NCERT Class 4 Maths · Chapter 7
The Cleanest Village
Adding and subtracting 2- and 3-digit numbers with regrouping, money and change, estimation, and fun number puzzles.
📌 What you’ll learn in this chapter
- Adding with regrouping (10 ones = 1 ten, 10 tens = 1 hundred)
- Subtracting with regrouping (1 ten = 10 ones, 1 hundred = 10 tens)
- Money: finding the total cost and the change (balance)
- Estimating before calculating
- Quick mental tricks and missing-digit puzzles
🛍️ Let’s Begin: The Weekly Haat
Anu goes to the Sunday haat with Nani. Tomatoes cost ₹38, and onions cost ₹45. Nani gives the shopkeeper a ₹100 note.
“How much will we get back?” asks Anu. First, add: 38 + 45 = 83. Then subtract: 100 − 83 = ₹17 change.
➕ Part 1: Adding with Regrouping
Line up the Ones under Ones and Tens under Tens. Start from the Ones.
Example: 367 + 258
| H | T | O | |
|---|---|---|---|
| Regroup | 1 | 1 | |
| 3 | 6 | 7 | |
| + | 2 | 5 | 8 |
| = | 6 | 2 | 5 |
Ones: 7 + 8 = 15 → write 5, move 1 ten over. Tens: 6 + 5 + 1 = 12 → write 2, move 1 hundred over. Hundreds: 3 + 2 + 1 = 6. So 625.
➖ Part 2: Subtracting with Regrouping
If the top digit is too small, break 1 ten into 10 ones (or 1 hundred into 10 tens).
Example: 502 − 167
Ones: 2 − 7? Not possible. The tens place has 0, so break 1 hundred: 5 H → 4 H + 10 T. Then break 1 ten: 10 T → 9 T + 10 O. Now ones = 12.
12 − 7 = 5 · 9 − 6 = 3 · 4 − 1 = 3 → 335
Check: 335 + 167 = 502 ✅
⚠️ Common mistake
72 − 38: writing “8 − 2 = 6” in the ones place. ❌
✅ Always take the bottom from the top. 2 is smaller than 8, so regroup: 12 − 8 = 4, and 6 − 3 = 3 → 34.
✅ Always take the bottom from the top. 2 is smaller than 8, so regroup: 12 − 8 = 4, and 6 − 3 = 3 → 34.
💰 Part 3: Money and Change
| Cost | Paid | Change (Balance) |
|---|---|---|
| ₹64 | ₹100 | ₹36 |
| ₹278 | ₹500 | ₹222 |
| ₹395 | ₹400 | ₹5 |
💡 Shopkeeper’s trick: count up
Cost ₹278, paid ₹500: 278 → 280 (+2) → 300 (+20) → 500 (+200). Change = 2 + 20 + 200 = ₹222.
🎯 Part 4: Estimate First
Round the numbers to get a quick idea. 438 + 476 is about 400 + 500 = 900, so the answer should be near 900. (Exact: 914.) If you get 814 or 1,914, check again!
⚡ Part 5: Quick Mental Tricks
- +99: add 100, take away 1 → 245 + 99 = 344
- −19: take away 20, add 1 → 563 − 19 = 544
- Make a ten: 326 + 25 → 326 + 4 = 330, + 21 = 351
✏️ Practice Time
Try these on your own first, then check your answer below each question.
Q1. 456 + 378 = ?
✅ Answer834
Q2. 700 − 245 = ?
✅ Answer455
Q3. A school bag costs ₹365. You pay ₹500. What is the change?
✅ Answer₹135
Q4. A bus had 48 passengers. 19 got off and 27 got on. How many are on the bus now?
✅ Answer48 − 19 + 27 = 56
Q5. Estimate 612 − 289, then find the exact answer.
✅ AnswerAbout 600 − 300 = 300. Exact = 323
📘 NCERT Textbook Activity Help
Hints and answers for the activities in the textbook, page by page. Try each one yourself before looking at the answer!
Pages 96–97 · Sapan Dada’s cartCosts of fruits and vegetables
✅ Answer2 kg beans = ₹190 · custard apple + sapota = ₹115 · onion + potato = ₹69 · radish + yam = ₹68 · 2 kg radish + 2 kg papaya = ₹176 · 2 kg onion + 2 kg potato = ₹138
The last cost is double ₹69 (twice as much of each).
₹163 could be: beans + custard apple + radish (95 + 45 + 23). Try to find other combinations!
Page 98 · Balance tableThe last cost is double ₹69 (twice as much of each).
₹163 could be: beans + custard apple + radish (95 + 45 + 23). Try to find other combinations!
Cost, paid, and balance
✅ Answer₹113 / ₹150 / ₹37 (given) · ₹185 / ₹200 → ₹15 · cost ₹200 / ₹200 / 0 · ₹435 / ₹500 → ₹65 · ₹149 / ₹500 → ₹351 · ₹46 / e.g. ₹50 → ₹4 · cost ₹125 / ₹200 / ₹75 · ₹580 / ₹700 / ₹120 · The last row is your own example.
Bananas: 3 kg × ₹55 = ₹165. Choose any option that adds up to at least ₹165 (a ₹200 note works). Count each bundle in your book.
Page 99 · A Strange PuzzleBananas: 3 kg × ₹55 = ₹165. Choose any option that adds up to at least ₹165 (a ₹200 note works). Count each bundle in your book.
Oranges at ₹21 each
✅ AnswerEach child buys 2 oranges = ₹42. Krishna pays ₹50 → ₹8 · Sudama pays ₹100 → ₹58 · Mala pays ₹200 → ₹158 · Neela pays ₹500 → ₹458
Page 100 · Let Us PlayMagic triangle
✅ AnswerSum 9 (with 5 and 6 as given): top 3, left middle 4, bottom left 2, bottom right 1. Check: 3 + 4 + 2 = 9, 3 + 5 + 1 = 9, 2 + 6 + 1 = 9 ✅
Sum 10: top 1, left middle 6, bottom left 3, bottom middle 2, bottom right 5, right middle 4. Check: 1 + 6 + 3 = 10, 3 + 2 + 5 = 10, 5 + 4 + 1 = 10 ✅
Other sums: 9, 10, 11, and 12 are possible. 13 is not possible, because even with the biggest corners (4, 5, 6), the largest side sum is 12.
Strategy: put big numbers in the corners for a big sum (corners are counted twice).
Pages 101–105 · Add UpSum 10: top 1, left middle 6, bottom left 3, bottom middle 2, bottom right 5, right middle 4. Check: 1 + 6 + 3 = 10, 3 + 2 + 5 = 10, 5 + 4 + 1 = 10 ✅
Other sums: 9, 10, 11, and 12 are possible. 13 is not possible, because even with the biggest corners (4, 5, 6), the largest side sum is 12.
Strategy: put big numbers in the corners for a big sum (corners are counted twice).
Teachers, children, and pusaw
✅ Answer24 + 28 = 52 teachers · 438 + 476 = 914 children · Pusaw: 38 + 16 = ₹54 (4 T + 14 O = 5 T + 4 O) · Trip money: 185 + 125 = ₹310
Kalakshitij: boys 78 + 532 = 610 · girls 95 + 346 = 441 · tabla players 173 · singers 878 · Girls playing tabla after 15 join: 110
Q2: (a) 79 (b) 749 (c) 409 (d) 800 (e) 989 (f) 1,017
Q3: 423 + 178 = 601 children
Pages 106–109 · Subtract ItKalakshitij: boys 78 + 532 = 610 · girls 95 + 346 = 441 · tabla players 173 · singers 878 · Girls playing tabla after 15 join: 110
Q2: (a) 79 (b) 749 (c) 409 (d) 800 (e) 989 (f) 1,017
Q3: 423 + 178 = 601 children
Pusaw, bridge, and mangoes
✅ Answer83 − 46 = 37 · 438 − 215 = 223 waiting · 310 − 179 = ₹131 spent
Mangoes: 527 − 264 = 263 more · Dolls left: 639 − 531 = 108
Q5: (a) 54 (b) 222 (c) 326 (d) 453 (e) 572
Pages 109–110 · Library booksMangoes: 527 − 264 = 263 more · Dolls left: 639 − 531 = 108
Q5: (a) 54 (b) 222 (c) 326 (d) 453 (e) 572
Pages read
✅ Answer(a) Rami: 236 pages. Kesu: 96 + 30 + 90 = 216. Rami read 20 more pages.
(b) 128 − 23 = 105 pages
(c) All books = 759 pages. Read = 179 + 96 + 50 = 325. Left = 434 pages.
Pages 110–111 · Delhi–Aligarh train(b) 128 − 23 = 105 pages
(c) All books = 759 pages. Read = 179 + 96 + 50 = 325. Left = 434 pages.
Passengers
✅ AnswerNew Delhi: 894 → Ghaziabad: 894 + 158 − 23 = 1,029 → Dadri: 1,029 + 67 − 75 = 1,021
(a) 1,021 passengers leave Dadri (b) All 1,021 get off at Aligarh (the last stop) (c) 127 more at Aligarh than at New Delhi (d) Total who travelled = 894 + 158 + 67 = 1,119
Pages 111–112 · Let Us Solve(a) 1,021 passengers leave Dadri (b) All 1,021 get off at Aligarh (the last stop) (c) 127 more at Aligarh than at New Delhi (d) Total who travelled = 894 + 158 + 67 = 1,119
Columns and quick ways
✅ Answer(a) 452 + 89 = 541 (b) 641 − 273 = 368
(c) 326 + 25 = 351 · 675 + 5 = 680 · 410 − 12 = 398 · 204 − 10 = 194 · 811 + 99 = 910 · 945 − 19 = 926
(d) 1. 981 2. 770 3. 897 4. 107 5. 309 6. 826
(e) Examples: 856 = 500 + 356 · 563 = 900 − 337
Pages 112–113 · Number Pair Hunt(c) 326 + 25 = 351 · 675 + 5 = 680 · 410 − 12 = 398 · 204 − 10 = 194 · 811 + 99 = 910 · 945 − 19 = 926
(d) 1. 981 2. 770 3. 897 4. 107 5. 309 6. 826
(e) Examples: 856 = 500 + 356 · 563 = 900 − 337
Largest and smallest
✅ AnswerThere are 24 number pairs. 1. Greatest sum: 225 + 190 = 415 2. Smallest sum: 68 + 54 = 122 3. Greatest difference: 321 − 48 = 273 4. Smallest difference: 68 − 54 = 14 (look at the numbers that are close together; you don’t need to check every pair).
Page 113 · Missing digitsFill the boxes
✅ Answer36 + 14 = 50 · 1_ + 2_ = 38, e.g. 15 + 23 · 302 + 588 = 890 · 7_ − 4_ = 27, e.g. 70 − 43 · 65 − 40 = 25 · 47_ − 14_ = 327, e.g. 470 − 143 (the ones digit at the bottom is 3 more than the one at the top)
Page 114 · Let Us DoAdd and subtract
✅ AnswerAdd: (a) 512 (b) 400 (c) 686 (d) 134 (e) 796 (f) 143 (g) 787 (h) 999 (i) 1,094
Subtract: (a) 255 (b) 694 (c) 497 (d) 455 (e) 598 (f) 345 (g) 158 (h) 216 (i) 8
Subtract: (a) 255 (b) 694 (c) 497 (d) 455 (e) 598 (f) 345 (g) 158 (h) 216 (i) 8
👨👩👧 Tips for Parents
- Let your child calculate the bill total and the change when shopping.
- Ask them to estimate first, then check.
- Make up missing-digit puzzles for each other.