NCERT Solutions Class 5 Maths Chapter 1 We the Travellers I

F R E E S T U D Y M AT E R I A L F O R E V E R Y S T U D E N T

C L A S S 5 · M AT H S

NCERT Solutions

Chapter 1: We the Travellers—I

NCERT Textbook — Math Mela

BOOK PAGES SECTIONS QUESTIONS MEDIUM

1 – 16 12 96 English

Solutions, notes, sample papers & more at 78 pages

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

CLASS 5 · MATHS · MATH MELA

NCERT Solutions — Chapter 1: We the Travellers—I
Chapter 1 of Math Mela takes you on a journey — bullock carts, cycles, trains, ships and spacecraft — and uses
that journey to open the door to five-digit numbers. You will learn to read, write, compare and round
numbers up to 99,999, and finish with two clever puzzles: Mira's subtraction trick and the King's 20 horses.

TEXTBOOK BOOK PAGES

Math Mela (Class 5) 1 – 16

SECTIONS QUESTIONS

12 96

MEDIUM

English

In-text Questions — Page 1
Opening page and Reading and writing large numbers

Q1 When was the last time you went on a long trip? Where did you go? How did you
travel? What was the duration of your trip? How much distance did you cover? Ask
the elders who went with you to help you answer these questions.

This is about your own trip, so your answer will be your own. Here is how to find each piece of
information.

1. When: ask at home for the month and year of the trip.
2. Where: the name of the place you went to.
3. How: bus, train, car, boat, aeroplane — the vehicle you sat in.
4. Duration: how long the travelling took. Count in hours, or in days if it was long.
5. Distance: ask an elder, or look at the ticket. Distance is written in kilometres (km).

Sample answer: Last December my family went from Jaipur to Delhi. We went by
train. The train took about 5 hours. The distance is about 300 km.

Try This: Write your five answers in a small table — When · Where · How · Duration ·
Distance. Then compare with a friend. Whose trip was longer in hours? Whose was
longer in kilometres? They need not be the same trip.

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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Q2 Do you know how many vehicles are currently there in your state?

Nobody can guess this correctly — it has to be looked up. The count runs into lakhs and crores,
so it is a very big number.
Here is how to find it.

1. Every vehicle in India must be registered with the Regional Transport Office (RTO) — the
government office that gives number plates.
2. Each state's transport department publishes the total. Your teacher can help you look it up.
3. Write the number down and count its digits.

Sample answer: Uttar Pradesh has more than 4 crore registered vehicles. That
number has 8 digits. My state's figure is ______ (fill in what you find).

Why it matters here: The chapter is about numbers that are too big to count on
fingers. Vehicles in a state is one such number. In this chapter we will get
comfortable with numbers up to 5 digits first.

Q3 How do you write numbers to show several thousand objects?

You group the objects into thousands, and then write how many thousands you have, followed
by what is left over.
Think of counting bricks at a building site.

1. Make bundles of 1,000 bricks each.
2. Count the bundles. Say you get 7 bundles.
3. Count the loose bricks left over. Say 209 are left.
4. Write the thousands first, then the rest: 7,209.

7 thousands + 2 hundreds + 0 tens + 9 ones

= 7,000 + 200 + 0 + 9

= 7,209

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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Tip: The comma in 7,209 is not decoration. It marks the end of the thousands.
Everything to the left of the comma is counted in thousands.

Q4 Let us start with 1,000. What numbers do we get when we keep adding a thousand?
[1,000] [2,000] [ ] [ ] [ ] [ ] [ ] [ ] [9,000]

Each new box is one thousand more than the box before it. The six empty boxes are:

1,000 → 2,000 → 3,000 → 4,000 → 5,000 → 6,000 → 7,000 → 8,000 → 9,000

Notice how easy it is to say them: one thousand, two thousand, three thousand … nine
thousand.

Why it happens: Only the thousands digit is changing — 1, 2, 3, 4, 5, 6, 7, 8, 9. The
hundreds, tens and ones stay 0 the whole time, because we are adding whole
thousands and nothing smaller.

Check it yourself: Count backwards from 9,000, taking away a thousand each time.
You should land exactly on 1,000 after eight steps.

Q5 What number do we get when we add a thousand to 9,000? We get ten thousand.
How do we write this number?

We write it as 10,000.

9,000 + 1,000 = 10,000 (read as ten thousand)

It has five digits — a 1 followed by four zeros.

Why it happens: 9,000 already has 9 thousands. Adding one more makes 10
thousands. But the thousands column can hold only the digits 0 to 9. Ten thousands
will not fit, so they are carried one step to the left into a brand new column — the
ten thousands column, written TTh.

Page 3 of 78

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Class 5 Maths Chapter 1 We the Travellers—I
a g l AglaSem · NCERT Solutions

co m
m.
Tip: This is exactly what happened before. 9 ones + 1 one = 10. 90 + 10 = 100. 900 +

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100 = 1,000. Each time the column filled up and a new column opened on the left.

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In-text Questions — Page 2
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The place value chart and the Indian place value system

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Q1 agnotice the pattern of writing numbers. In the place
Look at the table below and
value chart, we have added another column, TTh. It stands for ten thousand. In the

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same way, 10 Thousands = Ten Thousand = 10,000.

m ase
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a s em ×10 ×10 ×10 ×10

ag l

m a s
Them .co H agl
TTh
s T O
a gla
1
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m 1 ase 0
m .co agl
l a se
a g 1 0 0

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1 com 0 0 0 g l a
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1 agl 0 0 0 0

. c om
s e m the place on its right.
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The place value chart printed on page 2. Each place is ten times

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a s em
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.

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The pattern is simple: each column is ten times the column on its right.
. co
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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

10 Ones = 1 Ten = 10

10 Tens = 1 Hundred = 100

10 Hundreds = 1 Thousand = 1,000
10 Thousands = 1 Ten Thousand = 10,000

So the chart now has five columns:

TTH TH H T O

1

1 0

1 0 0

1 0 0 0

1 0 0 0 0

Reading down the last column of numbers: 1, 10, 100, 1,000, 10,000. Every step to the left adds
one more zero, because every step to the left means ×10.

Tip: The comma is written after the thousands digit. It splits 10,000 into 10 and 000,
which is why we say ten thousand.

Q2 Do you remember how we read and write numbers in the Indian place value
system? We use the same ten digits 0–9 in different places to write larger numbers.
For example, 1,380 = 1 Thousand + 3 Hundreds + 8 Tens + 0 Ones. 9,123 = 9 Thousands
+ 1 Hundred + 2 Tens + 3 Ones.

Yes. We have only ten digits — 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. What makes a number big is not a new
digit but the place a digit sits in.
1,380 broken up:

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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

1 Thousand = 1,000

3 Hundreds = 300

8 Tens = 80
0 Ones = 0

1,000 + 300 + 80 + 0 = 1,380

9,123 broken up:

9 Thousands = 9,000

1 Hundred = 100

2 Tens = 20

3 Ones = 3

9,000 + 100 + 20 + 3 = 9,123

Why it happens: The same digit 1 is worth 1,000 in 1,380 but only 100 in 9,123. Its
value comes from where it stands. That is the whole idea of a place value system.

Check it yourself: Write 3,081. Which digit is worth nothing here? The 0 in the
hundreds place. But you cannot remove it — without it the number becomes 381,
which is quite different. A zero holds the place open.

In-text Questions — Pages 3–4
Writing and naming numbers beyond 10,000 (token table)

Q1 Page 3, row 5. Tokens: 10,000 + 10 + 10 + 10 + 1 + 1 + 1. Number Name: Ten thousand
thirty-three. Fill in the Number and the digits in the TTh, Th, H, T and O columns.

The number is 10,033.
Step 1 — add up the tokens.

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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

One 10,000 token = 10,000

Three 10 tokens = 30

Three 1 tokens = 3
10,000 + 30 + 3 = 10,033

Step 2 — put each digit in its column.

NUMBER TTH TH H T O

10,033 1 0 0 3 3

Why the two zeros: There is no 1,000 token and no 100 token in the row. So the
thousands place and the hundreds place get 0. Those zeros are needed to keep the 1
sitting in the ten-thousands place.

Q2 Page 3, last row. Number: 10,458. Number Name: Ten thousand four hundred fifty-
eight. Fill in the digits in the TTh, Th, H, T and O columns.

Read the number from the left, one digit to one column.

NUMBER TTH TH H T O

10,458 1 0 4 5 8

Check with the tokens shown in the book:

One 10,000 token = 10,000

Four 100 tokens = 400

Five 10 tokens = 50

Eight 1 tokens = 8

10,000 + 400 + 50 + 8 = 10,458 ✓

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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Q3 Page 4, row 1. Tokens: 10,000 + 1,000 + 100 + 100 + 10 + 1 + 1 + 1 + 1. Digits given: TTh
= 1, Th = 1, H = 2, T = 1, O = 4. Fill in the Number and the Number Name.

The number is 11,214, read as eleven thousand two hundred fourteen.
Step 1 — add up the tokens.

10,000

+ 1,000

+ 100 + 100 = 200

+ 10

+1+1+1+1=4

Total = 11,214

Step 2 — check against the digits already printed.

TTh = 1, Th = 1, H = 2, T = 1, O = 4 → 1 1 2 1 4 → 11,214 ✓

Step 3 — say the name. Split at the comma: 11 | 214.

11 thousand … 214 → eleven thousand two hundred fourteen

Q4 Page 4, row 2. Number: 13,520. Number Name: Thirteen thousand five hundred
twenty. Fill in the digits in the TTh, Th, H, T and O columns.

NUMBER TTH TH H T O

13,520 1 3 5 2 0

Check with the tokens:

Page 8 of 78

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Class 5 Maths Chapter 1 We the Travellers—I
a g l AglaSem · NCERT Solutions

co m
em.
One 10,000 + three 1,000 tokens = 13,000
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Five 100 tokens = 500
m a g
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Two 10 tokens = 20
a13,000 + 500 + 20 = 13,520 ✓

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Tip: There is no 1 token in this row, so the ones place is 0. That is why the name
g
stops at twenty. a

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m l as
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Q5 Page 4, row 3. Number: 20,000. Number Name: Twenty thousand. Fill in the digits in

a s em the TTh, Th, H, T and O columns.
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agANSWER
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NUMBER TTH H T O

20,000
a2 gl 0 0 0 0

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Two 10,000 tokens = 10,000 + 10,000 = 20,000
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a s eWhy
agl four zeros: Twenty thousand means 2 in the ten-thousands place and nothing
anywhere else. The four zeros are there to hold the 2 in its place. Remove them and
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you would be left with 2.
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Q6 Page 4, row 4. Number: 45,867. Number Name: Forty-five thousand eight hundred
sixty-seven. Fill in the digits in the TTh, Th, H, T and O columns.
co m
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m as e
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a g l
a s em
agl NUMBER TTH TH H T O

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45,867 4 5 8 6 7

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Check with the tokens shown in the book:
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a

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m as e
.co


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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Four 10,000 tokens = 40,000

Five 1,000 tokens = 5,000

Eight 100 tokens = 800
Six 10 tokens = 60

Seven 1 tokens = 7

40,000 + 5,000 + 800 + 60 + 7 = 45,867 ✓

Tip: To read any 5-digit number, look at the comma. 45 before it and 867 after it. Say
the first part, add the word thousand, then say the second part: forty-five thousand,
eight hundred sixty-seven.

Let Us Do — Page 5
Question 1 — continuing number patterns

LET US DO

Q1 1. Fill in the blanks by continuing the pattern in each of the following sequences.
Discuss the patterns in class. (a)

456 567 678

Sequence (a) as printed on page 5 — three numbers are given and four boxes are empty.

Step 1 — find the jump. Take one number away from the next one.

567 – 456 = 111

678 – 567 = 111

So the rule is: add 111 each time.

Step 2 — keep adding 111.

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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

678 + 111 = 789

789 + 111 = 900

900 + 111 = 1,011
1,011 + 111 = 1,122

The full chain:

456 → 567 → 678 → 789 → 900 → 1,011 → 1,122

Discuss in class: The first four numbers look like a staircase — 456, 567, 678, 789.
Each digit goes up by 1. But the pattern of digits breaks at 900, because 789 + 111
needs carrying. The rule add 111 never breaks, only the pretty look of the digits
does.

Q2 1. (b) 1,050 → __ → 3,150 → 4,200 → __ → __ → __

Step 1 — find the jump. Use two numbers that are next to each other.

4,200 – 3,150 = 1,050

So the rule is: add 1,050 each time.

Step 2 — fill the gap in the middle.

1,050 + 1,050 = 2,100

Check: 2,100 + 1,050 = 3,150 ✓

Step 3 — carry on to the end.

4,200 + 1,050 = 5,250

5,250 + 1,050 = 6,300

6,300 + 1,050 = 7,350

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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

1,050 → 2,100 → 3,150 → 4,200 → 5,250 → 6,300 → 7,350

Tip: These are the numbers you get by counting in 1,050s — 1 × 1,050, 2 × 1,050, 3 ×
1,050 and so on. The seventh one is 7 × 1,050 = 7,350 ✓

Q3 1. (c) 5,501 → 6,401 → 7,301 → __ → __ → __ → __

Step 1 — find the jump.

6,401 – 5,501 = 900

7,301 – 6,401 = 900

Rule: add 900 each time.

Step 2 — keep adding 900.

7,301 + 900 = 8,201

8,201 + 900 = 9,101
9,101 + 900 = 10,001

10,001 + 900 = 10,901

5,501 → 6,401 → 7,301 → 8,201 → 9,101 → 10,001 → 10,901

Discuss in class: Watch what happens at 9,101 + 900. The hundreds are 1 + 9 = 10
hundreds, which is a whole thousand. That thousand joins the 9 thousands to make
10 thousands — and a 5-digit number appears: 10,001.

Q4 1. (d) 10,100 → 10,200 → 10,300 → __ → __ → __ → __ ↓ __ ← 10,900 ← __

Step 1 — find the jump.

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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

10,200 – 10,100 = 100 → rule: add 100 each time.

Step 2 — finish the top row (it runs left to right).

10,300 + 100 = 10,400

10,400 + 100 = 10,500

10,500 + 100 = 10,600

10,600 + 100 = 10,700

Step 3 — the arrow turns down, then the bottom row runs right to left.

10,700 + 100 = 10,800 (bottom row, right box)

10,800 + 100 = 10,900 (already printed ✓)
10,900 + 100 = 11,000 (bottom row, left box)

The full chain: 10,100 · 10,200 · 10,300 · 10,400 · 10,500 · 10,600 · 10,700 · 10,800 · 10,900 ·
11,000

Check it yourself: The printed 10,900 lands exactly where our counting says it
should. That is a good sign the rule is right.

Q5 1. (e) 10,105 → 10,125 → __ → __ → __ → __ → __ ↓ __ ← __ ← __

Step 1 — find the jump.

10,125 – 10,105 = 20 → rule: add 20 each time.

Step 2 — top row, left to right.

Page 13 of 78

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Class 5 Maths Chapter 1 We the Travellers—I
a g l AglaSem · NCERT Solutions

co m
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10,125 + 20 = 10,145
m l as
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10,145 + 20 = 10,165
m a g
l a se
g
10,165 + 20 = 10,185
a10,185 + 20 = 10,205

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10,205 + 20 = 10,225

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g to left.
Step 3 — down, then bottom rowaright

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10,225 + 20 = 10,245

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10,245 + 20 = 10,265
a g l
a s em + 20 = 10,285
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10,265
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The full chain: 10,105 · 10,125 · 10,145 · 10,165 · 10,185 · 10,205 · 10,225 · 10,245 · 10,265 ·
a s
10,285
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l a se
a g
Discuss in class: Every number in this chain ends in 5. That is because we started at
a number ending in 5 and kept adding 20 — and 20 never changes the ones digit.

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a s em
Q6 1. (f) 10,992 → 10,993 → __ → __ → __ → __ → __ ↓ __ ← __ ← __

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Step 1 — find the jump.
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10,993 – 10,992 = 1 → rule: add 1 each time.

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Step 2 — just count on.

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m 10,994 · 10,995 · 10,996 · 10,997 · 10,998 · 10,999 · 11,000 · 11,001 a g
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The full chain: 10,992 · 10,993 · 10,994 · 10,995 · 10,996 · 10,997 · 10,998 · 10,999 · 11,000 ·
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11,001

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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Discuss in class: The interesting box is the one after 10,999. Nine hundreds, nine
tens and nine ones are all full. Adding one more makes them all roll over to 0 and
pushes 1 into the thousands: 10,999 + 1 = 11,000. This is exactly like an odometer in
a bus turning over.

Q7 1. (g) 10,794 → 10,796 → 10,798 → __ → __ → __ → __ ↓ __ ← __ ← __

Step 1 — find the jump.

10,796 – 10,794 = 2

10,798 – 10,796 = 2 → rule: add 2 each time.

Step 2 — keep adding 2.

10,798 + 2 = 10,800

10,800 + 2 = 10,802

10,802 + 2 = 10,804

10,804 + 2 = 10,806
10,806 + 2 = 10,808

10,808 + 2 = 10,810

10,810 + 2 = 10,812

The full chain: 10,794 · 10,796 · 10,798 · 10,800 · 10,802 · 10,804 · 10,806 · 10,808 · 10,810 ·
10,812

Tip: Every number here is even, because we started at an even number and kept
adding 2.

Q8 1. (h) 73,005 → 72,004 → __ → __ → __ → __ → __ ↓ __ ← __ ← __

This chain goes down, not up.

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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Step 1 — find the jump.

73,005 – 72,004 = 1,001 → rule: take away 1,001 each time.

Step 2 — keep subtracting 1,001. An easy way: take away 1,000, then take away 1 more.

72,004 – 1,001 = 71,003

71,003 – 1,001 = 70,002

70,002 – 1,001 = 69,001

69,001 – 1,001 = 68,000

68,000 – 1,001 = 66,999

66,999 – 1,001 = 65,998

65,998 – 1,001 = 64,997

64,997 – 1,001 = 63,996

The full chain: 73,005 · 72,004 · 71,003 · 70,002 · 69,001 · 68,000 · 66,999 · 65,998 · 64,997 ·
63,996

Discuss in class: Look at 68,000 – 1,001. There are no ones and no thousands to
take from, so we have to borrow — and the answer jumps to 66,999, not 67,999.
Many children make this slip. Always take away 1,000 first, then the extra 1.

Q9 1. (i) 82,350 → 83,350 → __ → __ → __ → __ → __ ↓ __ ← __ ← __

Step 1 — find the jump.

83,350 – 82,350 = 1,000 → rule: add 1,000 each time.

Step 2 — keep adding 1,000. Only the thousands digit changes.

84,350 · 85,350 · 86,350 · 87,350 · 88,350 · 89,350 · 90,350 · 91,350

Page 16 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

The full chain: 82,350 · 83,350 · 84,350 · 85,350 · 86,350 · 87,350 · 88,350 · 89,350 · 90,350 ·
91,350

Discuss in class: Notice 89,350 + 1,000. Nine thousands plus one more thousand
makes ten thousands, which carries into the ten-thousands place: 8 becomes 9 and
the thousands digit becomes 0 → 90,350.

Let Us Do — Pages 6–7
Questions 2 to 5 — number names, order, comparing and digit swap

LET US DO

Q1 2. Fill in the blanks appropriately. Use commas as required. (Table of Numbers and
Number Names: 8,045 · 7,209 · 10,599 · Ten thousand seven hundred forty-three ·
20,869 · 13,579 · Ten thousand ten · Fifty-six thousand four hundred ninety-one ·
45,045 · 39,593 · 50,005 · 26,050 · 81,200 · Ninety thousand nine · Twenty-three
thousand two hundred thirty · Thirty-six thousand one)

Here is the whole table filled in. The orange cells are the ones you had to write.

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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

NUMBER NUMBER NAME

8,045 Eight thousand forty-five

7,209 Seven thousand two hundred nine

10,599 Ten thousand five hundred ninety-nine

10,743 Ten thousand seven hundred forty-three

20,869 Twenty thousand eight hundred sixty-nine

13,579 Thirteen thousand five hundred seventy-nine

10,010 Ten thousand ten

56,491 Fifty-six thousand four hundred ninety-one

45,045 Forty-five thousand forty-five

39,593 Thirty-nine thousand five hundred ninety-three

50,005 Fifty thousand five

26,050 Twenty-six thousand fifty

81,200 Eighty-one thousand two hundred

90,009 Ninety thousand nine

23,230 Twenty-three thousand two hundred thirty

36,001 Thirty-six thousand one

How to turn a number into its name — 3 steps.

1. Look at the comma. Read the part on its left, then say the word thousand.
2. Read the part on its right like an ordinary 3-digit number.
3. If a place has 0, say nothing for it.

45,045 → 45 thousand … 045 → forty-five thousand forty-five

How to turn a name into a number — 3 steps.

1. Write the thousands part first. Ninety thousand → 90.
2. Write the rest as a 3-digit block, filling with zeros. Nine → 009.
3. Join them and put in the comma: 90,009.

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Class 5 Maths Chapter 1 We the Travellers—I
a g l AglaSem · NCERT Solutions

co m
m.
Why zeros matter: Ninety thousand nine is 90,009, not 90,900 and not 909. The zeros

m as e
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in the hundreds and tens places show that there are no hundreds and no tens.

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Q2 3. Arrange the numbers below in increasing order. You can use the number line

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below, if required.

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40,347 34,407 40,473 34,740 73,404 74,430 47,340 18,926

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m l as
m .co 0 20,000 40,000
a g
60,000 80,000

l a se
a g The eight numbers and the number line printed on page 6.

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Increasing order means smallest first.

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18,926 < 34,407 < 34,740 < 40,347 < 40,473 < 47,340 < 73,404 < 74,430
m .
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.c sort them — compare from the left. a g
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s1.e Look at the ten-thousands digit first. They are 1, 3, 3, 4, 4, 4, 7, 7. So 18,926 (a 1) is the
How to

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smallest, and the two numbers starting with 7 are the biggest.

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2. Where two numbers tie, move one place right. 34,407 and 34,740 both start 34. Compare

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the hundreds: 4 against 7. So 34,407 is smaller.

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3. Keep moving right until they l asdiffer. 40,347 and 40,473 both start 40. Hundreds: 3 against
4. So 40,347 is smaller. a

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4. 73,404 and 74,430: thousands digit 3 against 4. So 73,404 is smaller.

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Roughly where they sit on the number line:
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l a se
ag 34,407 · 34,740 47,340
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18,926 40,347 · 40,473 73,404 · 74,430
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20,000em
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0 40,000 60,000 80,000

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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

The eight numbers marked on the number line from 0 to 80,000.

Tip: All eight numbers here have 5 digits, so counting digits does not help.
Comparing digit by digit from the left always does.

Q3 4. A student said 9,990 is greater than 49,014 because 9 is greater than 4. Is the
student correct? Why or why not?

No, the student is not correct. 49,014 is the bigger number.
Step 1 — count the digits.

9,990 has 4 digits

49,014 has 5 digits

A 5-digit number is always bigger than a 4-digit number.

Step 2 — line them up in the place value chart.

TTH TH H T O

9,990 0 9 9 9 0

49,014 4 9 0 1 4

In the TTh column, 9,990 has nothing (0) and 49,014 has 4. So 49,014 wins straight away.

Where the student went wrong: They compared the first digit they saw — the 9 of
9,990 and the 4 of 49,014. But those two 9 and 4 are not in the same column. The 9
of 9,990 is worth 9,000. The 4 of 49,014 is worth 40,000. You may only compare digits
that sit in the same place.

Tip: Always compare the number of digits first. Only if the digit counts are equal do
you go place by place from the left.

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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Q4 4. Use the number line below to find the position of the numbers. Fill in the blanks.

5,000 10,000 50,000

TTh Th H T O

9 9 9 0

4 9 0 1 4

You can use this place value chart to compare the
numbers.

The number line and the place value chart printed on page 7. Nine boxes are yours to
fill.

Step 1 — find the size of one step.

10,000 – 5,000 = 5,000

So each box goes up by 5,000.

Step 2 — fill the seven empty boxes.

5,000 · 10,000 · 15,000 · 20,000 · 25,000 · 30,000 · 35,000 · 40,000 · 45,000 · 50,000

Check: the last box works out to 50,000, exactly as printed. ✓
Step 3 — place the two numbers.

9,990 sits just before the 10,000 mark — only 10 short of it.
49,014 sits just after the 45,000 mark, close to 50,000.

49,014
9,990

5,000 10,000 15,000 20,000 25,000 30,000 35,000 40,000 45,000 50,000

Page 21 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

9,990 is just short of 10,000; 49,014 is almost at 50,000. The picture makes it obvious which is bigger.

Q5 5. Digit swap. (a) In the number 1,478, interchanging the digits 7 and 4 gives 1,748.
Now, interchange any two digits in the number 1,478 to make a number that is
larger than 5,500.

Two swaps work. Either one is a correct answer.

Swap the 1 and the 7 : 1,478 → 7,418

Swap the 1 and the 8 : 1,478 → 8,471

How to find them — think about the thousands place.

1. To be larger than 5,500, the number must start with a digit bigger than 5.
2. The digits available are 1, 4, 7, 8. The ones bigger than 5 are 7 and 8.
3. So bring the 7 to the front (swap it with the 1) → 7,418. Or bring the 8 to the front → 8,471.
4. Check: 7,418 > 5,500 ✓ and 8,471 > 5,500 ✓

Check the other swaps: 4,178 (swap 1 and 4), 1,748 (swap 4 and 7), 1,874 (swap 4
and 8) and 1,487 (swap 7 and 8) are all smaller than 5,500. Only the two above work.

Q6 5. (b) Interchange two digits of 10,593 to make a number i) Between 11,000 and
15,000. ii) More than 35,000.

The digits of 10,593, in order, are 1 · 0 · 5 · 9 · 3.
(i) Between 11,000 and 15,000 → 13,590

1. The number must still start with 1, and its thousands digit must be 1, 2, 3 or 4.
2. The thousands digit is now 0. Swap it with the 3 at the end.
3. 10,593 → 13,590
4. Check: 11,000 < 13,590 < 15,000 ✓

(ii) More than 35,000 → 50,193 (or 90,513)

1. The ten-thousands digit is only 1. Put a bigger digit there.
2. Swap the 1 with the 5: 10,593 → 50,193. Check: 50,193 > 35,000 ✓
3. Or swap the 1 with the 9: 10,593 → 90,513. Check: 90,513 > 35,000 ✓

Page 22 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Careful: Swapping the 1 with the 3 gives 30,591, and 30,591 is less than 35,000. So
that swap does not work.

Q7 5. (c) Interchange two digits of 48,247 to make a number i) As small as possible. ii)
As big as possible.

The digits of 48,247, in order, are 4 · 8 · 2 · 4 · 7.
(i) As small as possible → 28,447

1. The first digit matters most, so make it as small as you can.
2. The smallest digit in the number is 2. It sits in the hundreds place.
3. Swap the leading 4 with that 2. The 4 moves into the hundreds place.
4. 48,247 → 28,447

(ii) As big as possible → 84,247

1. Make the first digit as large as you can.
2. The largest digit in the number is 8. It sits in the thousands place.
3. Swap the leading 4 with that 8.
4. 48,247 → 84,247

Why the first digit decides: The first digit of a 5-digit number counts ten-
thousands. Changing it by 1 changes the number by 10,000. No swap further to the
right can make up for that. So always fix the first digit first.

Nearest Tens (10s), Hundreds (100s), and Thousands (1,000s) — Pages 7–8
Nearest Tens (10s), Hundreds (100s), and Thousands (1,000s)

Q1 The rabbit is at 2,346. Its food has been kept at its neighbouring tens. On which
tens should the rabbit go to get its food, with the least number of steps?

The rabbit should go to 2,350.

Page 23 of 78

as e
Class 5 Maths Chapter 1 We the Travellers—I
a g l AglaSem · NCERT Solutions

co m
m.
se 2,350
om a
2,346
.
2,340
c ag l
s e m
a
agl 6 steps back 4 steps forward

co m
e m . ag
as
2,346 sits between 2,340 and 2,350. It is nearer to 2,350.

a g l
Step 1 — name the two neighbouring tens. They are 2,340 and 2,350.
Step 2 — measure the two distances.
co m
em.
m l as
.co a g
em– 2,346 = 4 steps
2,346 – 2,340 = 6 steps

a s
a gl 2,350

m a s
.co agl
Step 3 — pick the shorter one. 4 is less than 6, so the rabbit goes forward to 2,350, needing 4
jumps.
se m
g l a
a
Why it happens: Look only at the ones digit, 6. If the ones digit is 5 or more, the

m
number is past the middle, so the nearest ten is the one ahead. If it is 4 or less, the
. co
m
nearest ten is the one behind.

m as e
.co a g l
s m the nearest ten of 2,346 is 2,350.
eSo:
gl a
a
se m
o m
c been kept at its neighbouring hundreds. Which of ag
The rabbit is at 2,346. Its food .has
l a
Q2
the two hundreds shouldsthe
m
e rabbit go to? ______ is the nearest hundred of 2,346. It
l a
agto reach ______.
will need ______ jumps

co m
m .
m as e
.co l
2,300 is the nearest hundred of 2,346. It will need 46 jumps to reach 2,300.
a g
se m
g l a
a c
2,346
m .
2,300
m
2,400
a s e
.co agl
2,350 (middle)

se m
g l a
46 jumps back 54 jumps forward
a

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m .
m ase
.co


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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

2,346 is on the left half of the road from 2,300 to 2,400, so 2,300 is nearer.

Step 1 — name the two neighbouring hundreds. 2,300 and 2,400.
Step 2 — measure both distances.

2,346 – 2,300 = 46

2,400 – 2,346 = 54

Step 3 — pick the shorter one. 46 < 54, so the rabbit goes back to 2,300.

A quicker way: The halfway mark between 2,300 and 2,400 is 2,350. Our number
2,346 has not yet reached 2,350, so it is still closer to 2,300. Just look at the last two
digits: 46 is less than 50.

Q3 The rabbit is at 2,346. Its food has been kept at its neighbouring thousands. Which
number should the rabbit go to? ______ is the nearest thousand of 2,346. It will need
______ jumps to reach ______.

2,000 is the nearest thousand of 2,346. It will need 346 jumps to reach 2,000.

2,346
2,000 3,000
2,500 (middle)

346 jumps back 654 jumps forward

2,346 has not yet crossed the middle mark 2,500, so 2,000 is its nearest thousand.

Step 1 — name the two neighbouring thousands. 2,000 and 3,000.
Step 2 — measure both distances.

2,346 – 2,000 = 346

3,000 – 2,346 = 654

Step 3 — pick the shorter one. 346 < 654, so the rabbit goes back to 2,000.

Page 25 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

A quicker way: The middle of 2,000 and 3,000 is 2,500. Look at the last three digits
of 2,346 — they are 346, which is less than 500. So the number is still in the first half,
and 2,000 is nearer.

Q4 Fill in the boxes appropriately. Number / Nearest Tens / Nearest Hundreds / Nearest
Thousands, for 3,176 · 4,017 · 5,789 · 8,203.

NUMBER NEAREST TENS NEAREST HUNDREDS NEAREST THOUSANDS

3,176 3,180 3,200 3,000

4,017 4,020 4,000 4,000

5,789 5,790 5,800 6,000

8,203 8,200 8,200 8,000

The three rules, in one line each.

1. Nearest ten: look at the ones digit. 5 or more → go up. 4 or less → go down.
2. Nearest hundred: look at the last two digits. 50 or more → go up. 49 or less → go down.
3. Nearest thousand: look at the last three digits. 500 or more → go up. 499 or less → go
down.

Worked out, row by row.

3,176 → ones is 6 (≥5) → 3,180 ; last two are 76 (≥50) → 3,200 ; last three are 176 (<500)

→ 3,000

4,017 → ones is 7 (≥5) → 4,020 ; last two are 17 (<50) → 4,000 ; last three are 017 (<500)

→ 4,000

5,789 → ones is 9 (≥5) → 5,790 ; last two are 89 (≥50) → 5,800 ; last three are 789 (≥500)

→ 6,000

8,203 → ones is 3 (<5) → 8,200 ; last two are 03 (<50) → 8,200 ; last three are 203 (<500)
→ 8,000

Page 26 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Did you notice? For 4,017 the nearest hundred and the nearest thousand are the
same number, 4,000. For 8,203 the nearest ten and the nearest hundred are both
8,200. This can happen, and Question 3 of Let Us Think asks you to find more such
numbers.

Let Us Think — Pages 8–9
Rounding off, and numbers that share the same neighbour

LET US THINK

Q1 1. Vijay rounded off a number to the nearest hundred. Suma rounded off the same
number to the nearest thousand. Both got the same result. Circle the numbers they
might have used. 7,126 · 7,835 · 7,030 · 6,999

Circle 7,030 and 6,999.
Step 1 — round each number to the nearest hundred (look at the last two digits).
Step 2 — round each number to the nearest thousand (look at the last three digits).
Step 3 — see where the two answers match.

NUMBER VIJAY: NEAREST HUNDRED SUMA: NEAREST THOUSAND SAME?

7,126 7,100 7,000 No

7,835 7,800 8,000 No

7,030 7,000 7,000 Yes ✓
6,999 7,000 7,000 Yes ✓

Why these two: Rounding to the nearest hundred and to the nearest thousand give
the same answer only when the number is sitting very close to a whole thousand.
7,030 is 30 above 7,000. 6,999 is just 1 below 7,000. Both land on 7,000 either way.

Try This: Find two more numbers that work. Any number from 6,950 up to 7,049 will
do, because all of them round to 7,000 both ways.

Page 27 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Q2 2. Think and write two numbers that have the same — (a) Nearest ten. (For
example, 19 and 21 have the same nearest ten, that is, 20.)

Sample answer: 71 and 73. Both have nearest ten 70.

71 → ones digit 1, which is less than 5 → nearest ten is 70

73 → ones digit 3, which is less than 5 → nearest ten is 70

How to make your own pair — 3 steps.

1. Choose any ten, say 250.
2. Numbers from 245 to 254 all round to 250.
3. Pick any two from that list, for example 246 and 253.

More correct answers: 3,171 and 3,174 (both → 3,170) · 8,896 and 8,899 (both →
8,900) · 45 and 54 (both → 50).

Q3 2. (b) Nearest hundred.

Sample answer: 512 and 549. Both have nearest hundred 500.

512 → last two digits 12, less than 50 → nearest hundred is 500

549 → last two digits 49, less than 50 → nearest hundred is 500

How to make your own pair — 3 steps.

1. Choose any hundred, say 3,600.
2. Numbers from 3,550 to 3,649 all round to 3,600.
3. Pick any two, for example 3,562 and 3,631.

More correct answers: 2,780 and 2,812 (both → 2,800) · 9,951 and 10,020 (both →
10,000).

Page 28 of 78

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Class 5 Maths Chapter 1 We the Travellers—I
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co m
m.
2. (c) Nearest thousand.
e
Q4

m l as
.co a g
a
s em
agl answer: 4,120 and 4,480. Both have nearest thousand 4,000.
Sample

co m
. ag
4,120 → last three digits 120, less than 500 → nearest thousand is 4,000
e m
g l as
4,480 → last three digits 480, less than 500 → nearest thousand is 4,000
a
How to make your own pair — 3 steps.
co m
em.
as
1. Choose any thousand, say 26,000.
m l
.co
2. Numbers from 25,500 to 26,499 all round to 26,000.
m a g
l a se
3. Pick any two, for example 25,690 and 26,340.

a g
Tip: A whole thousand has 999 other numbers rounding to it — 500 below it and 499
m a s
.co agl
above it. So there are plenty of correct answers.

se m
g l a
a
m
3. Think and write the numbers that have the same — (a) Nearest ten and nearest

co
Q5
hundred.
m .
as e
. com a g l
em answer: 302.

a s
agl Sample

se m
com g l a
.
Nearest ten of 302 → ones digit 2, less than 5 → 300
m a
ase
agl
Nearest hundred of 302 → last two digits 02, less than 50 → 300

Both are 300, so they match ✓

co m
m .
e
How to find such numbers.
m l as
.co
1. Start from any whole hundred, say 300.
a g
a s em2. Take a number very close to it — within 4 on either side is safest.
agl
c
3. Examples: 297, 298, 301, 302, 303, 304. All of them have nearest ten 300 and nearest

m .
e
hundred 300.
m a s
e m . co agl
g l as
a

co m
m .
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.co


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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Why closeness matters: The nearest hundred can only be a whole hundred. So for
the two answers to match, the nearest ten must itself be a whole hundred. That
happens only when the number is huddled around a whole hundred — from 95
below to 49 above it, roughly. For example 8,246: nearest ten 8,250, nearest hundred
8,200 — these do not match.

More correct answers: 4,999 (ten → 5,000, hundred → 5,000) · 7,103 (ten → 7,100,
hundred → 7,100).

Q6 3. (b) Nearest hundred and nearest thousand.

Sample answer: 4,020.

Nearest hundred of 4,020 → last two digits 20, less than 50 → 4,000

Nearest thousand of 4,020 → last three digits 020, less than 500 → 4,000

Both are 4,000 ✓

How to find such numbers.

1. Pick a whole thousand, say 9,000.
2. Stay within about 49 of it on either side.
3. Examples: 8,970 · 8,999 · 9,010 · 9,043. All give 9,000 both ways.

This is the same idea as Question 1 above: 7,030 and 6,999 were exactly numbers
of this kind.

Q7 3. (c) Nearest ten, hundred and thousand.

Sample answer: 5,002. All three roundings give 5,000.

Page 30 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Nearest ten → ones digit 2, less than 5 → 5,000

Nearest hundred → last two digits 02, less than 50 → 5,000

Nearest thousand → last three digits 002, less than 500 → 5,000

Another one: 2,998.

Nearest ten → ones digit 8, 5 or more → 3,000

Nearest hundred → last two digits 98, 50 or more → 3,000
Nearest thousand → last three digits 998, 500 or more → 3,000

How to find such numbers — 2 steps.

1. Pick any whole thousand, for example 6,000.
2. Take a number within 4 of it: 5,996 · 5,997 · 5,998 · 5,999 · 6,001 · 6,002 · 6,003 · 6,004. Every
one of them rounds to 6,000 all three ways.

Why it must be so close: All three answers must be the same number, and the
nearest thousand is always a whole thousand. So the nearest ten must also be that
whole thousand — and that only happens when the number is within 5 of it.

Let Us Do — Page 10
Travelling, Now and Then — speed and how many vehicles

LET US DO

Q1 1. A cyclist can cover 15 km in one hour. How much distance will she cover in 4
hours, if she maintains the same speed?

She will cover 60 km.
Step 1 — name what we know. In 1 hour she covers 15 km, and her speed does not change.
Step 2 — add hour by hour.

Page 31 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

After 1 hour : 15 km

After 2 hours : 15 + 15 = 30 km

After 3 hours : 30 + 15 = 45 km
After 4 hours : 45 + 15 = 60 km

Step 3 — the short way.

4 × 15 = 60 km

Check it yourself: Go backwards. 60 ÷ 4 = 15 km in one hour, which is what the
question said. ✓

Why multiplying works: Each hour adds the same 15 km. Adding the same number
4 times is exactly what 4 × 15 means. Multiplication is a short way of doing repeated
addition.

Q2 2. A school has 461 girls and 439 boys. How many vehicles are needed for all of them
to go on a trip using the following modes of travel? (a) Bicycle (2)

Step 1 — find the total number of children.

461 girls + 439 boys

461 + 439 = 900 children

Step 2 — one bicycle carries 2 people. Share 900 into groups of 2.

900 ÷ 2 = 450

Answer: 450 bicycles are needed.

Check it yourself: 450 × 2 = 900 ✓ Everyone gets a seat and no bicycle is left half
empty.

Page 32 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Keep 900 in mind: Every part of this question uses the same 900 children. Only the
number of people per vehicle changes.

Q3 2. (b) Autorickshaw (3)

Total children = 900. One autorickshaw carries 3.

900 ÷ 3 = 300

Answer: 300 autorickshaws.

Check it yourself: 300 × 3 = 900 ✓

Tip: 900 ÷ 3 is easy if you think of it as 9 hundreds shared among 3 → 3 hundreds
each → 300.

Q4 2. (c) Car (4)

Total children = 900. One car carries 4.

900 ÷ 4

4 × 200 = 800, leaving 100
4 × 25 = 100, leaving 0

200 + 25 = 225

Answer: 225 cars.

Check it yourself: 225 × 4 = 900 ✓

Page 33 of 78

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Class 5 Maths Chapter 1 We the Travellers—I
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co m
m.
2. (d) Big car (6)
e
Q5

m l as
.co a g
a s em
aglchildren = 900. One big car carries 6.
Total

co m
. ag
900 ÷ 6
e m
6 × 100 = 600, leaving 300
g l as
6 × 50 = 300, leaving 0
a

co m
m.
100 + 50 = 150

as e
combig cars.
Answer: .150 a g l
a s em
agl Check it yourself: 150 × 6 = 900 ✓

om a s
e
. c
mas an autorickshaw, so we need one third as agl
s
Tip: A big car holds 3 times as many

a
many vehicles: 300 ÷ 2 … no —
gla300 was for 3 people, and 6 is double 3, so 300 ÷ 2 =
150 ✓

co m
m .
as e
om
Q6 .c2. (e) Tempo traveller (10) a g l
a s em
l
ag ANSWER
se m
Total children = 900. One tempo traveller carries 10.
com g l a
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ase
900 ÷ 10 = 90
agl

co m
.
Answer: 90 tempo travellers.

em
m l as
m .co a g
Why it is so quick: Dividing by 10 just removes one zero from the end. 900 → 90.

l a se
ag
.c
s e m
m a
co agl
2. (f) Boat (20)
.
Q7

e m
g l as
a
Total children = 900. One boat carries 20.

co m
m .
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.co


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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

900 ÷ 20

20 × 40 = 800, leaving 100

20 × 5 = 100, leaving 0

40 + 5 = 45

Answer: 45 boats.

Check it yourself: 45 × 20 = 900 ✓

Q8 2. (g) Minibus (25)

Total children = 900. One minibus carries 25.

900 ÷ 25

25 × 20 = 500, leaving 400

25 × 16 = 400, leaving 0

20 + 16 = 36

Answer: 36 minibuses.

Check it yourself: 36 × 25 = 900 ✓ (Think of 25 as a quarter of 100: four 25s make
100, so 36 twenty-fives make 9 hundreds.)

Q9 2. (h) Aeroplane (180)

Total children = 900. One aeroplane carries 180.

Page 35 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

900 ÷ 180

180 × 5 = 900, leaving 0

So the answer is 5

Answer: 5 aeroplanes.

Check it yourself: 180 × 5 = 900 ✓

Look at the whole list: 450 bicycles · 300 autos · 225 cars · 150 big cars · 90 tempo
travellers · 45 boats · 36 minibuses · 5 aeroplanes. The bigger the vehicle, the fewer
you need. The number of children never changed — only the size of the groups did.

Finding Large Numbers Around Us — Pages 10–11
Finding Large Numbers Around Us

TRY THIS

Q1 Find something in the textbook whose count is a 4-digit number.

A 4-digit number is anything from 1,000 to 9,999. Do not count one by one — estimate, which
means make a careful guess using multiplication.
Method — 3 steps.

1. Count the thing carefully on ONE page.
2. Count how many pages there are.
3. Multiply.

Sample answer: The number of words in this chapter.
One page has about 150 words. The chapter has 16 pages.
150 × 16 = 2,400 words — a 4-digit number.

Other good answers:

The number of letters printed on one page (about 900–1,200).
The number of full stops in the whole book.
The number of squares in all the grids and tables of the book.

Page 36 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Q2 Now, let us try this with our school. (a) Our school has ________ classrooms.

This is about your own school, so go and count.
Method — 3 steps.

1. Walk down each corridor and count the rooms where classes are held.
2. Do not count the office, the store room or the toilets.
3. Add the counts from every floor.

Sample answer: Our school has 12 classrooms — 5 on the ground floor and 7 on
the first floor.

Notice the size: This is a 2-digit number. Not everything around us is big. Part of the
fun is finding out which counts are small and which run into thousands.

Q3 (b) There are ________ students in my class.

Count the children in your own classroom.
Method — 2 steps.

1. Count row by row, not all at once, so nobody is missed or counted twice.
2. Add the row totals. Remember to include children who are absent today.

Sample answer: My class has 38 students — 6 rows of 6, and 2 more children on the
last bench. 6 × 6 = 36, and 36 + 2 = 38.

Tip: The attendance register already has the answer. Use it to check your count.

Q4 (c) Our classroom has ________ books in total.

Count all the books in the room — textbooks, notebooks and library books.
Method — 3 steps.

Page 37 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

1. Find how many books one child has in the bag. Say 6 textbooks and 6 notebooks = 12.
2. Multiply by the number of children.
3. Add the books kept in the class cupboard.

12 books × 38 children = 456

456 + 44 books in the cupboard = 500 books

Sample answer: Our classroom has about 500 books in total.

Why we multiply: Counting 500 books one by one would take a long time and
mistakes would creep in. Finding one child's share and multiplying is faster and
safer.

Q5 Find something in the classroom whose count is a — (i) 4-digit number. (ii) 5-digit
number.

(i) A 4-digit count (1,000 to 9,999)

Sample answer: The total number of pages in all the notebooks of the class.
Each notebook has about 100 pages. Each child has 6 notebooks. There are 38
children.
100 × 6 = 600 pages per child
600 × 38 is too big — so take just 2 notebooks: 100 × 2 × 38 = 7,600 pages. A 4-digit
number.

(ii) A 5-digit count (10,000 to 99,999)

Sample answer: The number of bricks in the classroom walls.
One wall is about 6 m long and 3 m high. About 60 bricks fit along it and about 40
layers go up.
60 × 40 = 2,400 bricks in one wall
There are 4 walls: 2,400 × 4 = 9,600
Counting both the inside and the outside face of each wall doubles this: 9,600 × 2 =
19,200 bricks. A 5-digit number.

Page 38 of 78

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Class 5 Maths Chapter 1 We the Travellers—I
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Other good answers: the number of letters printed in all the textbooks in the room; the
co m
number of grains of rice in the mid-day-meal pot; the number of threads in the class curtain.
em.
m l as
.co a g
s em
The idea to hold on to: Big numbers do not come from counting faster. They come
a
gl counting a small part and then multiplying.
afrom

com
e m . ag
Q6
l as
List some quantities whose count is a 4-digit or a 5-digit number in the context of —
g
(i) A tree. a

co m
m.

m as e
l
Take a full-grown mango tree in the village.

m .co a g
l a se
WHAT WE COUNT ROUGH COUNT HOW MANY DIGITS
g
a Mangoes on the tree in one season about 1,500 4-digit

m a s
m .co about 25,000 agl
se
Leaves on the tree 5-digit

g l a
a
Flowers when the tree blossoms about 40,000 5-digit

m
Seeds dropped in a year about 1,500 4-digit

. co
a s em
com
Days the tree has been alive (about 15 years) about 5,475 4-digit

. a gl
a s
Howemto estimate the leaves — 3 steps.
agl 1. Count the leaves on one small branch. Say 120.

se m
a
2. Count the branches. Say about 200.
3. 120 × 200 = 24,000 leaves.
.com a g l
m
ase
agl
Sample answer: A mango tree has about 1,500 mangoes (4-digit) and about 25,000
leaves (5-digit).

co m
m .
m as e
.co a g l
s e mQ7 List some quantities whose count is a 4-digit or a 5-digit number in the context of —

agla (ii) Your village/town/city, or any other place of your choice.

.c
s e m
m a
c o agl

Choose your own village or townm .
a s e and fill in real figures where you can. Here is a filled-in

agl
example.

co m
m .
m ase
.co


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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

WHAT WE COUNT ROUGH COUNT HOW MANY DIGITS

People living in the village about 4,800 4-digit

Houses in the village about 1,100 4-digit

People living in a small town about 45,000 5-digit

Two-wheelers in the town about 12,000 5-digit

Trees along the town roads about 3,000 4-digit

Students in all the schools of the town about 10,500 5-digit

Where to find the real numbers.

1. The gram panchayat or municipal office keeps the population and house count.
2. The school office knows how many children study there.
3. For houses, count the houses in one lane and multiply by the number of lanes.

Sample answer: My village has about 4,800 people (4-digit) and about 1,100 houses
(4-digit). The nearest town has about 45,000 people (5-digit).

Pastime Mathematics — Pages 11–13

Page 40 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Pastime Mathematics — Sanju and Mira's puzzles on the train

TRY THIS MATH TALK

Q1 1. Mira poses the river crossing puzzle to Sanju. A boatman wants to cross a river in
a boat. He has to take a lion, a sheep, and a bundle of grass with him. He can take
one of them at a time. If the sheep and grass are left on the shore, the sheep will
eat the grass. And, if the sheep and lion are left on the shore, the lion will eat the
sheep. How can the boatman take the lion, sheep, and grass across the river? Help
him so that he can ferry the lion, sheep, and grass across the river safely, and in the
minimum number of trips.

grass lion sheep

River

boatman

The river crossing puzzle. The grass, the lion and the sheep are all on this bank; the
boatman must take them across, one at a time.

It can be done in 7 trips. The trick is that the boatman is allowed to bring something back.

Page 41 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

TRIP WHAT THE BOATMAN LEFT BEHIND ON THIS WAITING ON THE FAR
DOES SIDE SIDE

1 Takes the sheep across lion, grass sheep

2 Comes back alone lion, grass sheep

3 Takes the grass across lion sheep, grass

4 Brings the sheep back lion, sheep grass

5 Takes the lion across sheep lion, grass

6 Comes back alone sheep lion, grass

7 Takes the sheep across — lion, sheep, grass

Check every stage. The lion and the sheep are never left alone together. The sheep and the
grass are never left alone together. So nothing gets eaten.

Why the sheep goes first: The sheep is the troublemaker — it is in danger from the
lion and it is a danger to the grass. The lion and the grass, however, can safely sit
together, because a lion does not eat grass. So the sheep must be moved out of the
way first, and moved back later to keep the lion and grass apart.

Try This: Play it with three paper slips on your desk. Then try starting with the grass
instead of the sheep and see how quickly it goes wrong.

Q2 2. Sanju introduces a game called pile of pebbles to Mira. There are two piles of
pebbles. Each pile contains 7 pebbles. Each player can pick as many pebbles they
want from either of the piles. The player who picks the last pebble wins. Try this
game with your friends. Now, how do you play so that you win? To find a winning
strategy, try playing with 1 pebble in each pile, two in each, three in each, and so
on.

Play second, and always make the two piles equal again. Do that every turn and you will win.
Step 1 — try the smallest game: 1 pebble in each pile. Whatever the first player takes, one
pebble is left in the other pile, and you take it and win. So the second player wins.
Step 2 — try 2 in each pile. Say the first player takes 1 from a pile, leaving 1 and 2. You take 1
from the other pile, making it 1 and 1 — back to the game you already know you win. If instead
they take both from a pile, you take both from the other. Second player wins again.

Page 42 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Step 3 — try 3 in each. Same thing. Copy their move in the other pile, so the piles stay equal.
Step 4 — the rule for 7 and 7.

Let the other player go first.

Whatever they take from one pile, take exactly the same number from the other pile.

The piles are equal after every one of your turns.

An example game:

MOVE PLAYER TAKES PILES NOW

Start — — 7·7

1 Friend 3 from pile A 4·7

2 You 3 from pile B 4·4

3 Friend 4 from pile B 4·0

4 You 4 from pile A 0 · 0 — you took the last pebble, you win

Why copying works: As long as the piles are equal, there is always something for
you to copy — the other pile still has at least as many pebbles as your friend just
removed. So you can never get stuck. And you always leave equal piles behind,
which means your friend can never leave the table empty. The person who empties
it is always you.

Try This: Start with unequal piles, say 5 and 3. Now the first player wins: take 2 from
the pile of 5 to make it 3 and 3, and then just copy.

Page 43 of 78

as e
Class 5 Maths Chapter 1 We the Travellers—I
a g l AglaSem · NCERT Solutions

co m
m.
3. Now, it's Mira's turn. She gives a fun puzzle to Sanju: (a) Take any two different
se
Q3

o m l a
digits. (b) Make two 2-digit numbers using them. (c) Subtract the smaller number
c bigger number. Now, use the two digits in the difference
from .the g and repeat steps
m a
l a se and (c). Continue until you get a 1-digit number. Mira exclaimed, No matter
(b)
a g which two numbers you choose, you will get 9 in the end. How did Mira know what
the 1-digit number in the end would be?

co m
m . ag
l a se
agyou can ever get is a number in the 9 times table, and
Mira knew because every difference
the chain of 9s always ends at 9 itself.

co m
m.
Step 1 — see what one subtraction really does. Take the digits 3 and 7.

m as e
. conumbers a g l
e m
The two
s
are 73 and 37.

a gla73 = 7 tens + 3 ones
s
37 = 3 tens + 7 ones
com– 4 ones a
em
.
73 – 37 = (7 – 3) tens – (7 – 3) ones = 4 tens agl
a s
= 40 – 4 = 36
agl

co m
.
Step 2 — say the rule.

e m
c o m of the numbers = 9 × (difference of the two digits) glas
m . a
e
Difference
as
agl
Here: 7 – 3 = 4, and 9 × 4 = 36 ✓

se m
com g l a
.
Step 3 — so every answer is a multiple of 9. The only 2-digit multiples of 9 are 18, 27, 36, 45,
m a
ase
54, 63, 72, 81. Whichever one you land on, its two digits get subtracted again — and that gives
another multiple of 9.
a gl
Step 4 — follow the book's chain.

co m
m .
as e
com
73 – 37 = 36

.63 a g l
se m – 36 = 27

g l a
a 72 – 27 = 45
c
m .
54 – 45 = 9
m a s e
e m . co agl
g l as
a

com
m .
m ase
.co


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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Why it always stops at 9: The only 1-digit multiple of 9 is 9 itself. So once the chain
shrinks to one digit, that digit has to be 9. There is nowhere else for it to land.

Q4 (1) Observe the differences you get in each step above. Do you notice anything in
common?

The differences in the book's example are 36, 27, 45, 9. Two things are true of every one of
them.

1. Each one is in the 9 times table.
2. The digits of each one add up to 9.

DIFFERENCE IS IT 9 × SOMETHING? DIGITS ADDED

36 9×4 3+6=9

27 9×3 2+7=9

45 9×5 4+5=9

9 9×1 9

Tip: Adding the digits is a quick test for the 9 times table. If the digits of a number
add up to 9, the number is a multiple of 9.

Page 45 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Q5 (2) Try the puzzle using any other pair of digits. What is common to these
differences? What do you get in the end?

For example

(a) Take any two different digits. 3 and 7

(b) Make two 2-digit numbers 37 and 73
using them.

(c) Subtract the smaller number 73 – 37 = 36
from the bigger number.
Now use the two digits in the difference and
repeat steps (b) and (c).

The steps of Mira’s puzzle, with the book’s worked example beside them.

Take the digits 2 and 9.

Step 1 : 92 – 29 = 63

Step 2 : 63 – 36 = 27

Step 3 : 72 – 27 = 45

Step 4 : 54 – 45 = 9

Take the digits 5 and 6.

Step 1 : 65 – 56 = 9

Take the digits 1 and 4.

Step 1 : 41 – 14 = 27

Step 2 : 72 – 27 = 45

Step 3 : 54 – 45 = 9

What is common: every difference is a multiple of 9 — 63, 27, 45, 9. And you always end at 9,
however many steps it takes.

Page 46 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Why: One subtraction always gives 9 × (difference of the digits), so the answer can
only be 9, 18, 27, 36, 45, 54, 63, 72 or 81. Each of these feeds back into the machine
and gives another multiple of 9. The chain shrinks until only the single-digit multiple
of 9 is left — and that is 9.

Q6 (3) What digits can you choose so that you get a 1-digit number in the first step
itself? Give some examples. Describe the pattern in the digits.

For example

(a) Take any two different digits. 3 and 7

(b) Make two 2-digit numbers 37 and 73
using them.

(c) Subtract the smaller number 73 – 37 = 36
from the bigger number.
Now use the two digits in the difference and
repeat steps (b) and (c).

The steps of Mira’s puzzle, with the book’s worked example beside them.

Choose two digits that are next-door neighbours — digits that differ by 1.

Examples:

2 and 3 → 32 – 23 = 9

4 and 5 → 54 – 45 = 9

6 and 7 → 76 – 67 = 9

8 and 9 → 98 – 89 = 9

The full list of such pairs: (1, 2) · (2, 3) · (3, 4) · (4, 5) · (5, 6) · (6, 7) · (7, 8) · (8, 9).
The pattern: the two digits are consecutive — one is exactly 1 more than the other.

Page 47 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Why it works: The difference is always 9 × (difference of the digits). To get a 1-digit
answer, that difference must be 9 itself. So 9 × (difference of digits) = 9, which means
the two digits must differ by exactly 1.

Careful: The pair (0, 1) does not work, because the two numbers would be 10 and 01
— and 01 is not a proper 2-digit number.

Q7 (4) Now, find different digits such that the difference between the numbers is 27.

Choose two digits that are 3 apart.

Why 3? Because difference of numbers = 9 × (difference of digits)

27 = 9 × 3, so the digits must differ by 3.

All the pairs that work:

DIGITS THE TWO NUMBERS SUBTRACTION

1, 4 41 and 14 41 – 14 = 27

2, 5 52 and 25 52 – 25 = 27

3, 6 63 and 36 63 – 36 = 27

4, 7 74 and 47 74 – 47 = 27

5, 8 85 and 58 85 – 58 = 27

6, 9 96 and 69 96 – 69 = 27

Check it yourself: Pick any row and do the subtraction on paper. Every single one
gives 27.

Page 48 of 78

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Class 5 Maths Chapter 1 We the Travellers—I
a g l AglaSem · NCERT Solutions

co m
m.
(5) Mira found an interesting relationship between the two digits and the difference
e
Q8

m l as
.co
obtained. Can you see it in the table that Mira made?

a g
se m
g l a
a DIGITS DIFFERENCES IN DIFFERENCE IN NUMBERS FORMED BY THE

co73m– 37 = 36
DIGITS DIGITS

e m . ag
as
3, 7 7–3=4

a g l
1, 9 9–1=8 91 – 19 = 72

co m
m.
2, 8 8–2=6 82 – 28 = 54

m as e
.co
4, 5 5–4=1 54 – 45 = 9
a g l
se m
g l a
a
The table Mira made, printed on page 13.

m a s
m .co agl
se

g l a
Yes. The relationship is:
a

co m
.
Difference in the numbers = 9 × Difference in the digits
em
citom g l as
m . a
se
Check on every row of Mira's table.

g l a
a DIGITS DIFFERENCE IN DIGITS 9 × THAT DIFFERENCE IN NUMBERS

se m
com
✓
g l a
.
3, 7 4 9 × 4 = 36 73 – 37 = 36

m a
ase
agl
1, 9 8 9 × 8 = 72 91 – 19 = 72 ✓
2, 8 6 9 × 6 = 54 82 – 28 = 54 ✓
✓.com
se m
4, 5 1 9×1=9 54 – 45 = 9

com g l a
m .Why the 9 appears: Say the bigger digit is written first.a The bigger number has that
as e
agl digit in the tens place; the smaller number has it in the ones place. So the tens go up
c
m .
e
by the digit difference and the ones go down by the same digit difference. That is 10
m a s
co agl
times it minus 1 times it — which is 9 times it.
m .
as e
a g l

co m
m .
m ase
.co


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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Q9 Extend this table by choosing appropriate digits so that the resulting differences
are 2, 3, 5, and 7 respectively.

DIGITS DIFFERENCES IN DIFFERENCE IN NUMBERS FORMED BY THE
DIGITS DIGITS

3, 7 7–3=4 73 – 37 = 36

1, 9 9–1=8 91 – 19 = 72

2, 8 8–2=6 82 – 28 = 54

4, 5 5–4=1 54 – 45 = 9

The table Mira made, printed on page 13, with four empty rows for you to add.

Mira's table already covers digit differences 4, 8, 6 and 1. The four missing ones are 2, 3, 5 and 7.
Here they are.

DIGITS DIFFERENCE IN DIGITS DIFFERENCE IN THE NUMBERS FORMED

3, 5 5–3=2 53 – 35 = 18

1, 4 4–1=3 41 – 14 = 27

2, 7 7–2=5 72 – 27 = 45

1, 8 8–1=7 81 – 18 = 63

Check each one against the rule (difference in numbers = 9 × difference in digits):

Page 50 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

9 × 2 = 18 ✓

9 × 3 = 27 ✓

9 × 5 = 45 ✓

9 × 7 = 63 ✓

Other correct choices: for a digit difference of 2 you could take 4 and 6, or 7 and 9
— any pair 2 apart. The answer 18 stays the same.

Q10 What do the differences between the digits indicate?

The difference between the two digits tells you which multiple of 9 you will get. Multiply it by
9.

DIFFERENCE IN DIGITS 1 2 3 4 5 6 7 8

DIFFERENCE IN NUMBERS 9 18 27 36 45 54 63 72

So the digit difference is like a code number. Once you know it, you know the answer without
subtracting at all.

Digits 2 and 9 → difference 7 → answer must be 9 × 7 = 63

Check: 92 – 29 = 63 ✓

Try This: Ask a friend to pick two digits and tell you only how far apart they are.
Announce the subtraction answer before they finish working it out.

Q11 List the numbers that give a 1-digit number in the third subtraction.

You reach 9 on the third subtraction when your two digits are 3 apart or 8 apart.
Digits 3 apart — for example 1 and 4:

Page 51 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

1st subtraction : 41 – 14 = 27

2nd subtraction : 72 – 27 = 45

3rd subtraction : 54 – 45 = 9 ✓

The numbers are: 41 and 14 · 52 and 25 · 63 and 36 · 74 and 47 · 85 and 58 · 96 and 69.
Digits 8 apart — the pair 1 and 9:

1st subtraction : 91 – 19 = 72

2nd subtraction : 72 – 27 = 45

3rd subtraction : 54 – 45 = 9 ✓

The numbers are: 91 and 19.

Tip: The chain always runs 27 → 45 → 9, or 72 → 45 → 9. Both routes take exactly
three subtractions.

Q12 Identify pairs of digits that lead to the 1-digit number after the maximum possible
number of subtractions. Compare your answers with your friends.

The longest possible chain takes 5 subtractions. It happens when the two digits are exactly 2
apart.
The pairs: (1, 3) · (2, 4) · (3, 5) · (4, 6) · (5, 7) · (6, 8) · (7, 9).
Worked out with 1 and 3:

1st : 31 – 13 = 18

2nd : 81 – 18 = 63

3rd : 63 – 36 = 27

4th : 72 – 27 = 45

5th : 54 – 45 = 9

How many subtractions each starting pair needs:

Page 52 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

DIGITS ARE … APART FIRST DIFFERENCE SUBTRACTIONS NEEDED

1 9 1

2 18 5 ← the longest

3 27 3

4 36 4

5 45 2

6 54 2

7 63 4

8 72 3

Why 18 takes the longest: 18 sends you to 63, and 63 still needs three more rounds
(27, then 45, then 9). Every other starting point joins the chain further along. The
book's own example, 3 and 7, starts at 36 and takes 4 subtractions — one short of
the record.

Let Us Do — Pages 13–15
Questions 1 to 9 — writing numbers in between, ordering, expanded form and counting notes

LET US DO

Q1 1. Write 5 numbers between the numbers 23,568 and 24,234.

Sample answer: 23,600 · 23,750 · 23,900 · 24,000 · 24,150
How to choose them — 3 steps.

1. The numbers must be bigger than 23,568 and smaller than 24,234.
2. Start just above 23,568 and walk upwards, keeping well inside the two ends.
3. Check each one: 23,568 < 23,600 < 24,234 ✓ … and so on for all five.

23,568 < 23,600 < 23,750 < 23,900 < 24,000 < 24,150 < 24,234

Page 53 of 78

ase
Class 5 Maths Chapter 1 We the Travellers—I
a g l AglaSem · NCERT Solutions

co m
m.
Tip: There is no single right answer. Any five numbers from 23,569 up to 24,233 will

m as e
l
do. That is 665 numbers to choose from.

m .co a g
l a se
a g
Q2 2. Write 5 numbers that are more than 38,125 but less than 38,600.

com
m . ag
l a se
ag · 38,500 · 38,550
Sample answer: 38,200 · 38,300 · 38,400
How to choose them.

co m
1. All five numbers start with 38, because both ends do.
e m.
c o m g l as
.
2. The last three digits must be more than 125 and less than 600.
3. Pickm
e a
s
easy ones: 200, 300, 400, 500, 550.

a gla
38,125 < 38,200 < 38,300 < 38,400 < 38,500 < 38,550 < 38,600
m a s
m .co agl
l a se
g
Careful: 38,600 itself is not allowed. The question says less than 38,600, not up to it.
a

. c om
m a s emhas been driven
3. Ravi's car has been driven for 56,987 km till now. Sheetal's car
o km. Whose car has been driven more? gl
Q3

. c67,543 a
a s em
l
ag ANSWER
se m
a
Sheetal's car has been driven more.

. com a g l
m
Step 1 — count the digits. Both numbers have 5 digits, so we must compare place by place.
Step 2 — start from the left. ase
agl
TTH TH H T O

. com
m 8
ase
Ravi 56,987 5 6 9 7

. com67,543 agl5
m
ase
Sheetal 6 7 4 3

agl c
m .
In the TTh column: 6 is more than 5
m a s e
So 67,543 > 56,987 → Sheetal's car
e m . co agl
g l as
Step 3 — how much more? a

com
m .
m ase
.co


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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

67,543 – 56,987 = 10,556 km more

Careful: Do not be tricked by the 9 and 8 in Ravi's number. Those sit in the hundreds
and tens places. The ten-thousands place decides first, and it decides for Sheetal.

Q4 4. The following are the prices of different electric bikes. Arrange the prices in
ascending (increasing) order. ₹90,000 · ₹89,999 · ₹94,983 · ₹49,900 · ₹93,743 · ₹39,999

Ascending order means cheapest first.

₹39,999 < ₹49,900 < ₹89,999 < ₹90,000 < ₹93,743 < ₹94,983

How to sort them — 3 steps.

1. Group by the ten-thousands digit: 3 → 39,999 · 4 → 49,900 · 8 → 89,999 · 9 → 90,000;
94,983; 93,743.
2. Order the groups: 3, then 4, then 8, then all the 9s.
3. Sort inside the group of 9s by the next digit: 90,000 (0), 93,743 (3), 94,983 (4).

The tricky pair: ₹89,999 and ₹90,000 look almost the same in size and differ by only
₹1. But 8 is less than 9 in the ten-thousands place, so ₹89,999 comes first. A single
rupee decides the order.

Check it yourself: The cheapest bike costs ₹39,999 and the costliest ₹94,983. The
difference is 94,983 – 39,999 = ₹54,984.

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Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

Q5 5. The following table shows the population of some towns. Arrange them in a
descending (decreasing) order.

TOWN POPULATION

Town 1 65,232

Town 2 53,231

Town 3 56,380

Town 4 51,336

Town 5 45,858

Town 6 66,540

The population table printed on page 14.

Descending order means biggest first.

66,540 > 65,232 > 56,380 > 53,231 > 51,336 > 45,858

PLACE TOWN POPULATION

1st (largest) Town 6 66,540

2nd Town 1 65,232

3rd Town 3 56,380

4th Town 2 53,231

5th Town 4 51,336

6th (smallest) Town 5 45,858

How to sort them.

1. Ten-thousands digits are 6, 5, 5, 5, 4, 6. The 6s are biggest, then the 5s, then the 4.
2. Between the two 6s — 66,540 and 65,232 — look at the thousands: 6 beats 5. So 66,540 first.

Page 56 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

3. Among the three 5s — 56,380 · 53,231 · 51,336 — the thousands are 6, 3 and 1. So the order
is 56,380, then 53,231, then 51,336.

Check it yourself: Read your answer backwards. It should be the ascending order:
45,858 · 51,336 · 53,231 · 56,380 · 65,232 · 66,540 ✓

Q6 6. Find numbers between 42,750 and 53,500 such that the ones, tens, and hundreds
digits are all 0.

There are 11 such numbers:

43,000 · 44,000 · 45,000 · 46,000 · 47,000 · 48,000 · 49,000 · 50,000 · 51,000 · 52,000 ·

53,000

How to find them — 3 steps.

1. If the ones, tens and hundreds digits are all 0, the number ends in 000. So it is a whole
number of thousands.
2. The smallest whole thousand above 42,750 is 43,000.
3. The largest whole thousand below 53,500 is 53,000. Now list every thousand in between.

Count them:

From 43,000 to 53,000, counting in thousands:

53 – 43 = 10, and adding 1 for the starting number gives 11 numbers ✓

Careful: 42,750 is not a whole thousand, so it is not on the list. Neither is 53,500.
And 54,000 is beyond the upper end, so it does not count either.

Q7 7. Write the following numbers in the expanded form. One has been done for you:
(a) 783 = 700 + 80 + 3. (b) 8,062 =

8,062 = 8,000 + 60 + 2
Step 1 — put each digit in its place.

Page 57 of 78

Class 5 Maths Chapter 1 We the Travellers—I AglaSem · NCERT Solutions

TH H T O

8 0 6 2

Step 2 — write what each digit is worth.

8 in the thousands place = 8,000

0 in the hundreds place = 0

6 in the tens place = 60
2 in the ones place = 2

Step 3 — add them, leaving out the zero.

8,062 = 8,000 + 60 + 2

Tip: You may also write 8,000 + 0 + 60 + 2. Both are correct, but a 0 adds nothing, so
it is usually left out.

Q8 7. (c) 9,980 =

9,980 = 9,000 + 900 + 80

9 thousands = 9,000
9 hundreds = 900

8 tens = 80

0 ones = 0

9,000 + 900 + 80 = 9,980 ✓

Check it yourself: Add the parts back up. 9,000 + 900 = 9,900, and 9,900 + 80 = 9,980
✓

Page 58 of 78

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Class 5 Maths Chapter 1 We the Travellers—I
a g l AglaSem · NCERT Solutions

co m
m.
7. (d) 10,304 =
e
Q9

m l as
.co a g
a
s em
agl = 10,000 + 300 + 4
10,304

m
.co ag
TTH TH H T O

a sem 3
agl
1 0 0 4

1 ten thousand = 10,000
co m
e m.
m l as
0 thousands = 0
. c o a g
s e m = 300
3 hundreds
la
ag 0 tens = 0
4 ones = 4
m a s
m .co agl
se
10,000 + 300 + 4 = 10,304 ✓

g l a
a
Why we still write the zeros in the number: The zeros do not add anything, but
co m
they hold the 1 and the 3 in their proper places. Take them out and you get 134, a
m .
m as e
.co l
completely different number.
a g
se m
g l a
a
Q10 7. (e) 23,004 =
se m
com g l a
m . a
ase
agl

23,004 = 20,000 + 3,000 + 4

co m
2 ten thousands = 20,000
m .
m as e
.co
3 thousands = 3,000
a g l
se m 0 hundreds = 0
g l a
a c
0 tens = 0
m .
m a s e
. co agl
4 ones = 4
e m
20,000 + 3,000 + 4 = 23,004 ✓
g l as
a

co m
m .
m ase
.co


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