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CBSE · Class 5 · Math Mela

Chapter 9: Coconut Farm (Division)

6 concepts · 48 practice questions with answers · Free to read

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Division facts: N = D × Q

From daily life

A farmer plants 24 coconut saplings in 4 equal rows. How many in each row? Sharing equally is division, and it is the opposite of multiplication.

Simple definition

Division is equal sharing or equal grouping. In N ÷ D = Q, N is the dividend, D the divisor and Q the quotient. Every multiplication fact gives two division facts.

Formula: N = D × Q. N ÷ 1 = N, N ÷ N = 1, 0 ÷ N = 0. Never divide by 0.

4 × 6 = 2424 ÷ 4 = 624 ÷ 6 = 44 rows of 6

In the figure: An array of 4 rows with 6 in each row shows 4 × 6 = 24, and also 24 ÷ 4 = 6 and 24 ÷ 6 = 4.

Rule 1: Multiplication gives division — If D × Q = N, then N ÷ D = Q and N ÷ Q = D. Use the tables you know to find division answers.

  • Easy: 7 × 8 = 56, so 56 ÷ 7 = 8 and 56 ÷ 8 = 7.
  • Medium: 9 × 12 = 108, so 108 ÷ 9 = 12.
  • Exam-type: 15 × 6 = 90, so 90 ÷ 15 = 6.

Rule 2: Special cases — A number divided by 1 stays the same; a number divided by itself is 1; 0 divided by any number is 0.

  • Easy: 45 ÷ 1 = 45.
  • Medium: 19 ÷ 19 = 1.
  • Exam-type: 0 ÷ 8 = 0.
Remember

Division undoes multiplication. Check: Quotient × Divisor = Dividend.

Common mistake

Swapping dividend and divisor (writing 6 ÷ 24), or trying to divide by 0.

Shortcut

Think: "what times D makes N?" Memory clue: "Multiply to check, divide to share."

Spot the difference

MultiplicationDivision 1Division 2
4 × 6 = 2424 ÷ 4 = 624 ÷ 6 = 4
5 × 9 = 4545 ÷ 5 = 945 ÷ 9 = 5
12 × 3 = 3636 ÷ 12 = 336 ÷ 3 = 12

Practice questions

Easy
  1. 17 × 8 = 56. Write the two division facts.
  2. 263 ÷ 9 = ?
  3. 3Fill in: ___ ÷ 6 = 9
Medium
  1. 415 × 12 = 180. What is 180 ÷ 15?
  2. 5What are 9 ÷ 9 and 0 ÷ 9?
  3. 6108 chairs are set in rows of 12. How many rows?
Challenging
  1. 7Fill in: 144 ÷ ___ = 12
  2. 8A box holds 16 pens. How many boxes are needed for 176 pens?
Show answers (try them yourself first)
  1. 156 ÷ 7 = 8 and 56 ÷ 8 = 7
  2. 27
  3. 354
  4. 412
  5. 51 and 0
  6. 69 rows
  7. 712
  8. 8176 ÷ 16 = 11 boxes

Dividing by 10, 100 and multiples of ten

From daily life

A shopkeeper packs 1,500 pencils into packs of 30. If you know 15 ÷ 3 = 5, the answer is quick: 1,500 ÷ 30 = 50.

Simple definition

Zeros follow a pattern in division: remove the same number of zeros from the dividend and the divisor, divide the small numbers, and keep the rest of the zeros in the answer.

Formula: N ÷ 10 removes one zero from a multiple of 10. 4,200 ÷ 70 = 420 ÷ 7 = 60.

15 ÷ 3 = 5150 ÷ 3 = 501,500 ÷ 3 = 50015,000 ÷ 3 = 5,000Same digits, more zeros

In the figure: Each time the dividend gets one more zero, the answer also gets one more zero.

Rule 1: Divide by 10 or 100 — Dividing a multiple of 10 by 10 takes off one zero; a multiple of 100 by 100 takes off two zeros.

  • Easy: 3,400 ÷ 10 = 340.
  • Medium: 7,200 ÷ 100 = 72.
  • Exam-type: 900 ÷ 100 = 9.

Rule 2: Divide by tens — Cancel zeros from both numbers, divide, then check by multiplying.

  • Easy: 2,400 ÷ 60 = 240 ÷ 6 = 40.
  • Medium: 560 ÷ 70 = 56 ÷ 7 = 8.
  • Exam-type: 9,000 ÷ 300 = 90 ÷ 3 = 30.
Remember

Remove the same number of zeros from both numbers, never different numbers.

Common mistake

Removing zeros from only one number (2,400 ÷ 60 ≠ 24 ÷ 60), or forgetting leftover zeros.

Shortcut

Cancel equal zeros, divide, check by multiplying. Memory clue: "Zeros leave in pairs."

Spot the difference

DivisionCancel zerosAnswer
1,500 ÷ 30150 ÷ 350
4,200 ÷ 70420 ÷ 760
8,000 ÷ 40080 ÷ 420

Practice questions

Easy
  1. 180 ÷ 4 = ?
  2. 2900 ÷ 3 = ?
  3. 32,500 ÷ 5 = ?
Medium
  1. 4960 ÷ 12 = ?
  2. 54,200 ÷ 70 = ?
  3. 6Fill in: ___ ÷ 40 = 30
Challenging
  1. 7Fill in: 3,600 ÷ ___ = 90
  2. 8₹7,200 is paid equally to 80 workers. How much does each get?
Show answers (try them yourself first)
  1. 120
  2. 2300
  3. 3500
  4. 480
  5. 560
  6. 61,200
  7. 740
  8. 8₹90

Mental strategies for division

From daily life

Share ₹1,248 equally among 6 friends in your head: ₹1,200 gives ₹200 each, ₹48 gives ₹8 each, so ₹208 each. Smart splitting beats long working.

Simple definition

Three quick tricks: split the dividend into easy parts; use a nearby round number and adjust; halve repeatedly to divide by 4 or 8.

Formula: (A + B) ÷ D = A ÷ D + B ÷ D. (A − B) ÷ D = A ÷ D − B ÷ D. ÷ 4 = halve twice, ÷ 8 = halve three times.

1,2481,20048÷ 6 = 200÷ 6 = 8200 + 8 = 208

168÷ 284÷ 242÷ 221÷ 8 = ÷ 2, ÷ 2, ÷ 2168 ÷ 8 = 21

In the figure: Top: split 1,248 into 1,200 and 48, divide each by 6, add: 200 + 8 = 208. Bottom: dividing by 8 means halving three times: 168, 84, 42, 21.

Rule 1: Split or use a nearby number — Break the dividend into parts that your tables divide easily, or use a round number just above or below and correct it.

  • Easy: 936 ÷ 3 = 900 ÷ 3 + 36 ÷ 3 = 300 + 12 = 312.
  • Medium: 1,596 ÷ 4 = (1,600 − 4) ÷ 4 = 400 − 1 = 399.
  • Exam-type: 1,224 ÷ 12 = 1,200 ÷ 12 + 24 ÷ 12 = 100 + 2 = 102.

Rule 2: Halve repeatedly — Because 4 = 2 × 2 and 8 = 2 × 2 × 2, halve twice to divide by 4 and three times to divide by 8.

  • Easy: 132 ÷ 4: 132 → 66 → 33.
  • Medium: 240 ÷ 8: 240 → 120 → 60 → 30.
  • Exam-type: 456 ÷ 8: 456 → 228 → 114 → 57.
Remember

Pick the trick that fits the numbers: split for 3-digit numbers, halving for 4 and 8, nearby round number when the dividend is just below a round number.

Common mistake

Forgetting to divide the small part too (1,596 ÷ 4 = 400 − 4), or halving only once for 4.

Shortcut

Split, divide each part, add or subtract the answers. Memory clue: "Two halves make a quarter, three halves make an eighth."

Spot the difference

TrickExampleAnswer
Split936 ÷ 3312
Nearby number1,596 ÷ 4399
Halve twice132 ÷ 433
Halve thrice240 ÷ 830

Practice questions

Easy
  1. 1840 ÷ 4 = ? (split 800 and 40)
  2. 2396 ÷ 3 = ? (split 300, 90, 6)
  3. 3192 ÷ 8 by halving three times
Medium
  1. 41,996 ÷ 4 = ? (use 2,000 − 4)
  2. 5252 ÷ 6 = ?
  3. 6560 ÷ 8 = ?
Challenging
  1. 72,994 ÷ 6 = ? (use 3,000 − 6)
  2. 81,236 ÷ 12 = ?
Show answers (try them yourself first)
  1. 1210
  2. 2132
  3. 324
  4. 4499
  5. 542
  6. 670
  7. 7499
  8. 8103

Long division: place value and partial quotients

From daily life

A farm packs 3,208 coconuts into crates of 8. Dividing the thousands, hundreds, tens and ones one after another is long division.

Simple definition

In long division we share place by place, from the biggest place to the ones. Each place is divided, the leftover is exchanged for the next smaller place, and the digits of the quotient are written in order. A place with nothing to share gets a 0 in the quotient.

Formula: Quotient digits come from: share, multiply back, subtract, bring down the next digit.

324 ÷ 3H31T20O48NQ3 H ÷ 3 = 1 H · 2 T ÷ 3 = 0 T (carry 2 T) · 24 ÷ 3 = 8324 ÷ 3 = 108

In the figure: 324 ÷ 3: 3 hundreds ÷ 3 = 1 hundred; 2 tens cannot be shared by 3, so 0 tens and 2 tens become 20 ones; 24 ones ÷ 3 = 8 ones. Quotient 108.

Rule 1: Place by place — Start from the biggest place. If it cannot be shared, put 0 and join it with the next place.

Live figure

Long division: place value and partial quotients

In the app you can move this figure with your finger.

Open in the app
  • Easy: 468 ÷ 4: 4 H → 1 H; 6 T → 1 T, 2 T left = 20 ones + 8 = 28; 28 ÷ 4 = 7. So 117.
  • Medium: 3,208 ÷ 8: 32 H ÷ 8 = 4 H; 0 T; 8 ones ÷ 8 = 1. So 401.
  • Exam-type: 735 ÷ 5: 7 H ÷ 5 = 1 H, 2 H = 20 T; 23 T ÷ 5 = 4 T, 3 T = 30 ones; 35 ÷ 5 = 7. So 147.

Rule 2: Two-digit divisors — Use partial quotients: find easy multiples of the divisor, subtract them again and again, then add the multipliers.

  • Easy: 1,248 ÷ 16: 16 × 50 = 800, left 448; 16 × 20 = 320, left 128; 16 × 8 = 128. 50 + 20 + 8 = 78.
  • Medium: 6,075 ÷ 15: 15 × 400 = 6,000, left 75; 15 × 5 = 75. 405.
  • Exam-type: 7,104 ÷ 32: 32 × 200 = 6,400, left 704; 32 × 20 = 640, left 64; 32 × 2 = 64. 222.
Remember

A quotient digit goes in every place, even when it is 0. Check by Quotient × Divisor.

Common mistake

Skipping the 0 in the quotient (3,208 ÷ 8 = 41 instead of 401), or forgetting to bring down the next digit.

Shortcut

Estimate first: 3,208 ÷ 8 is about 3,200 ÷ 8 = 400. Memory clue: "Share, multiply, subtract, bring down."

Spot the difference

StepDo this
1 ShareDivide the biggest place
2 MultiplyQuotient digit × divisor
3 SubtractFind what is left
4 Bring downNext digit joins the leftover

Practice questions

Easy
  1. 1468 ÷ 4 = ?
  2. 2735 ÷ 5 = ?
  3. 3How many digits does 2,500 ÷ 5 have?
Medium
  1. 43,208 ÷ 8 = ?
  2. 51,248 ÷ 16 = ?
  3. 66,075 ÷ 15 = ?
Challenging
  1. 79,024 ÷ 24 = ?
  2. 87,104 ÷ 32 = ?
Show answers (try them yourself first)
  1. 1117
  2. 2147
  3. 3500 → 3 digits
  4. 4401
  5. 578
  6. 6405
  7. 7376
  8. 8222

Remainders: N = D × Q + R

From daily life

97 coconuts are packed 25 to a bag. 3 bags are full and 22 coconuts are left over. The bags needed are 4, because the leftover also needs a bag.

Simple definition

When a number does not divide exactly, the part left over is the remainder R. It is always smaller than the divisor.

Formula: N = D × Q + R, with 0 ≤ R < D. Q = whole number of full groups.

25252522+13 full bags of 25 = 75 · 22 left97 ÷ 25 = 3 R 22 → 4 bags needed

In the figure: 97 = 25 × 3 + 22. Three bags are full and 22 coconuts are left; they need a 4th bag.

Rule 1: Find Q and R — Find the biggest multiple of D that is not more than N. That multiple is D × Q; the difference is R.

Live figure

Remainders: N = D × Q + R

In the app you can move this figure with your finger.

Open in the app
  • Easy: 47 ÷ 6: 6 × 7 = 42, 47 − 42 = 5. Q = 7, R = 5.
  • Medium: 365 ÷ 7: 7 × 52 = 364, 365 − 364 = 1. Q = 52, R = 1.
  • Exam-type: 1,000 ÷ 12: 12 × 83 = 996, 1,000 − 996 = 4. Q = 83, R = 4.

Rule 2: What to do with the remainder — Read the question: sometimes the remainder is ignored (full boxes only), sometimes one more group is needed (all must be carried).

  • Easy: 250 children, 30 in a bus: 250 ÷ 30 = 8 R 10, so 9 buses (everyone must travel).
  • Medium: 250 eggs in trays of 30: 8 full trays, 10 eggs extra.
  • Exam-type: Check: 30 × 8 + 10 = 250.
Remember

The remainder is always less than the divisor. Check: D × Q + R must give N back.

Common mistake

A remainder equal to or bigger than the divisor (it means Q is too small), or forgetting the extra group in "how many are needed" questions.

Shortcut

Multiply back and add R. If the result is N, the division is right. Memory clue: "Leftover is smaller than the sharer."

Spot the difference

N ÷ DQRCheck
47 ÷ 6756 × 7 + 5 = 47
365 ÷ 75217 × 52 + 1 = 365
250 ÷ 3081030 × 8 + 10 = 250

Practice questions

Easy
  1. 147 ÷ 6 = ? Write Q and R.
  2. 2100 ÷ 9 = ? Write Q and R.
  3. 3Can 9 be a remainder when dividing by 8?
Medium
  1. 4365 ÷ 7 = ? Write Q and R.
  2. 51,000 ÷ 12 = ? Write Q and R.
  3. 6Find N: N = 17 × 23 + 9
Challenging
  1. 7250 children, 30 in each bus. How many buses are needed?
  2. 82,000 ÷ 45 = ? Write Q and R and check.
Show answers (try them yourself first)
  1. 1Q = 7, R = 5
  2. 2Q = 11, R = 1
  3. 3No, remainder must be less than 8
  4. 4Q = 52, R = 1
  5. 5Q = 83, R = 4
  6. 6400
  7. 79 buses
  8. 8Q = 44, R = 20; 45 × 44 + 20 = 2,000

Division word problems and statements

From daily life

A vendor sells vegetables for ₹40 per kg and earns ₹1,400. How many kg did he sell? Real problems mix division with other operations and sometimes miss a fact.

Simple definition

Read the problem, decide what is asked, choose the operations, solve and check. A mathematical statement with an = sign is true if both sides have the same value.

Formula: Total ÷ price per kg = kg. Total ÷ number of days = per day. Left side = Right side.

4 × 6 = 2424 ÷ 4 = 624 ÷ 6 = 44 rows of 6

In the figure: Equal groups in rows and columns: total ÷ groups = size of each group.

Rule 1: Solve in steps — Write each step: find the total, divide, then use the answer in the next step.

  • Easy: Three friends spent ₹180, ₹240 and ₹210: total ₹630, each pays 630 ÷ 3 = ₹210.
  • Medium: 360 km in 6 hours is 60 km an hour; in 9 hours: 60 × 9 = 540 km.
  • Exam-type: ₹2,400 for 8 kg: ₹2,400 ÷ 8 = ₹300 per kg.

Rule 2: Statements and missing facts — Work out both sides of a statement before deciding. If a fact needed for the answer is not given, say what is missing.

  • Easy: 6 × 4 = 12 × 2: both sides 24, so true.
  • Medium: 20 − 6 = 7 × 3: 14 and 21, so false.
  • Exam-type: 12 notebooks and 8 pens: the price of one notebook and one pen is missing.
Remember

Estimate first and check the answer against the story. Always give the unit.

Common mistake

Dividing when you should multiply, or comparing only one side of a statement.

Shortcut

Underline numbers, circle what is asked, then do one step at a time. Memory clue: "Read, plan, solve, check."

Spot the difference

Problem typeOperation
Total from partsadd
Equal sharingdivide
Many equal groupsmultiply
What is leftsubtract

Practice questions

Easy
  1. 1144 pencils are shared equally in 12 boxes. How many in each box?
  2. 2₹2,400 is paid for 8 kg of rice. Price of 1 kg?
  3. 3Is 6 × 4 = 12 × 2 true or false?
Medium
  1. 4Fill in: 96 ÷ 8 = ___ + 4
  2. 5Three friends spent ₹180, ₹240 and ₹210 and share equally. Each pays?
  3. 6Is 7 × 8 = 60 − 4 true or false?
Challenging
  1. 7A bus covers 360 km in 6 hours. How far in 9 hours at the same speed?
  2. 8A hall has 480 seats in rows of 24. If 5 rows are empty, how many seats are in use?
Show answers (try them yourself first)
  1. 112
  2. 2₹300
  3. 3True (24 = 24)
  4. 48
  5. 5₹210
  6. 6True (56 = 56)
  7. 7540 km
  8. 8480 ÷ 24 = 20 rows; 15 rows × 24 = 360