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CBSE · Class 5 · Math Mela

Chapter 6: The Dairy Farm (Multiplication)

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

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Order of numbers and arrays in multiplication

From daily life

A dairy arranges butter packets in 3 rows of 6, or in 6 rows of 3. Looking at the tray from the side, the number of packets is the same. A rows-and-columns picture is called an array.

Simple definition

Multiplication counts equal groups. The product does not change if the numbers swap places: a × b = b × a. Any number × 0 = 0, and any number × 1 = itself.

Formula: a × b = b × a; a × b × c = a × c × b; a × 0 = 0; a × 1 = a.

3 × 6 = 186 × 3 = 18same dots, same total

In the figure: 3 rows of 6 dots and 6 rows of 3 dots both make 18: 3 × 6 = 6 × 3.

Rule 1: Swap the numbers — Number of groups and group size can swap places. Use the easier order.

Live figure

Order of numbers and arrays in multiplication

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  • Easy: 7 × 9 = 9 × 7 = 63.
  • Medium: 6 × 13 = 13 × 6 = 78.
  • Exam-type: 25 × 4 = 4 × 25 = 100 (4 × 25 is easier).

Rule 2: Factor pairs make arrays — A total can be arranged in many ways: every pair of numbers whose product is that total.

  • Easy: 24 = 1 × 24 = 2 × 12 = 3 × 8 = 4 × 6.
  • Medium: 120 = 10 × 12 = 8 × 15 = 6 × 20 = 4 × 30.
  • Exam-type: 5 × 25 = 125, so 5 × 25 is not a way to make 120.
Remember

Zero groups, or groups of zero, always give zero: 9 × 0 = 0 × 9 = 0.

Common mistake

Thinking order matters in a story: 6 trays of 5 packets and 5 trays of 6 packets look different, but both hold 30 packets.

Shortcut

Turn a hard multiplication around: 25 × 4 → 4 × 25 is quicker to count in fours. Memory clue: "Rows × columns = columns × rows" — turn the tray and the count stays.

Spot the difference

Point3 × 66 × 3
Rows × columns3 rows of 66 rows of 3
Total1818

Practice questions

Easy
  1. 1If 7 × 9 = 63, find 9 × 7.
  2. 2What is 0 × 14?
  3. 3Write 3 different arrangements of 24 packets in equal rows.
Medium
  1. 4Which is not equal to 10 × 12: 8 × 15, 6 × 20 or 5 × 25?
  2. 5A tray has 5 rows of 12 packets. Another has 12 rows of 5. Which holds more?
  3. 6Use the easier order: find 25 × 4.
Challenging
  1. 7Show that 6 × 5 × 4 = 4 × 5 × 6.
  2. 8How many ways can 36 chairs be arranged in equal rows (rows × chairs per row, order counted)?
Show answers (try them yourself first)
  1. 163
  2. 20
  3. 32 × 12, 3 × 8, 4 × 6 (also 1 × 24)
  4. 45 × 25 (= 125)
  5. 5Both hold 60
  6. 64 × 25 = 100
  7. 76 × 5 × 4 = 30 × 4 = 120 and 4 × 5 × 6 = 20 × 6 = 120
  8. 89 ways: 1×36, 2×18, 3×12, 4×9, 6×6, 9×4, 12×3, 18×2, 36×1

Multiplying by 10, 100 and 1,000

From daily life

A crate holds 100 pouches. Forty-five crates hold 45 × 100 = 4,500 pouches. When you multiply by 10, 100 or 1,000 you only add zeros — each digit slides to a bigger place.

Simple definition

Multiplying by 10 shifts each digit 1 place left, by 100 2 places left, by 1,000 3 places left (add 1, 2 or 3 zeros). For 30 × 20, multiply 3 × 2 = 6, then add the two zeros: 600.

Formula: n × 10 = n0; n × 100 = n00; n × 1,000 = n000. (a0) × (b0) = (a × b) with two zeros.

× 100 : every digit moves 2 places leftThHTO4747↓ × 10047004,700

In the figure: 47 × 100: the 4 and 7 each move two places to the left and zeros fill the empty places: 4,700.

Rule 1: Multiply by 10, 100, 1,000 — Write the number and add as many zeros as the multiplier has.

Live figure

Multiplying by 10, 100 and 1,000

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  • Easy: 47 × 10 = 470; 47 × 100 = 4,700.
  • Medium: 8 × 1,000 = 8,000.
  • Exam-type: 305 × 100 = 30,500.

Rule 2: Multiples of 10 and 100 — Multiply the non-zero digits, then put all the zeros of both numbers at the end.

  • Easy: 30 × 20 = (3 × 2) with 2 zeros = 600.
  • Medium: 40 × 50 = 20 and 2 zeros = 2,000.
  • Exam-type: 600 × 30 = 18 and 3 zeros = 18,000.
Remember

Count zeros carefully: 40 × 50 = 2,000 has three zeros, because 4 × 5 = 20 already ends in a zero.

Common mistake

Adding only the zeros of the multiplier: 40 × 50 = 200 (wrong). Include the zero from 4 × 5 = 20: 2,000.

Shortcut

First do the small multiplication, then attach zeros: 600 × 30 → 6 × 3 = 18 → 18,000. Memory clue: "Times 10 — digits climb one step; times 100 — two steps."

Spot the difference

Point× 10× 100
Digits move1 place2 places
47 becomes4704,700

Practice questions

Easy
  1. 1Find 63 × 100.
  2. 2Find 8 × 1,000.
  3. 3Find 30 × 20.
Medium
  1. 4Find 40 × 50.
  2. 5A crate holds 100 pouches. How many pouches in 45 crates?
  3. 6Find 600 × 30.
Challenging
  1. 7Find 3 × 5,000 and 8 × 3,000.
  2. 8How many zeros are in the answer of 400 × 50? Find the product.
Show answers (try them yourself first)
  1. 16,300
  2. 28,000
  3. 3600
  4. 42,000
  5. 54,500
  6. 618,000
  7. 715,000 and 24,000
  8. 84 zeros: 20,000

Doubling, halving and the nearest multiple

From daily life

To find 16 packets in each of 25 boxes, it is easier to think "8 boxes of 50, then 4 boxes of 100". And 6 × 29 is just 6 × 30 take away 6. Smart tricks make big multiplications easy.

Simple definition

Halve and double: halve one number and double the other — the product stays the same (works well with 5, 25, 50). Nearest multiple: use 20, 30, 50, 100 near the number, then add or subtract the extra.

Formula: a × b = (a ÷ 2) × (b × 2). a × (n − 1) = a × n − a. a × (n + 1) = a × n + a.

16 × 25 = 8 × 50 = 4 × 100 = 40016 × 25½ ×28 × 50½ ×24 × 100

In the figure: Each step halves the first number and doubles the second; the area (the product) never changes: 400.

Rule 1: Halve one, double the other — Halve an even number and double the other number. Repeat until the product is easy.

Live figure

Doubling, halving and the nearest multiple

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  • Easy: 14 × 25 = 7 × 50 = 350.
  • Medium: 24 × 15 = 12 × 30 = 360.
  • Exam-type: 16 × 25 = 8 × 50 = 4 × 100 = 400.

Rule 2: Use the nearest multiple — If one number is a little less (or more) than a round number, multiply by the round number and take away (or add) the extra copies.

  • Easy: 6 × 29 = 6 × 30 − 6 = 180 − 6 = 174.
  • Medium: 13 × 41 = 13 × 40 + 13 = 520 + 13 = 533.
  • Exam-type: 7 × 48 = 7 × 50 − 7 × 2 = 350 − 14 = 336.
Remember

Halving and doubling is best when one number is 5, 15, 25 or 50, because doubling makes it a round number.

Common mistake

Subtracting instead of adding (or the other way): 13 × 41 = 13 × 40 − 13 is wrong. 41 is more than 40, so ADD 13.

Shortcut

Ask: "Is the number a little below or above a round number?" Below → subtract the extra, above → add it. Memory clue: "Half one, double the other — same area." "Below the round number: take away; above: add on."

Spot the difference

PointHalve and doubleNearest multiple
Example14 × 25 = 7 × 506 × 29 = 6 × 30 − 6
Answer350174

Practice questions

Easy
  1. 1Find 14 × 25 by halving and doubling.
  2. 2Find 24 × 15 by halving and doubling.
  3. 3Find 6 × 29 using 30.
Medium
  1. 4Find 13 × 41 using 40.
  2. 5Find 8 × 99.
  3. 6Find 7 × 48 using 50.
Challenging
  1. 7Find 18 × 35 by halving and doubling.
  2. 8Give two examples where halving and doubling is helpful and solve them.
Show answers (try them yourself first)
  1. 17 × 50 = 350
  2. 212 × 30 = 360
  3. 36 × 30 − 6 = 174
  4. 413 × 40 + 13 = 533
  5. 58 × 100 − 8 = 792
  6. 67 × 50 − 7 × 2 = 336
  7. 79 × 70 = 630
  8. 8For example 12 × 25 = 6 × 50 = 300 and 22 × 15 = 11 × 30 = 330

Breaking numbers apart: area and partial products

From daily life

A hall has 47 rows with 36 seats. Counting 47 × 36 in one go is hard, so we break 47 into 40 + 7 and 36 into 30 + 6. A rectangle split into four boxes shows each part.

Simple definition

Partial products: break each number into tens and ones, multiply every part with every part, then add. 47 × 36 = (40 + 7) × (30 + 6) = 1,200 + 240 + 210 + 42 = 1,692.

Formula: (a + b) × (c + d) = a×c + a×d + b×c + b×d.

35 × 12 = 350 + 70 = 420305102300506010300 + 50 + 60 + 10 = 420

In the figure: 35 × 12 split as (30 + 5) × (10 + 2): 300 + 50 + 60 + 10 = 420.

Rule 1: 2-digit × 1-digit — Break the 2-digit number into tens and ones; multiply each by the 1-digit number; add.

Live figure

Breaking numbers apart: area and partial products

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  • Easy: 34 × 6 = 30 × 6 + 4 × 6 = 180 + 24 = 204.
  • Medium: 58 × 7 = 350 + 56 = 406.
  • Exam-type: 47 × 5 = 200 + 35 = 235.

Rule 2: 2-digit × 2-digit — Make four boxes (tens × tens, tens × ones, ones × tens, ones × ones) and add all four.

  • Easy: 23 × 15 = 200 + 100 + 30 + 15 = 345.
  • Medium: 41 × 32 = 1,200 + 80 + 30 + 2 = 1,312.
  • Exam-type: 47 × 36 = 1,200 + 240 + 210 + 42 = 1,692.
Remember

Every part must be multiplied by every part, so a 2-digit × 2-digit product always has four boxes.

Common mistake

Forgetting that tens × tens is hundreds: 40 × 30 is 1,200 (not 120 or 12).

Shortcut

Check by estimating: 47 × 36 is a little more than 40 × 30 = 1,200 — and 1,692 fits. Memory clue: "Four boxes, four products, one sum."

Spot the difference

PointBoxProduct
40 × 30tens × tens1,200
40 × 6tens × ones240
7 × 30ones × tens210
7 × 6ones × ones42

Practice questions

Easy
  1. 1Find 34 × 6 by breaking 34 into 30 + 4.
  2. 2Find 58 × 7.
  3. 3In the area model of 26 × 13, what is in the box for 20 × 10?
Medium
  1. 4Find 23 × 15 with four boxes.
  2. 5Find 41 × 32.
  3. 6Find 52 × 24.
Challenging
  1. 7Find 47 × 36 and check by estimating.
  2. 8Find 64 × 35.
Show answers (try them yourself first)
  1. 1180 + 24 = 204
  2. 2406
  3. 3200
  4. 4200 + 100 + 30 + 15 = 345
  5. 51,312
  6. 61,248
  7. 71,692 (about 40 × 30 = 1,200 and a bit more)
  8. 82,240

Multiplication word problems

From daily life

A farm has 165 cows and each needs 12 kg of fodder a day. A school library has 46 shelves with 128 books on each. Real life asks us to choose a strategy and use it flexibly.

Simple definition

In a word problem find the number of groups and the size of each group, then multiply. Choose the best strategy: swap, ×10/100, halve-double, nearest multiple or partial products.

Formula: total = number of groups × size of each group.

35 × 12 = 350 + 70 = 420305102300506010300 + 50 + 60 + 10 = 420

In the figure: A rectangle of 35 by 12 can stand for 35 rows of 12 seats: 420 seats.

Rule 1: Groups × size — Say the story in one line: "(number of groups) groups of (size) each". Then multiply.

Live figure

Multiplication word problems

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  • Easy: 28 rows of 36 seats: 28 × 36 = 1,008 seats.
  • Medium: 25 crates of 18 pouches: 25 × 18 = 450 pouches.
  • Exam-type: 24 bags at ₹450: 24 × 450 = ₹10,800.

Rule 2: More than one step — Do each multiplication separately, then add or subtract the results.

  • Easy: 12 pens at ₹18 and 15 notebooks at ₹25: 216 + 375 = ₹591.
  • Medium: 8 rows of 14 seats, half filled: 8 × 14 = 112, half = 56 people.
  • Exam-type: 4 kurtas need 16 m; 12 kurtas need 3 × 16 = 48 m.
Remember

Write the units in the answer: seats, ₹, kg, km. Then check if the size of the answer is sensible.

Common mistake

Adding instead of multiplying: 28 rows of 36 seats is 28 × 36, not 28 + 36.

Shortcut

Estimate first: 28 × 36 is about 30 × 40 = 1,200 — the exact 1,008 is a bit less. Memory clue: "Groups of size — multiply; then check with a rough guess."

Spot the difference

PointStoryMultiplication
Hall28 rows, 36 seats28 × 36 = 1,008
Farm165 cows, 12 kg165 × 12 = 1,980

Practice questions

Easy
  1. 1A hall has 28 rows with 36 seats in each. How many seats?
  2. 2Each cow gives 6 litres of milk a day. How many litres do 38 cows give?
  3. 3A dairy packs 18 pouches in each crate. How many in 25 crates?
Medium
  1. 424 bags of rice are sold at ₹450 each. How much money?
  2. 5A farm needs 12 kg of fodder per cow per day. How much for 165 cows?
  3. 6A family makes 28 kg of kitchen waste a month. How much in a year?
Challenging
  1. 7Mira buys 12 pens at ₹18 and 15 notebooks at ₹25. What is the total?
  2. 8A library has 46 shelves with 128 books on each shelf. How many books? Estimate first.
Show answers (try them yourself first)
  1. 11,008
  2. 2228
  3. 3450
  4. 4₹10,800
  5. 51,980 kg
  6. 6336 kg
  7. 7₹591
  8. 85,888 (estimate 50 × 130 = 6,500)