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CBSE · Class 5 · Math Mela

Chapter 4: We the Travellers — II (Addition and Subtraction)

5 concepts · 40 practice questions with answers · Free to read

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Adding with regrouping

From daily life

A tank has 36 litres of petrol and 58 litres more are poured in. How much is in the tank now? We add the ones, then the tens, and swap 10 ones for 1 ten when the ones add up to 10 or more.

Simple definition

Regrouping (carrying): when a column adds to 10 or more, write the ones part in that column and carry the tens part to the next column on the left. 10 ones = 1 ten, 10 tens = 1 hundred, 10 hundreds = 1 thousand.

Formula: Add ones → regroup → add tens (+ carry) → add hundreds (+ carry) → …

11148362975+78116+5=113+7+1=11carry 1

In the figure: Orange 1s are the carries. 6 + 5 = 11 gives a carry; 3 + 7 + 1 = 11 gives another; 8 + 9 + 1 = 18 gives another. Answer 7,811.

Rule 1: Align the digits and start from the ones — Write ones under ones, tens under tens, and so on. Add from the right, carrying when needed.

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Adding with regrouping

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  • Easy: 47 + 38: 7 + 8 = 15 (write 5, carry 1); 4 + 3 + 1 = 8 → 85.
  • Medium: 256 + 378 = 634 (6 + 8 = 14, 5 + 7 + 1 = 13, 2 + 3 + 1 = 6).
  • Exam-type: 3,764 + 2,859 = 6,623.

Rule 2: Use an easier way — Near 100? Add 100 and take away the little extra: + 99 means + 100 − 1.

  • Easy: 57 + 99 = 57 + 100 − 1 = 156.
  • Medium: 84 + 98 = 84 + 100 − 2 = 182.
  • Exam-type: 36 + 101 = 36 + 100 + 1 = 137.
Remember

Check your sum by adding in a different order or by subtracting one number from the answer.

Common mistake

Forgetting to add the carry: 47 + 38 written as 75 (4 + 3 = 7). The carry makes it 85.

Shortcut

Round-up trick: change one number to a round number, then fix the difference. Memory clue: "Ten or more? Write the one, carry the ten."

Spot the difference

PointWith carryWithout carry
Example47 + 3841 + 38
Ones7 + 8 = 15 → carry 11 + 8 = 9
Answer8579

Practice questions

Easy
  1. 1Find 68 + 59.
  2. 2Find 256 + 378.
  3. 3Find 125 + 99 in an easy way.
Medium
  1. 4A shop sold 318 bricks in the morning and 274 in the evening. How many in all?
  2. 5Find 3,764 + 2,859.
  3. 6Fill in the missing digit: 6_ + 27 = 95
Challenging
  1. 7Find 1,458 + 2,675 and check by subtraction.
  2. 8Find the easy way to add 268 + 199 and give the answer.
Show answers (try them yourself first)
  1. 1127
  2. 2634
  3. 3125 + 100 − 1 = 224
  4. 4592
  5. 56,623
  6. 68 (95 − 27 = 68)
  7. 74,133; check 4,133 − 2,675 = 1,458
  8. 8268 + 200 − 1 = 467

Subtracting with regrouping

From daily life

A store had 95 kg of rice and 68 kg were used. How much is left? When a ones digit is too small to subtract from, we break 1 ten into 10 ones.

Simple definition

Regrouping (borrowing): if the top digit is smaller than the bottom digit, borrow 1 from the next column on the left. 1 ten = 10 ones, 1 hundred = 10 tens, 1 thousand = 10 hundreds. The difference + the smaller number = the bigger number.

Formula: big − small = difference; difference + small = big (check).

41191452042867−2337borrowcheck:2,337 + 2,867

In the figure: Red numbers show the regrouping: the ones become 14, the tens 9 (after lending), the hundreds 11 and the thousands 4. Answer 2,337, and 2,337 + 2,867 = 5,204.

Rule 1: Borrow when the top digit is smaller — Take 1 from the next column; it is worth 10 in this column. If that column is 0, borrow from the one after it.

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Subtracting with regrouping

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  • Easy: 72 − 35: 2 < 5, so 12 − 5 = 7 and 6 − 3 = 3 → 37.
  • Medium: 504 − 267: the tens digit is 0, borrow from the hundreds → 237.
  • Exam-type: 6,000 − 2,475 = 3,525.

Rule 2: Check by adding back — Add the answer to the smaller number. You must get the bigger number.

  • Easy: 83 − 27 = 56; check 56 + 27 = 83 ✓.
  • Medium: 823 − 456 = 367; 367 + 456 = 823 ✓.
  • Exam-type: A wrong answer fails the check: 91 − 46 = 55 gives 55 + 46 = 101 ✗.
Remember

Always subtract the smaller number from the bigger number, and check your answer by adding.

Common mistake

Subtracting the smaller digit from the bigger digit in every column: 82 − 37 becomes 55 (8 − 3 = 5 and 7 − 2 = 5). The answer is 45.

Shortcut

To subtract from 100 or 1,000, use "take from the end": 1,000 − 346 = 654 (9 − 3, 9 − 4, 10 − 6). Memory clue: "Too small on top? Borrow a ten and make it 10 ones."

Spot the difference

PointCorrectCommon mistake
82 − 374555
Ones step12 − 7 = 5 (borrowed)7 − 2 = 5 (swapped)

Practice questions

Easy
  1. 1Find 72 − 35.
  2. 2Find 504 − 267.
  3. 3Check: is 91 − 46 = 45 correct?
Medium
  1. 4A store had 240 litres of fuel and used 175. How much is left?
  2. 5Find 700 − 284.
  3. 6Find 4,052 − 1,876.
Challenging
  1. 7The sum of two numbers is 150 and one number is 68. Find the other and check.
  2. 8Find 6,000 − 2,475 and check by adding.
Show answers (try them yourself first)
  1. 137
  2. 2237
  3. 3Yes: 45 + 46 = 91
  4. 465
  5. 5416
  6. 62,176
  7. 782; check 82 + 68 = 150
  8. 83,525; check 3,525 + 2,475 = 6,000

Addition and subtraction fact families

From daily life

A bag has 38 red and 27 blue marbles, 65 in all. If you take out the 27 blue ones, 38 red ones are left. Addition and subtraction tell the same story.

Simple definition

Three numbers a, b and a + b make a fact family of 4 sentences: a + b = s, b + a = s, s − a = b and s − b = a. The sum is the whole; the other two are parts.

Formula: part + part = whole; whole − part = other part.

65382738 + 27 = 65 27 + 38 = 6565 − 27 = 38 65 − 38 = 27

In the figure: The top number 65 is the whole; 38 and 27 are the parts. The four sentences are written below.

Rule 1: From addition to subtraction — If part + part = whole, then whole − one part = the other part.

  • Easy: 36 + 29 = 65, so 65 − 29 = 36 and 65 − 36 = 29.
  • Medium: 58 + 17 = 75, so 75 − 17 = 58.
  • Exam-type: 45 + 38 = 83, so 83 − 45 = 38.

Rule 2: From subtraction to addition — If big − small = difference, then difference + small = big.

  • Easy: 172 − 48 = 124, so 124 + 48 = 172.
  • Medium: 205 − 87 = 118, so 205 − 118 = 87.
  • Exam-type: 340 − 95 = 245, so 245 + 95 = 340.
Remember

The biggest number of the family is the whole (the sum). A subtraction always starts with it.

Common mistake

Writing 27 − 65 = 38. You cannot take a bigger number from a smaller one here; start with the whole: 65 − 27 = 38.

Shortcut

To find a missing part, subtract: part = whole − other part. Memory clue: Triangle of three: sum on top, two parts at the bottom.

Spot the difference

PointAdditionSubtraction
Sentence38 + 27 = 6565 − 27 = 38
Findsthe wholea part

Practice questions

Easy
  1. 1If 36 + 29 = 65, find 65 − 29.
  2. 2If 58 + 17 = 75, find 75 − 58.
  3. 3If 172 − 48 = 124, fill in: 124 + ___ = 172.
Medium
  1. 4Write all four sentences for the numbers 26, 19 and 45.
  2. 5If 205 − 87 = 118, fill in: 205 − ___ = 87.
  3. 6Which is NOT in the family of 54 + 28 = 82: 82 − 28 = 54, 82 + 54 = 28, 28 + 54 = 82?
Challenging
  1. 7Seema had some stickers. After getting 45 more she had 120. How many did she have first?
  2. 8Three numbers are 83, 45 and 38. Which one is the whole? Write one addition and two subtraction sentences.
Show answers (try them yourself first)
  1. 136
  2. 217
  3. 348
  4. 426 + 19 = 45; 19 + 26 = 45; 45 − 19 = 26; 45 − 26 = 19
  5. 5118
  6. 682 + 54 = 28
  7. 7120 − 45 = 75
  8. 883; 45 + 38 = 83; 83 − 45 = 38; 83 − 38 = 45

Sums of consecutive numbers

From daily life

Seats in a row are numbered 14, 15, 16: each number is 1 more than the one before. Such numbers are called consecutive. Their sums follow neat patterns.

Simple definition

Consecutive numbers follow one another without skipping any number (23, 24, 25). The sum of an odd count (3, 5, 7…) of consecutive numbers = count × middle number.

Formula: 3 consecutive: sum = 3 × middle. 5 consecutive: sum = 5 × middle. 2 consecutive: sum is odd.

4564 + 5 + 6 = 153 × 5 = 15middle × how manysum15

In the figure: 4 + 5 + 6 = 15 and 3 × 5 = 15: the sum of three consecutive numbers is 3 times the middle one.

Rule 1: Odd count: count × middle — For 3 or 5 consecutive numbers, find the middle number and multiply by 3 or 5.

  • Easy: 14 + 15 + 16 = 3 × 15 = 45.
  • Medium: 20 + 21 + 22 + 23 + 24 = 5 × 22 = 110.
  • Exam-type: Three consecutive numbers add to 87: middle = 87 ÷ 3 = 29, so they are 28, 29, 30.

Rule 2: Even count: pair them — For 4 or 6 consecutive numbers, pair first with last, second with second-last. Every pair has the same sum.

  • Easy: 24 + 25 + 26 + 27 = (24 + 27) + (25 + 26) = 51 + 51 = 102.
  • Medium: Sums of 4 consecutive numbers go up by 4 each time (1+2+3+4 = 10, 2+3+4+5 = 14).
  • Exam-type: For k consecutive numbers, successive sums differ by k.
Remember

Two consecutive numbers always have one even and one odd number, so their sum is odd.

Common mistake

Using the first number instead of the middle: 14 + 15 + 16 is not 3 × 14. Use the middle number 15.

Shortcut

Odd count → the middle number is the average, so sum = count × middle. Memory clue: "Middle man multiplied by how many men."

Spot the difference

Point3 consecutive4 consecutive
Example14 + 15 + 1624 + 25 + 26 + 27
Method3 × 15pairs of 51
Sum45102

Practice questions

Easy
  1. 1Find 38 + 39 + 40.
  2. 2Is the sum of 2 consecutive numbers odd or even?
  3. 3Find 45 + 46 + 47 + 48 + 49.
Medium
  1. 4Find 52 + 53 + 54 + 55.
  2. 5Three consecutive numbers add to 51. Find them.
  3. 6By how much does the sum increase when 5 consecutive numbers start one number later?
Challenging
  1. 7Find 63 + 64 + 65 + 66 + 67 + 68.
  2. 8The sum of five consecutive numbers is 135. Find the smallest and the largest.
Show answers (try them yourself first)
  1. 1117 (3 × 39)
  2. 2Odd
  3. 3235 (5 × 47)
  4. 4214 (107 + 107)
  5. 516, 17, 18
  6. 65
  7. 7393 (3 pairs of 131)
  8. 8Middle 27: smallest 25 and largest 29

Large numbers: adding, subtracting and estimating

From daily life

A truck covers 48,365 km in one year and 27,689 km in the next. To get a quick idea of the total, round to the nearest thousand: about 48,000 + 28,000 = 76,000 km.

Simple definition

Big numbers are added and subtracted exactly like small ones — align the places and start from the ones. Estimating means rounding the numbers first to get an answer that is close and easy to check.

Formula: Estimate = round each number, then add or subtract.

48,365 + 27,689 ≈ ?48,365 → 48,00027,689 → 28,00048,000 + 28,000 = 76,000exact: 76,054

In the figure: Rounding both numbers to the nearest thousand gives 48,000 + 28,000 = 76,000, very close to the exact 76,054.

Rule 1: Add and subtract large numbers — Line up ones under ones, tens under tens, and so on. Work from the right and regroup when needed.

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Large numbers: adding, subtracting and estimating

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  • Easy: 36,450 + 14,780 = 51,230.
  • Medium: 83,406 − 27,158 = 56,248; check 56,248 + 27,158 = 83,406.
  • Exam-type: 50,000 − 23,764 = 26,236 (borrow across the zeros).

Rule 2: Estimate by rounding — Round each number to the nearest thousand (or hundred), then add or subtract the rounded numbers.

  • Easy: 63,120 + 39,870 ≈ 63,000 + 40,000 = 103,000.
  • Medium: 74,215 − 48,630 ≈ 74,000 − 49,000 = 25,000.
  • Exam-type: For the closest sum, try pairs and compare how far each total is from the target.
Remember

An estimate tells you roughly how big the answer should be. If your exact answer is far from it, check again.

Common mistake

Misaligning digits: writing 4,578 + 345 with the 345 under thousands. Keep ones under ones.

Shortcut

To subtract from a number with many zeros, think: 50,000 − 1 = 49,999, then adjust. Memory clue: "Round first, guess the size, then work it out and compare."

Spot the difference

PointEstimateExact
48,365 + 27,68976,00076,054
Used forquick checkfinal answer

Practice questions

Easy
  1. 1Find 36,450 + 14,780.
  2. 2Find 83,406 − 27,158.
  3. 3Estimate 48,365 + 27,689 by rounding to the nearest thousand.
Medium
  1. 4A museum has 31,275 visitors in one month and 28,940 in the next. How many in all?
  2. 5Find 50,000 − 23,764.
  3. 6A school collected ₹58,400 and spent ₹36,750. How much is left?
Challenging
  1. 7Estimate 74,215 − 48,630, then find the exact difference.
  2. 8Among 3,410, 6,250, 7,980, 4,730 and 8,120, which two numbers have a sum closest to 11,000?
Show answers (try them yourself first)
  1. 151,230
  2. 256,248
  3. 376,000
  4. 460,215
  5. 526,236
  6. 6₹21,650
  7. 7Estimate 25,000; exact 25,585
  8. 84,730 + 6,250 = 10,980