We the Travellers – II
Adding and subtracting big numbers, quick mental tricks, consecutive numbers, palindromes, and even and odd numbers.
- Adding and subtracting with regrouping (carrying and borrowing), up to 5-digit numbers
- How addition and subtraction are connected (fact families)
- Patterns in sums of consecutive numbers
- Quick tricks: making 100 or 1,000, and subtracting 9 or 99
- Palindrome numbers, and even and odd numbers
🚗 Let’s Begin: A Family Road Trip
Ishaan’s family drove from Jaipur to Udaipur (395 km) and then to Ahmedabad (260 km). “How far have we come, Papa?” asked Ishaan.
Papa said, “Add them and tell me!” Ishaan wrote 395 + 260 = 655 km.
Then Papa said, “The whole trip to Mumbai is 1,180 km. How much is left?” Ishaan needed subtraction: 1,180 − 655 = 525 km.
In this chapter we practise adding and subtracting numbers like these, plus some clever shortcuts.
➕ Part 1: Adding with Regrouping
Write the numbers one below the other so that Ones are under Ones, Tens under Tens, and so on. Start adding from the right (Ones).
Example: A petrol pump sold 23,675 litres on Monday and 18,549 litres on Tuesday. Total?
| TTh | Th | H | T | O | |
|---|---|---|---|---|---|
| Carry | 1 | 1 | 1 | 1 | |
| 2 | 3 | 6 | 7 | 5 | |
| + | 1 | 8 | 5 | 4 | 9 |
| = | 4 | 2 | 2 | 2 | 4 |
Ones: 5 + 9 = 14 → write 4, carry 1. Tens: 7 + 4 + 1 = 12 → write 2, carry 1. Hundreds: 6 + 5 + 1 = 12 → write 2, carry 1. Thousands: 3 + 8 + 1 = 12 → write 2, carry 1. Ten thousands: 2 + 1 + 1 = 4.
Total: 42,224 litres
- Adding 99? Add 100 and take away 1: 57 + 99 = 157 − 1 = 156
- Make a ten: 48 + 27 → 50 + 25 = 75 (give 2 from 27 to 48)
- Adding 20 or 30? Only the tens change: 64 + 30 = 94
➖ Part 2: Subtracting with Regrouping
When the top digit is smaller, borrow 1 from the next place on the left. 1 ten = 10 ones, 1 hundred = 10 tens, and so on.
Example: A train route is 3,400 km. The train has covered 1,768 km. How much is left?
3,400 − 1,768: Ones: 0 − 8, can’t do, and tens is also 0. So borrow from hundreds: 4 hundreds → 3 hundreds, 10 tens. Then 10 tens → 9 tens, 10 ones.
Ones: 10 − 8 = 2 · Tens: 9 − 6 = 3 · Hundreds: 3 − 7, can’t do, so borrow: 13 − 7 = 6 · Thousands: 2 − 1 = 1
Answer: 1,632 km. Check: 1,632 + 1,768 = 3,400 ✅
✅ Always do top − bottom. If the top is smaller, borrow first. 52 − 27 = 25.
Addition and subtraction are a family
One fact gives us three more:
35 + 48 = 83 → 83 − 48 = 35 → 83 − 35 = 48 → 48 + 35 = 83
Use this to check every subtraction: add the answer to the number you subtracted. You should get the first number back.
🔢 Part 3: Sums of Consecutive Numbers
Consecutive numbers come one after another without skipping, like 14, 15, 16 or 99, 100, 101.
- 3 consecutive numbers: sum = 3 × middle. 31 + 32 + 33 = 3 × 32 = 96
- 5 consecutive numbers: sum = 5 × middle. 18 + 19 + 20 + 21 + 22 = 5 × 20 = 100
- Even count (4, 6 numbers)? Add the first and last, then multiply by half the count. 10 + 11 + 12 + 13 = (10 + 13) × 2 = 46
Another pattern: The sum of 2 consecutive numbers is always odd (one even + one odd). And when you move to the next group, the sum of 3 consecutive numbers goes up by 3, of 4 numbers by 4, and so on.
⚡ Part 4: Quick Sums and Differences
Making 100, 1,000, or 10,000
What goes with 46 to make 100? Think: make every digit add to 9, and the last digit add to 10.
46 → 4 + 5 = 9, 6 + 4 = 10. So 46 + 54 = 100 ✅
For 1,000: 283 → 2 + 7 = 9, 8 + 1 = 9, 3 + 7 = 10 → 717.
Subtracting 9 or 99 quickly
To subtract 9, take away 10 and add 1: 75 − 9 = 65 + 1 = 66.
To subtract 99, take away 100 and add 1: 325 − 99 = 225 + 1 = 226.
🪞 Part 5: Palindromes, and Even and Odd
A palindrome reads the same forwards and backwards, like the word “NAYAN” or the numbers 44, 525, 7,117, and 34,543.
Even numbers end in 0, 2, 4, 6, or 8. They can be put into pairs with nothing left over. Odd numbers end in 1, 3, 5, 7, or 9. There is always one left without a partner.
| Add | Answer is | Example |
|---|---|---|
| Even + Even | Even | 14 + 8 = 22 |
| Odd + Odd | Even (the two leftover ones make a pair!) | 7 + 9 = 16 |
| Odd + Even | Odd | 7 + 10 = 17 |
❌ Common Mistakes to Avoid
✅ Line up the Ones digits on the right.
✅ Write the small carry digit on top of the next column.
✅ Cross it out and write one less.
✅ Answer + smaller number = bigger number.
✏️ Practice Time
Try these on your own first, then check your answer below each question.
📘 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!
Page 42 · Making Sums EqualSwap numbers to make sums equal
Hint: Find the difference between the two sums. A swap changes the difference by twice the gap between the two numbers you swap.
- (a) 19 and 21 (difference 2): swap 2 and 3 → 20 and 20 (1 move)
- (b) 39 and 47 (difference 8): swap 5 and 9 (or 7 and 11) → 43 and 43 (1 move)
- (c) 68 and 76 (difference 8): no single swap works. Swap 11 ↔ 13 and 15 ↔ 17 → 72 and 72 (2 moves)
- (d) 314 and 330 (difference 16): swap 77 ↔ 81 and 78 ↔ 82 → 322 and 322 (2 moves)
Adding 2-digit numbers
Let Us Solve: (a) 15 + 79 = 94 (b) 46 + 99 = 145 (think 46 + 100 − 1) (c) 38 + 35 = 73 (d) 5 + 89 = 94 (e) 76 + 28 = 104 (f) 69 + 20 = 89
Fact families
Q2: (a) 242 − 164 = 78, 242 − 78 = 164 (b) 1,301 − 839 = 462, 1,301 − 462 = 839 (c) 784 + 137 = 921, 921 − 784 = 137 (d) 590 + 234 = 824, 824 − 590 = 234
Minibus: 65 − 18 = 47 litres filled
Subtraction
Sums and patterns
Q2: The difference is 2 in the first box, 3 in the second, and 4 in the third. It stays the same, because each number in the group goes up by 1.
Q3: (a) 5 (b) 6
Page 46: (a) 67 + 68 + 69 = 3 × 68 = 204 (b) 24 + 25 + 26 + 27 = 2 × 51 = 102 (c) 48 + … + 52 = 5 × 50 = 250 (d) 237 + … + 242 = 3 × 479 = 1,437
Longest routes and Let Us Solve
Q1: (a) 605 (b) 13,579 (c) 135 (d) 59,010 (e) 9,667 (f) 19,239
Q2: 1,600 + 590 + 670 + 1,055 = 3,915 km
Q3: (a) 5,205 + 4,840 = 10,045 (b) 6,220 + 8,455 = 14,675 (c) 8,455 + 4,840 = 13,295 (d) 7,095 + 8,455 = 15,550
Ships, roads, and Let Us Solve
Q2 Mary: 12,540 − 3,275 + 4,900 − 2,645 − 1,275 = ₹10,245
Q3 (a) Estimate: about ₹40,000 + ₹10,000 + ₹20,000 = ₹70,000, so it’s very close. (b) Exact: 39,785 + 9,545 + 19,548 = ₹68,878. Yes, it’s enough, with ₹1,622 left.
Q4 (a) 3,675 + 2,850 = 6,525 kg (b) 8,250 − 6,525 = 1,725 kg more
Sukanta’s and Namita’s tricks
Ending in 0: the “+1” trick needs care. (a) 180 + 820 (b) 760 + 240 (c) 400 + 600
Namita: (a) 58 (b) 74 (c) 135 (d) 88 (e) 148 (f) 664
Getting 9 or 99: (a) 32 − 23 = 9 (b) 56 − 47 = 9 (c) 877 − 778 = 99 (d) 666 − 567 = 99
Palindromes and grids
900–1,200: 909, 919, 929, 939, 949, 959, 969, 979, 989, 999, 1,001, 1,111
25,000–27,000: 25,052, 25,152, 25,252 … 25,952 (10 numbers) and 26,062, 26,162 … 26,962 (10 numbers)
Q2 (reading rows left to right and columns top to bottom; other answers are possible):
| All inc | All dec | Rows dec, cols inc | Rows dec, dec, inc; cols dec, dec, inc | Rows inc, inc, dec; cols inc, dec, dec |
|---|---|---|---|---|
| 1 2 3 4 5 6 7 8 9 | 9 8 7 6 5 4 3 2 1 | 3 2 1 6 5 4 9 8 7 | 8 6 1 7 5 2 3 4 9 | 1 6 8 2 5 7 9 4 3 |
Even numbers and paired arrangements
Q2: Adding 2 to 18 adds one more pair, and there is still no leftover (20 is even). Adding 2 to 23 adds one more pair, but the leftover one stays (25 is odd).
Q3: (a) even + even is always even (b) odd + odd is always even (the two leftovers join into a pair) (c) odd + even is always odd
Coins, torch, and mountains
Q2: ON. The torch is ON after every odd press (1, 3, 5 …) and OFF after every even press (2, 4, 6 …). 23 is odd.
Q3: (a) Mount Everest, 8,848 m (b) 8,848 − 5,642 = 3,206 m (c) 8,586 − 5,642 = 2,944 m (d) 2013 − 20 = 1993
Certificates and practice sums
Q1: (a) 9,397 (b) 97,555 (c) 1,665 (d) 2,468 (e) 56,845 (f) 78,554 (f) 15,143 (g) 13,086 (h) 1,05,050
Q2: (a) 232 (b) 3,328 (c) 18,148 (d) 1,111 (e) 11,111 (f) 56,733 (f) 76,215 (g) 826 (h) 527
Q3: Needed 26,000 + 17,000 + 19,873 = ₹62,873. Yes, he has enough, with ₹29,502 more than he needs.
Q4: 85,300 − 54,000 = 31,300
Q5: 27,599 + 6,758 = 34,357 runs
👨👩👧 Tips for Parents
- Use shopping bills: add the items, then subtract the total from the note you paid with.
- On trips, add the distances on milestones together.
- Ask quick questions at dinner: “What goes with 73 to make 100?”