Add Subtract Decimals
Align decimal points; add/subtract in word problems.
Add Subtract Decimals
Add and Subtract Decimals
What you'll learn
- To align decimal points before adding or subtracting — the non-negotiable rule from NCERT Math-Magic 5, Chapter 10.
- To add and subtract decimals in money problems (₹ bills, change, total cost).
- To handle regrouping (carrying/borrowing) across the decimal point correctly.
- To check answers using estimation before final calculation.
Key concepts
Level 1 — Alignment rule
Verbal: Line up decimal points vertically so ones stay with ones, tenths with tenths, and so on.
Symbolic: 12.6 + 3.45 → write as 12.60 + 3.45 (pad with zero if needed).
| Step | Add 12.6 + 3.45 | Subtract 8.0 − 2.75 |
|---|---|---|
| Align | 12.60 + 3.45 | 8.00 − 2.75 |
| Compute | 16.05 | 5.25 |
| Check | ≈ 13 + 3 = 16 ✓ | ≈ 8 − 3 = 5 ✓ |
NCERT link: Math-Magic 5, Ch 10 — shop bills combining rupees and paise.
Level 2 — Word problems with ₹ and measurement
Verbal: When buying multiple items, add prices; when finding change, subtract from amount paid.
Symbolic: Total = ₹a + ₹b + ₹c; Change = Amount paid − Bill total.
Real-life: Riya buys a pencil ₹8.50, eraser ₹5.25, ruler ₹12.00. She pays ₹30. Change = 30 − (8.50 + 5.25 + 12.00) = 30 − 25.75 = ₹4.25.
| Operation | When to use | Example |
|---|---|---|
| Add | Total cost, combined length | 2.3 m + 1.45 m = 3.75 m |
| Subtract | Change, difference, remaining | 5.0 L − 1.25 L = 3.75 L |
Worked example
Arjun buys a book for ₹245.75 and a bag for ₹189.50. He pays ₹500. How much change does he get?
Step 1 — Total cost: 245.75 + 189.50 = 435.25
Step 2 — Change: 500.00 − 435.25 = 64.75
Step 3 — Estimate check: ≈ 250 + 190 = 440; 500 − 440 = 60 ✓ close
Answer: ₹64.75
Find 6.4 − 2.875
Step 1 — Pad: 6.400 − 2.875
Step 2 — Subtract column by column (borrow as needed): 3.525
Answer: 3.525
Common mistakes
| Mistake | Why it happens | Fix |
|---|---|---|
| Adding 12.6 + 3.45 as 15.105 | Aligning right digits, not decimal points | Decimal points in one column |
| Forgetting to pad with zeros | 8 − 2.75 written as 8 − 2.75 without padding | Write 8.00 − 2.75 |
| Dropping the decimal in the answer | Treating like whole-number addition | Decimal point goes directly below others |
| Wrong change when paise > rupees paid | Not regrouping from rupees column | Borrow 1 rupee = 100 paise when needed |
Quick check
- Evaluate: 15.6 + 8.34 and 20.0 − 7.85.
- Three items cost ₹12.50, ₹8.75, and ₹5.00. Total?
- A rope is 4.2 m long. 1.35 m is cut off. Length left?
- Stretch: ₹1000 − (₹456.80 + ₹312.45) = ? (₹230.75)
Revision tip: Rule on your notebook margin: "Decimal points line up — always." Do three shop-bill problems using real prices from your kitchen or stationery shop.
Open the Practice tab for graded questions on Add and Subtract Decimals.
Key Takeaways (TL;DR)
- What you'll learn
- Key concepts
- Worked example
- Common mistakes
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