
Greater than | “More candies than Tom” → 5 > 3 |
< |
Less than | “Less money than Mary” → 2 < 4 |
= |
Equal to | “Same number of apples” → 4 = 4 |
Tip: Think of a balance scale. If one side goes down, that side is greater.
2. Comparing Whole Numbers
- Look at the first digit from the left.
If the digits differ, the larger digit wins. - If digits are the same, move to the next digit.
- Repeat until you find a difference.
Tiny Example
- Compare 378 and 275
3 > 2 → 378 is larger.
3. Comparing Fractions
Fractions are written as numerator / denominator (e.g., 3/4).
3.1 Same Denominator
- Compare numerators directly.
| Fraction | Numerator | Denominator |
|---|---|---|
| 2/5 | 2 | 5 |
| 4/5 | 4 | 5 |
- 4 > 2 → 4/5 is larger.
3.2 Different Denominators
- Find a common denominator (a number that both denominators can divide into).
- Convert each fraction to an equivalent fraction with that common denominator.
- Compare the numerators as in 3.1.
Tiny Example
Compare 2/3 and 3/4.
| Step | Calculation | Result |
|---|---|---|
| 1 | Common denominator = 12 | |
| 2 | 2/3 = 8/12 (×4) | |
| 3 | 3/4 = 9/12 (×3) | |
| 4 | Compare numerators: 9 > 8 | 3/4 is larger |
4. Comparing Decimals
Decimals are numbers with a decimal point (e.g., 0.75).
- Equalize the number of digits after the decimal by adding zeros if needed.
- Read left to right just like whole numbers.
Tiny Example
Compare 0.58 and 0.587
- Add a zero to the first: 0.580
- Compare: 580 > 587? No → 0.587 is larger.
5. Comparing Percentages
Percentages are “out of 100”.
- To compare, you can convert to decimals or keep as percentages.
Tiny Example
Compare 45 % and 3/7 %
- 45 % = 0.45
- 3/7 % = (3/7) % = 0.042857…
- 0.45 > 0.042857 → 45 % is larger.
6. Quick Checklist
| When to use | How to compare |
|---|---|
| Whole numbers | Look at left‑most digits |
| Fractions (same denominator) | Compare numerators |
| Fractions (different denominators) | Convert to common denominator, then compare numerators |
| Decimals | Equalize digits, compare like whole numbers |
| Percentages | Convert to decimals or compare directly |
7. Practice Problems
- Which is larger: 7/8 or 3/4?
- Compare 0.32 and 0.4.
- Is 5 % greater than 1/20 %?
- Which is smaller: 123 or 132?
- Compare 2/5 and 3/10.
(Try to solve them before checking the answers below.)
Answers
- 7/8 > 3/4
- 0.4 > 0.32
- 5 % > 1/20 %
- 123 < 132
- 3/10 > 2/5 (common denominator 10 → 4/10 vs 6/10)
8. Summary
- Comparing is all about seeing which quantity is bigger, smaller, or equal.
- Use the balance‑scale idea: the side that goes down is larger.
- For fractions, make the denominators the same first.
- For decimals, pad with zeros to match the number of places.
- For percentages, think of them as parts of 100.
Remember:
- Look at the first differing digit.
- Convert fractions if needed.
- Practice, practice, practice!
Happy comparing! 🚀