NCERT Class 4 Maths · Chapter 13

The Transport Museum

Building times-tables up to 20, multiplying by 10s and 100s, the box (grid) method for big multiplications, and division with remainders.

📌 What you’ll learn in this chapter
  • Making times-tables for 11 to 20 by splitting (15 = 10 + 5)
  • Multiplying by 10, 100, 20, 200… using “tens” and “hundreds”
  • The box method: 15 × 14 = 100 + 40 + 50 + 20
  • Long division by taking away big groups, and remainders
  • Word problems from travel and daily life

🚂 Let’s Begin: A Museum Trip

Class 4 visits a railway museum. An old steam train has 12 coaches, and each coach seats 16 people. How many people could the train carry?

12 × 16: that’s a big multiplication! Let’s learn some clever ways to do it.

📋 Part 1: Building Bigger Tables

To make the table of 15, split 15 into 10 and 5:

7 × 15 = 7 × 10 + 7 × 5 = 70 + 35 = 105

Times-15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150

Compare: Times-15 = times-5 + times-10. Each answer in the 15 table is 10, 20, 30… more than the answer in the 5 table.

Doubling trick: 6 × 14 is double 6 × 7 → 42 + 42 = 84. Tables of 12, 14, 16, and 18 can be made by doubling the tables of 6, 7, 8, and 9.

🔟 Part 2: Multiplying by 10s and 100s

  • 23 × 10 = 23 tens = 230
  • 23 × 100 = 23 hundreds = 2,300
  • 14 × 30 = 14 × 3 tens = 42 tens = 420
  • 12 × 200 = 12 × 2 hundreds = 24 hundreds = 2,400
💡 Doubles and halves 14 × 500 = 7,000. Halving 500 halves the answer: 14 × 250 = 3,500. Doubling 14 doubles it: 28 × 500 = 14,000.

🟩 Part 3: The Box Method

Let’s solve the train problem: 12 × 16. Break 12 = 10 + 2 and 16 = 10 + 6.

×106
1010060
22012

Add all the boxes: 100 + 60 + 20 + 12 = 192 people.

It works for bigger numbers too: 45 × 123 → split 123 = 100 + 20 + 3 and 45 = 40 + 5, fill 6 boxes, and add.

➗ Part 4: Division with Big Groups

Example: 350 children need to travel in coaches of 16 seats. How many coaches?

Take away 10 coaches (160) → 190 left · 10 more coaches (160) → 30 left · 1 coach (16) → 14 left.

10 + 10 + 1 = 21 coaches, with 14 children remaining. They need 1 more coach, so 22 coaches.

Dividing by 10 and 100: 600 ÷ 10 = 60 · 600 ÷ 100 = 6 · 400 ÷ 20 = 20

⚠️ Common mistake Ignoring the remainder in real life. 14 children left over still need a seat, so add one more coach!

✏️ Practice Time

Try these on your own first, then check your answer below each question.

Q1. 8 × 15 = ? (split 15 into 10 + 5)
✅ Answer80 + 40 = 120
Q2. 36 × 100 = ? And 36 × 20 = ?
✅ Answer3,600 and 720
Q3. Use the box method: 23 × 17
✅ Answer200 + 140 + 30 + 21 = 391
Q4. 250 ÷ 12 = ? (find the remainder)
✅ Answer20, remainder 10
Q5. A bus seats 45. How many buses are needed for 200 people?
✅ Answer4 buses hold 180, and 20 are left, so 5 buses

📘 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 184 · Mystery Matrix

Fill the boxes

✅ AnswerBig grid: 42 and 21 are in the same column, so that column’s number must be 7. The rows are then 6 (6 × 7 = 42) and 3 (3 × 7 = 21). 32 = 4 × 8 and 45 = 5 × 9 (or swap them). One answer: rows 4, 6, 5, 3 and columns 8, 9, 7, and any number (e.g. 2). Then fill every box by multiplying.
Row/column puzzles: 7, 8 / 9, 6 (7 × 8 = 56, 9 × 6 = 54, 7 × 9 = 63, 8 × 6 = 48) and 6, 7 / 10, 5 (6 × 7 = 42, 10 × 5 = 50, 6 × 10 = 60, 7 × 5 = 35)
Times-10: 2 × 10 = 20 · 5 × 10 = 5 tens = 50 · 8 × 10 = 8 tens = 80 · 10 × 10 = 10 tens = 100
Pages 185–188 · Constructing tables

Times-15 and times-14

✅ Answer5 × 15 = 50 + 25 = 75 pebbles
Times-15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150 · Times-5: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50
The differences (15 − 5, 30 − 10…) are 10, 20, 30… This is the times-10 table!
Times-14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140 (each is double the times-7 answer). Tables of 12, 16, and 18 can also be made by doubling.
Pages 188–190 · Multiples of 10

Tens

✅ Answer(a) 15 tens = 150 (b) 16 tens = 160 (c) 19 tens = 190 (d) 20 tens = 200 · 10 × 10 = 100, and its double = 200
30 × 10 = 300 · 40 × 10 = 400 · 70 × 10 = 700 · 50 × 10 = 500 · 60 × 10 = 600 · 80 × 10 = 800 · 26 × 10 = 260
(a) 210 (b) 420 (c) 650 (d) 380 (e) 530 (f) 870
24 × 40 = 960 · 50 × 60 = 3,000 · 13 × 30 = 390 · 43 × 60 = 2,580 · 70 × 80 = 5,600
Pages 190–192 · Toy train

Coaches and Let Us Solve

✅ Answer15 × 14 = 210 children. 324 ÷ 14 = 23 coaches with 2 children remaining, so they need 24 coaches for everyone.
(a) 850 (b) 688 (c) 816 (d) 507 (e) 8 R 5 (f) 8 R 6 (g) 20 R 0 (h) 28 R 4
Pages 192–195 · Multiples of 100

Hundreds and patterns

✅ Answer3 hundreds = 300 · 5 hundreds = 500 · 8 hundreds = 800 · 12 × 100 = 1,200 · 15 × 100 = 1,500 · 27 × 100 = 2,700 · 70 × 100 = 7,000
3,000 · 4,000 · 5,000 · 2,400 · 5,300 · 1,900 · 80 × 50 = 4,000 (half of 8,000) · 40 × 50 = 2,000
11 × 100 = 1,100 · 22 × 100 = 2,200 · 11 × 200 = 2,200 · 22 × 200 = 4,400. Doubling either number doubles the answer.
18 × 100 = 1,800 · 5 × 500 = 2,500 · 15 × 200 = 3,000 · 14 × 300 = 4,200 · 23 × 200 = 4,600 · 7 × 800 = 5,600
Set A: 1,400 · 7,000 · 3,500 · 1,750 · 3,000 · 6,000 · 1,500 · 3,000 · Set B: 140 · 700 · 350 · 175 · 300 · 600 · 150 · 300 · Set C: 14 · 70 · 35 · 70 · 30 · 60 · 15 · 30
44 × 10 = 440 = 22 × 20 · 16 × 100 = 1,600 = 4 × 400
Pages 196–197 · Vande Bharat and snake boats

Big multiplication and division

✅ Answer64 × 152 = 9,728 people · 960 ÷ 64 = 15 boats
(a) 6,636 (b) 2,240 (c) 22,173 (d) 33 R 15 (e) 20 R 32 (f) 22 R 6
Pages 197–198 · Dividing by 10 and 100

Rice sacks and more

✅ Answer(a) 60 ÷ 10 = 6 sacks (b) 600 ÷ 10 = 60 sacks · 100 kg sacks: 600 ÷ 100 = 6
40 ÷ 10 = 4 · 400 ÷ 10 = 40 · 400 ÷ 100 = 4 · 4 ÷ 2 = 2 · 40 ÷ 20 = 2 · 400 ÷ 200 = 2 · 400 ÷ 2 = 200 · 400 ÷ 20 = 20
1. 870 ÷ 10 = 87 bunches 2. 1,000 ÷ 10 = ₹100 each
Pages 198–199 · Let Us Solve

Punjab Mail, Goa bus, bricks, and dolphins

✅ Answer1. (a) 96 ÷ 3 = 32 per coach (b) 24 × 72 = 1,728 people
2. (a) 36 children + 6 teachers = 42 people → 21 seats. The bus has 25 seats, so yes, there’s enough. (b) 36 × ₹359 = ₹12,924 (if you count only the 35 classmates, 35 × ₹359 = ₹12,565) (c) 6 × ₹899 = ₹5,394
3. (a) In a 30-day month: 125 × 30 = 3,750 bricks (b) 3,750 × ₹9 = ₹33,750
4. Each person pays ₹60 (bus) + ₹1,200 ÷ 8 (boat) = 60 + 150 = ₹210
Page 200 · Let Us Solve

Find sentences and solve

✅ AnswerQ5: Look for three numbers in a row or column that form a fact, like 250 × 4 = 1,000, 50 × 20 = 1,000, 525 ÷ 5 = 105, 26 × 4 = 104, 22 × 6 = 132.
Q6: (a) 2,660 (b) 10,146 (c) 4,482 (d) 3,738 (e) 1,265 (f) 5,865 (g) 1,452 (h) 7,744 (i) 8,294 (j) 153 (k) 43 (l) 33 R 6 (m) 25 R 4 (n) 74 R 4 (o) 23 R 9 (p) 60 (q) 20 R 18 (r) 108 R 2
Pages 201–202 · Chinnu’s coins

Ticket of ₹750

✅ Answer(a) Bujji: 4 notes of ₹200 (₹800, gets ₹50 change) · Munna: 15 notes of ₹50 · Balu: 38 notes of ₹20 (₹760, gets ₹10 change) · Chinnu: 150 coins of ₹5 · Sansu: 375 coins of ₹2
(b) Munna, Chinnu, and Sansu get no change. (c) Chinnu’s 150 coins take a long time to count, a few minutes!
Q2: Pattern: 1 | sum of the ones digits | product of the ones digits → 12 × 13 = 1 | 5 | 6 = 156. It works when the sum and product are both less than 10. More examples: 11 × 11 = 121, 11 × 13 = 143, 12 × 12 = 144, 11 × 15 = 165, 12 × 14 = 168.
Q3: 75 cycles → 75 · 52 autos (3 each) → 156 · 103 cars (4 each) → 412 · 20 minibuses (20 each) → 400 · 30 aeroplanes (152 each) → 4,560 · The sleeper coaches get the remaining 864. (864 isn’t exactly 15 × a whole number, so it looks like a small mistake in the book.)

👨‍👩‍👧 Tips for Parents

  • Build tables of 11–20 together by splitting (e.g. 13 = 10 + 3).
  • Practise “tens” talk: “24 × 10 is 24 tens, which is 240.”
  • Use travel plans: “40 people, 12-seater vans. How many vans?”
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