NCERT Solutions Class 5 Maths Chapter 5 Far and Near

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 5: Far and Near

NCERT Textbook — Math Mela

BOOK PAGES SECTIONS QUESTIONS MEDIUM

57 – 69 19 39 English

Solutions, notes, sample papers & more at 50 pages

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

CLASS 5 · MATHS · MATH MELA

NCERT Solutions — Chapter 5: Far and Near
Chapter 5 of Math Mela is about measuring length and distance. Saris in a weaving centre, the world's tallest
statues, a 3-km race, the longest train journey in India, a sprouting moong seed and a roll of cloth teach four
big ideas: pick the right unit for the thing you are measuring, change one unit into another (mm, cm, m,
km), add, subtract, multiply and divide lengths just as you do with plain numbers, and use a double
number line to see two units side by side.

TEXTBOOK BOOK PAGES

Math Mela (Class 5) 57 – 69

SECTIONS QUESTIONS

19 39

MEDIUM

English

Let Us Find — Page 57
Choosing the right unit of measurement

LET US FIND

Q1 Identify the appropriate units for measuring each of the following. (Height of India
Gate — 42; Length of a handkerchief — 40; Depth of a well — 50; Length of a mobile
phone — 13; Length of an elephant's trunk — 2; Distance between two buttons on a
shirt — 5)

Big things get metres (m). Small things get centimetres (cm). Here is the filled table.

Page 1 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

QUANTITY NUMBER UNIT WHY
GIVEN

Height of India Gate 42 metre (m) It is a huge gate — much taller
than your school

Length of a handkerchief 40 centimetre It fits in your pocket
(cm)

Depth of a well 50 metre (m) A well goes deep down into the
ground

Length of a mobile phone 13 centimetre It fits in your hand
(cm)

Length of an elephant's trunk 2 metre (m) A trunk is longer than you are tall

Distance between two buttons 5 centimetre It is only about a finger's width
on a shirt (cm)

Here is a quick way to decide.

1. Picture the thing. Close your eyes and see it.
2. Ask: can I hold it? If yes, use centimetres.
3. Ask: is it as tall as a room, a tree or a building? If yes, use metres.
4. Check by trying the other unit. If the answer sounds silly, you picked wrong.

Why the check works: Try 42 cm for India Gate. That is shorter than your school
bag — India Gate cannot be that small. Now try 40 m for a handkerchief. That is
longer than four buses in a line — no handkerchief is that big. The silly answer tells
you the unit is wrong.

Did you know? India Gate in New Delhi really is about 42 m tall. It was built to
remember Indian soldiers, and their names are carved on its walls.

Different Units but Same Measure — Pages 57–58

Page 2 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

Shikha and Sonu at the village weaving centre

DIFFERENT UNITS BUT SAME MEASURE

Q1 Fill in the blanks in the double number line. Top line (in cm): 100 cm, ____ cm, 400 cm,
500 cm, 700 cm. Bottom line (in m): 1 m, 2 m, ____ m, ____ m, ____ m.

100 cm ____ cm 400 cm 500 cm 700 cm
×2

×100

1m 2m ____ m ____ m ____ m

The double number line printed on page 57.

Top blank = 200 cm. Bottom blanks = 4 m, 5 m and 7 m.
The two lines are lined up tick for tick. Every tick shows one length written twice — once in cm
on top, once in m below.

×2

100 cm 200 cm 400 cm 500 cm 700 cm

×100

1m 2m 4m 5m 7m
Go down the arrow = multiply by 100. Go up = divide by 100.

The filled double number line. The red numbers are the ones you write in.

Page 3 of 50

as e
Class 5 Maths Chapter 5 Far and Near
a g l AglaSem · NCERT Solutions

co m
e m.
1 m = 100 cm
m l as
.co
2 m = 2 × 100 = 200 cm (the top blank)
m a g
l a se
g
400 cm = 400 ÷ 100 = 4 m
a500 cm = 500 ÷ 100 = 5 m

co m
. ag
700 cm = 700 ÷ 100 = 7 m
e m
g l as
a
Why it happens: One metre is made of 100 centimetres. So every metre on the
bottom line needs 100 centimetres on the top line. Counting in metres is like
co m
counting in hundreds of centimetres.
em.
m l as
.co a g
a s em it yourself: Cover the top line with your finger. Read the bottom line: 1, 2, 4,
gl
Check
a 5, 7 metres. Now add two zeros to each: 100, 200, 400, 500, 700. That is the top line

s
exactly.
m a
m .co agl
l a se
Q2
a g
Shikha and Sonu are measuring the lengths of saris and stoles in the village

m
weaving centre. Find which measures represent the same sari or stole. (204 cm, 540

. co
m
cm, 750 cm, 240 cm, 404 cm; 5 metre 40 cm, 2 metre 204 cm, 2 metre 4 cm, 2 metre

m as e
l
40 cm, 6 metre 150 cm)
.co a g
a s em
gl
a All five pairs match. Here they are.

se m
m
coAS g l a
MEASURE IN CM
m .
SAME WORKING
a
ase
204 cm
agl 2 metre 4 cm 200 + 4 = 204 cm ✓

om
540 cm 5 metre 40 cm 500 + 40 = 540 cm ✓

600 + 150m
. c
m
750 cm 6 metre 150 cm
a s e = 750 cm ✓
. cocm gl + 40 = 240 cm ✓
a200
m
ase
240 2 metre 40 cm

agl c
.
404 cm 2 metre 204 cm 200 + 204 = 404 cm ✓

s e m
m a
. co agl
Do it this way every time.

se m
l a
g centimetres. Multiply by 100. So 2 m = 200 cm.
1. Take the right-hand measure. It is written in two parts, like 2 metre 4 cm.
2. Change the metres a
into

m
3. Add the centimetres already there. 200 + 4 = 204 cm.

. co
e m
m l as
.co a g
Page 4 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

4. Look for that number on the left. 204 cm is there — so those two are the same cloth.

Why it happens: A length does not change when you write it differently. Cutting 204
cm of cloth is exactly the same as cutting 2 whole metres and then 4 more
centimetres. Only the words change, not the cloth.

Watch out for this one: 6 metre 150 cm looks odd, because 150 cm is more than a
whole metre. It is still correct — it just means 6 metres and then another metre and
a half, which is 7 m 50 cm, or 750 cm. In the same way, 2 metre 204 cm = 4 m 4 cm =
404 cm.

Let Us Compare — Page 58
Ritika's rods and the world's tallest statues

LET US COMPARE

Q1 Ritika is comparing the lengths of different rods. Compare them using <, =, > signs.
(a) 456 cm ____ 5 m (b) 55 cm + 200 cm ____ 200 cm + 54 cm (c) 6 m 5 cm ____ 6 m 50 cm
(d) 2 m 150 cm ____ 3 m 50 cm (e) 238 cm ____ 138 cm + 1 m

(a) < (b) > (c) < (d) = (e) =
The rule for every one of these: change both sides into centimetres first, then compare like
ordinary numbers.

PART LEFT SIDE IN CM RIGHT SIDE IN CM SIGN

(a) 456 cm and 5 m 456 5 × 100 = 500 <

(b) 55 + 200 and 200 + 54 255 254 >

(c) 6 m 5 cm and 6 m 50 cm 600 + 5 = 605 600 + 50 = 650 <

(d) 2 m 150 cm and 3 m 50 cm 200 + 150 = 350 300 + 50 = 350 =

(e) 238 cm and 138 cm + 1 m 238 138 + 100 = 238 =

Page 5 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

Why we must change the units first: The numbers 456 and 5 tell you nothing on
their own — one is counting centimetres, the other is counting metres. It is like
asking whether 456 marbles is more than 5 boxes. You cannot answer until you
know how many marbles are in a box. Here, one box (one metre) holds 100
centimetres.

Careful with part (c): Both rods start with 6 m, so you only need to compare the
leftover bits — 5 cm against 50 cm. 5 cm is much shorter. Many children read 6 m 5
cm as if the 5 were 50; look closely at the number of digits.

Tip for part (d): 2 m 150 cm is a strange way to write it, but it is allowed. 150 cm is 1
m 50 cm, so 2 m 150 cm = 3 m 50 cm. Both rods are the same length.

Q2 World's tallest statue. (a) What is the difference between the height of the tallest
statue in the world and the Statue of Liberty? (b) Identify the statues whose heights
have the least difference. (c) Identify the statues whose heights have the largest
difference. (d) The height of which statue will be equal to the height of the Statue of
Unity, if it is doubled?

First, the heights printed in the book, arranged from tallest to shortest.

STATUE COUNTRY HEIGHT

Statue of Unity India 182 m

Spring Temple Buddha China 128 m

Guanyin of Nanshan China 108 m

Statue of Liberty USA 93 m

The Motherland Calls Russia 91 m

Christ the Redeemer Brazil 38 m

Page 6 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

182 m

128 m
108 m
93 m 91 m

38 m

Unity Buddha Guanyin Liberty Motherland Christ
Each bar is drawn to scale — 1 metre of statue = 1 unit of bar.
The six statues as bars. Tallest on the left, shortest on the right.

(a) The difference is 89 m.

Tallest statue = Statue of Unity = 182 m

Statue of Liberty = 93 m

182 − 93 = 89 m

(b) The Statue of Liberty (93 m) and The Motherland Calls (91 m) — a difference of only 2 m.
Their bars in the picture are almost the same height.

93 − 91 = 2 m — the smallest gap on the whole list

(c) The Statue of Unity (182 m) and Christ the Redeemer (38 m) — a difference of 144 m.
The tallest and the shortest always give the biggest gap.

182 − 38 = 144 m

(d) The Motherland Calls, Russia. It is 91 m tall, and twice 91 is 182.

91 × 2 = 182 m = height of the Statue of Unity ✓

Page 7 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

How to find the answer to (d) without guessing: Halve the Statue of Unity. 182 ÷ 2
= 91. Then look down the list for a statue that is 91 m tall. That is The Motherland
Calls. Halving is quicker than doubling every statue one by one.

Did you know? The Statue of Unity stands in Gujarat, on an island in the Narmada
river. It shows Sardar Vallabhbhai Patel, and at 182 m it is the tallest statue in the
world.

Measuring Long Distances · Let Us Do — Page 59
Long Tape, Rodometer, Rangefinder, Laser Distance Meter

LET US DO

Q1 Measure 100 m and 200 m on your school playground, or any other place in and
around your school, using a Long Tape. Mark these points and draw a straight line.
Walk on the lines and count the number of steps. Use this relationship between the
number of steps taken and distance walked to find distances around you for at
least 3 locations. (a) Identify and write the locations that are the nearest and the
farthest from your home. (b) Write the distances obtained above in increasing
order. (c) Name a location that is equal to or more than 1,000 m from your home.

This one you must actually walk. Here is exactly how to do it, and then a sample answer you can
copy the shape of.

1. Lay the long tape on the playground. Mark the 0 point with a stone and the 100 m point
with another stone. Draw a straight line between them.
2. Walk the line normally. Do not take extra-long steps. Count every step out loud with a
friend.
3. Write down the count. Suppose you took 140 steps for 100 m.
4. Find one step. 100 m ÷ 140 steps is a little less than 1 m, so about 140 steps make 100 m.
This is your personal step rule.
5. Walk to a place and count. If you take 280 steps to the shop, that is 2 × 140 steps, so the
shop is about 200 m away.
6. If you cannot walk there (a big pond in between, a busy road), find the distance some other
way and work out how many steps it would take.

Page 8 of 50

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Class 5 Maths Chapter 5 Far and Near
a g l AglaSem · NCERT Solutions

co m
em.
140 steps = 100 m
m l as
.co
280 steps = 2 × 140 = 200 m
m a g
l a se
g
700 steps = 5 × 140 = 500 m
a1,400 steps = 10 × 140 = 1,000 m = 1 km

co m
em . ag
as
Sample answer:

a g l
PLACE STEPS COUNTED DISTANCE FROM HOME

co m
m.
Neighbour's house 70 50 m

m as e
.co
Village shop 280 200 m
a g l
se m
g l a
a
School 700 500 m

s
Bus stand 1,680 1,200 m = 1 km 200 m

om a
e
. c
m (50 m). Farthest location: the bus stand (1 km 200 agl
s
(a) Nearest location: the neighbour's house
m).
a gla
(b) In increasing order: 50 m, 200 m, 500 m, 1,200 m.

co m
.
(c) A location 1,000 m or more from home: the bus stand, which is 1,200 m — more than 1 km

e m
as
away.
m l
.co
m counting steps works: Your steps are all about the same size, so steps and a g
a s eWhy
agl metres go up together. Twice the steps means twice the distance. This is exactly
what the rodometer (measuring wheel) does — it counts turns of the wheel instead
se m
com g l a
.
of steps.
m a
ase
agl
Tip: Your friend's step rule will be different from yours, because your legs are
different lengths. That is fine. Each of you should measure your own 100 m and
co m
make your own rule.
m .
m as e
.co a g l
a s em
agl Let Us Explore — Page 59
.c
s e m
m a
e m . co agl
g l as
a

co m
m .
m as e
.co


a g l Page 9 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

1,000 m = 1 km

LET US EXPLORE

Q1 Fill in the table: Length of rope / Number of ropes needed to make 1 km. (1,000 m —
1; 100 m — ___; 10 m — ___; 200 m — ___; 500 m — ___; 250 m — ___)

LENGTH OF ROPE NUMBER OF ROPES NEEDED TO MAKE 1 KM

1,000 m 1

100 m

10 m

200 m

500 m

250 m

The table as printed on page 59.

Here is the filled table. Every time, ask: how many of these ropes, laid end to end, make 1,000
m?

LENGTH OF ROPE NUMBER OF ROPES NEEDED TO MAKE 1 KM HOW WE FOUND IT

1,000 m 1 1,000 ÷ 1,000 = 1

100 m 10 1,000 ÷ 100 = 10

10 m 100 1,000 ÷ 10 = 100

200 m 5 1,000 ÷ 200 = 5

500 m 2 1,000 ÷ 500 = 2

250 m 4 1,000 ÷ 250 = 4

Page 10 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

1 km = 1,000 m — made in different ways
one 1,000 m rope

500 m 500 m

four 250 m ropes

five 200 m ropes

The same kilometre, cut into different numbers of equal ropes.

Why it happens: Shorter rope, more ropes. If each rope is half as long, you need
twice as many. 500 m is half of 1,000 m, so you need 2. And 10 m is one hundredth
of 1,000 m, so you need 100.

Check it yourself: Multiply back. 4 ropes × 250 m = 1,000 m ✓. 5 ropes × 200 m =
1,000 m ✓. 100 ropes × 10 m = 1,000 m ✓. Every row works out to exactly 1 km.

Kilometre Race — Page 60
Sheena and Jennifer organise a 3-km race

KILOMETRE RACE

Q1 Water stations are to be arranged after every 500 m. How many water stations
must be set up? At what positions from the starting point will these water stations
be placed?

6 water stations. They go at 500 m, 1,000 m, 1,500 m, 2,000 m, 2,500 m and 3,000 m from the
start.
Work it out step by step.

1. Change the race into metres. The race is 3 km. Since 1 km = 1,000 m, the race is 3 × 1,000 =
3,000 m.
2. Count in jumps of 500 m. 500, 1,000, 1,500, 2,000, 2,500, 3,000.
3. Count the jumps. That is 6 marks.

Page 11 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

3 km = 3 × 1,000 = 3,000 m

3,000 ÷ 500 = 6 water stations

Positions: 500 m, 1 km, 1 km 500 m, 2 km, 2 km 500 m, 3 km

Start

500 m 1 km 1.5 km 2 km 2.5 km 3 km
Six blue dots = six water stations, one after every 500 m.
The 3,000 m track with a water station after every 500 m.

Why we divide: The question asks how many 500 m pieces fit inside 3,000 m.
Dividing is exactly the way to ask that question. 3,000 ÷ 500 = 6.

Think about it: The sixth station is right at the finish line, where the runners will
want water most. If a school decides not to put one at the finish, then only 5 stations
are needed. Say which choice you made when you answer.

Q2 Children need to stand at an interval of 300 m to direct the runners. How many
children are needed? At what positions from the starting point will the children be
standing?

10 children. They stand at 300 m, 600 m, 900 m, 1,200 m, 1,500 m, 1,800 m, 2,100 m, 2,400 m,
2,700 m and 3,000 m.

1. The race is 3,000 m long (3 km = 3 × 1,000).
2. Each gap between two children is 300 m.
3. Ask how many 300 m gaps fit in 3,000 m. Divide: 3,000 ÷ 300 = 10.
4. Write the positions by counting in 300s.

Page 12 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

3,000 ÷ 300 = 10 children

Positions: 300 m, 600 m, 900 m, 1,200 m, 1,500 m,

1,800 m, 2,100 m, 2,400 m, 2,700 m, 3,000 m

Why 10 and not 11: We are counting the marks along the track, starting 300 m after
the start line. If Sheena also wants one child standing at the start line itself, then 11
children are needed. Read the words carefully — "at an interval of 300 m" means the
first child is 300 m along.

Check it yourself: 10 children × 300 m = 3,000 m. The last child is exactly at the
finish line ✓

Q3 Red and blue flags are to be placed alternately at every 50 m. How many red and
blue flags are needed till the finish line?

60 flags in all — 30 red and 30 blue.

1. Find how many flag positions there are. The race is 3,000 m and a flag stands every 50 m.
3,000 ÷ 50 = 60 positions.
2. Now share these 60 positions between two colours. Alternately means red, blue, red,
blue, … all the way.
3. Split 60 into two equal groups. 60 ÷ 2 = 30.

3,000 ÷ 50 = 60 flag positions

60 ÷ 2 = 30 red flags and 30 blue flags

Total = 30 + 30 = 60 flags

The first 400 m of the track

50 m 100 m 150 m 200 m 250 m 300 m 350 m 400 m
Red, blue, red, blue … the pattern repeats every 100 m, so the
colours share equally.

Page 13 of 50

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Class 5 Maths Chapter 5 Far and Near
a g l AglaSem · NCERT Solutions

Alternating flags. In every 100 m there is one red flag and one blue flag.
co m
se m.
o m
c colours come out equal: The pattern red-blue repeats l a
g as one pair
Why the .two a
m
se100 m. The track is 3,000 m, which holds 30 such pairs. Each pair has one red
l a
g one blue, so there are 30 of each.
every
aand

. c om ag
Check it yourself: 30 pairs × 100 m = m
a s e 3,000 m ✓ And 30 + 30 = 60 flags, which

agl
matches 3,000 ÷ 50 = 60 ✓

co m
em.
com Dibrugarh to Kanniyakumari
Let Us Do: Longest Train Journey — Pages 60–61
g l as
. a
s em
The Vivek Express,
a
gl US DO
aLET
m a s
.co agl
The total length of the route from Dibrugarh to Kanniyakumari is _______ km.
m
Q1

l a se
ANSWER a g
m
4,187 km.

. co
e m
The table gives the distance of every station from Dibrugarh. Kanniyakumari is the last station,

m l as
.co g
so its distance is the whole journey.

em a
a s
agl Kanniyakumari is station number 65
Distance from Dibrugarh = 4,187 km
se m
com g l a
m . a
gl ase
a
Why you do not add up the rows: Each number in the table is already measured
from Dibrugarh, not from the station above it. If you added them you would count
the same track many times over.
co m
m .
o m l a se
agto cross India from Assam
.cDid you know? The Vivek Express takes about four days
m in the far north-east to the very tip of Tamil Nadu. It is the longest train route in
l a se
ag India.
.c
s e m
m a
e m . co agl
g l as
a

co m
m .
m ase
.co


a g l Page 14 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

Q2 The distance between Vijayawada and Jalpaiguri road is _______.

1,817 km.

1. Read both distances from the table. Vijayawada JN is 2,800 km from Dibrugarh. Jalpaiguri
Road is 983 km from Dibrugarh.
2. Subtract the smaller from the bigger. The gap between two stations is the difference of
their distances.

2,800 − 983

= 2,800 − 1,000 + 17

= 1,800 + 17

= 1,817 km

Dibrugarh Jalpaiguri Rd Vijayawada

0 km 983 km 2,800 km

1,817 km
Both distances start at Dibrugarh, so the gap between the two stations is the difference.

Check it yourself: Add back. 983 + 1,817 = 2,800 ✓ That is Vijayawada's distance, so
the subtraction was right.

Q3 Distance between Vijayawada and Visakhapatnam is _______.

350 km.

Page 15 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

Vijayawada JN = 2,800 km from Dibrugarh

Visakhapatnam = 2,450 km from Dibrugarh

2,800 − 2,450 = 350 km

Why it happens: Both stations lie on the same track, one after the other. The train
has already run 2,450 km when it reaches Visakhapatnam, and 2,800 km when it
reaches Vijayawada. The extra running in between is 350 km.

Check it yourself: 2,450 + 350 = 2,800 ✓

Q4 Which two stations are farther apart — Guwahati and Dimapur or Bhubaneswar
and Jalpaiguri Road?

Bhubaneswar and Jalpaiguri Road are farther apart — 1,024 km, against only 250 km for the
other pair.

Guwahati and Dimapur:

556 − 306 = 250 km

Bhubaneswar and Jalpaiguri Road:

2,007 − 983 = 1,024 km

1,024 km > 250 km

Guwahati — Dimapur
250 km

Bhubaneswar — Jalpaiguri Road
1,024 km

Page 16 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

Two bars drawn to the same scale. The second gap is about four times the first.

Tip: You do not always have to work out the exact numbers. Dimapur and Guwahati
are both in the north-east, only five stations apart. Jalpaiguri Road is in the north and
Bhubaneswar is on the east coast, twelve stations apart. A quick look at the station
numbers already suggests the answer — then the subtraction proves it.

Q5 What is the distance between Guwahati and Coimbatore JN?

3,119 km.

1. Coimbatore JN is 3,675 km from Dibrugarh.
2. Guwahati is 556 km from Dibrugarh.
3. Subtract. The track between them is the difference.

3,675
− 556

———————

3,119 km

Check it yourself: 556 + 3,119 = 3,675 ✓ The train runs 3,119 km more after leaving
Guwahati to reach Coimbatore.

Let Us Explore: The World of Small Things — Page 61
Sprout, small screws, nail — and the millimetre

LET US EXPLORE

Q1 How can we measure small things like the ones shown here? (a sprout, small
screws, a nail)

We measure them in millimetres (mm), using the tiny marks on the ruler.

Page 17 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

A centimetre is too big for these things. A small screw is not even one centimetre long. So we
need a smaller unit, and that unit is the millimetre.

1. Put the thing flat against the ruler. Its left end must sit exactly on the 0 mark, not on the
edge of the plastic.
2. Look where the right end stops. Note the last full centimetre it has passed.
3. Count the small marks after that. Each small gap is 1 mm.
4. Write both. For example, 2 cm and 4 small gaps more = 2 cm 4 mm, which is 24 mm.

1 cm = 10 mm

So a screw of 2 cm 4 mm = 20 + 4 = 24 mm

Why smaller marks help: If your ruler only had centimetre marks, you would have
to say "a bit more than 2 cm". The millimetre marks let you say exactly how much
more. That is what the book calls precision — how exact a measurement is.

Tip for round things: A curved sprout will not lie straight. Lay a thread along the
curve, mark where it ends, then straighten the thread against the ruler and read it.

Q2 Let us look at the scale. Do you notice the small marks between 1 cm and 2 cm?
Count how many marks are there between 1 cm and 2 cm?

There are 9 small marks between the 1 and the 2, and they cut that centimetre into 10
equal parts. Each part is 1 millimetre.

1 2 3 4 5 6 7 8 9

1 2 3

1 cm = 10 equal parts = 10 mm

Nine small marks make ten small gaps. Each gap is one millimetre.

Page 18 of 50

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Class 5 Maths Chapter 5 Far and Near
a g l AglaSem · NCERT Solutions

co m
m.
Why 9 marks give 10 parts: Think of a rope cut into 10 pieces. You need only 9 cuts,

m l a se
because the two ends are already there. In the same way, 9 lines split the centimetre
o
.c parts. a g
m
into 10 equal

l a se
g
aRemember: 1 cm = 10 mm. So 3 cm = 30 mm, and 45 mm = 4 cm 5 mm.

com
e m . ag
g l as
Let Us Measure — Page 61 a

co m
em.
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a g
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a
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m a s e
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co m
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m ase
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a g l Page 19 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

The design made of four shapes, one inside another

LET US MEASURE

Q1 Measure the lines in the design and write their measurements in cm and mm.

The design printed on page 61 — the small boxes are for writing the measurement of
the line beside each of them.

This one you must measure in your own book with your own ruler. Here is how, and then
the measurements we got so you can check yourself.

1. Put the 0 mark of the ruler exactly on one corner of the line. Not the edge of the plastic
— find the printed 0.
2. Turn the ruler so it lies along the line, even if the line is slanting. Hold the book steady.
3. Read the last full centimetre the other corner has crossed.

Page 20 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

4. Count the small marks after it. Each one is 1 mm.
5. Write it as cm and mm, for example 6 cm 8 mm. Then write the same thing in mm: 68 mm.
6. Write your answer in the small box printed beside that line.

outer four-sided figure

big diamond

rectangle

small tilted square

The design is four shapes, one inside the other. Measure every side of each shape.

What we measured (rounded to the nearest millimetre):

SHAPE ITS FOUR SIDES

Outer four-sided figure (black) 6 cm 8 mm, 6 cm 0 mm, 6 cm 1 mm, 6 cm 8 mm

Big diamond (blue) 4 cm 4 mm, 4 cm 1 mm, 4 cm 4 mm, 4 cm 8 mm

Rectangle (green) 3 cm 5 mm, 2 cm 8 mm, 3 cm 5 mm, 2 cm 7 mm

Small tilted square (red) 2 cm 5 mm, 2 cm 3 mm, 2 cm 2 mm, 1 cm 9 mm

Page 21 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

If your answer is 1 mm different, do not worry. Where exactly you put the ruler,
and how the page is printed, can shift a reading by a millimetre. What matters is that
you read the centimetre and the millimetre part, and write both.

Why we write cm and mm together: Saying "about 7 cm" throws away useful
information. Saying "6 cm 8 mm" tells the exact length. And 6 cm 8 mm can also be
written as 68 mm — same length, one unit instead of two.

Let Us Do — Page 62
Growing a moong or chana sprout and measuring it

LET US DO

Q1 Soak some seeds of whole moong or black or white chana overnight. Next morning,
take them out and wrap them in a moist cloth to sprout them. Over the next 4 days,
take out one seed each day and measure the length of sprout. Fill the table: Day 1,
Day 2, Day 3, Day 4 — Length of the sprout (in mm).

NUMBER OF DAYS LENGTH OF THE SPROUT (IN MM)

Day 1

Day 2

Day 3

Day 4

The table as printed on page 62 — write your own measurement in each row.

Do the activity for four days and write your own numbers in the table. Here is exactly how, and a
sample table.

1. Soak a handful of whole moong overnight in a bowl of water.
2. Next morning drain the water. Wrap the seeds in a wet cloth. Keep the cloth damp —
sprinkle water if it dries.
3. Each day take out one seed. Do not disturb the rest.
4. Lay the seed on paper. Mark where the sprout starts and where it ends with a pencil.

Page 22 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

5. Measure between the two marks with your ruler and read it in millimetres. A sprout is
small, so millimetres are the right unit.
6. If the sprout is curly, lay a thread along it, then straighten the thread on the ruler.

Sample answer:

NUMBER OF LENGTH OF THE SPROUT (IN GROWTH SINCE THE DAY
DAYS MM) BEFORE

Day 1 3 mm —

Day 2 8 mm 5 mm

Day 3 15 mm (1 cm 5 mm) 7 mm

Day 4 24 mm (2 cm 4 mm) 9 mm

What to notice: The sprout grows a little more each day, not the same amount
every day. On Day 1 it grew 3 mm; by Day 4 it added 9 mm in one day. Your own seed
may grow faster or slower — warmth and moisture change everything.

Try this: Grow two seeds — keep one in a warm dark place and one on a cold
windowsill. Measure both for four days. Which one grows longer? Write your finding
in one sentence.

Let Us Draw — Page 62
Drawing lines of a given length with a scale

LET US DRAW

Q1 Draw lines of the following lengths in your notebook using a scale. 1. 5 cm 5 mm 2. 3
cm 6 mm 3. 8 cm 3 mm 4. 36 mm 5. 67 mm

Draw each one like this.

1. Put the ruler flat on the page. Make a small dot at the 0 mark.
2. Find the finish point. Go to the centimetre number first, then count the small marks after it.
3. Make a second dot there.
4. Join the two dots along the edge of the ruler, in one clean stroke.
5. Write the length under the line.

Page 23 of 50

as e
Class 5 Maths Chapter 5 Far and Near
a g l AglaSem · NCERT Solutions

co m
m.
LINE WHERE THE SECOND DOT GOES SAME LENGTH IN MM

mpast 5, then 5 small marks more as e
5 cm 5 mm
.co
55 mm
a g l
se m
g l a past 3, then 6 small marks more
a
3 cm 6 mm 36 mm

8 cm 3 mm past 8, then 3 small marks more 83 mm

co m
36 mm same as 3 cm 6 mm
e m . 36 mm ag
same as 6 cm 7 mm gl
as
67 mm
a 67 mm

co m
se m.
m l a
m .co 5 cma5g mm = 55 mm
l a se
ag
3 cm 6 mm = 36 mm
om8 cm 3 mm = 83 mm a s
m .c agl
l a se
a g
36 mm = 3 cm 6 mm
co m
m .
m as e67 mm
.co a g l
se m The five lines drawn to the same scale. Notice that lines 2 and 4 are exactly the same length.
g l a
a
se m
com
Did you spot it? Line 2 and line 4 are the same line. 3 cm 6 mm and 36 mm are two
g l a
m . a
ase
names for one length.

agl

co m
.
Q2 How did you draw lines of lengths 36 mm and 67 mm? Share your thoughts in class.

em
com g l as
. a
sem

a
agl
Change the millimetres into centimetres and millimetres first. Your ruler has big numbers
for centimetres, so it is much easier to find 3 cm 6 mm than to count 36 tiny marks one by one.
.c
s e m
m a
co agl
1. Look at the mm number. 36 mm.

m .
2. Split off the tens. 36 = 30 + 6.
ase
a g l
3. Change the tens into centimetres. 30 mm = 3 cm, because 10 mm make 1 cm.
4. So 36 mm = 3 cm 6 mm. Go to the 3 on your ruler, then count 6 small marks more.

co m
m .
m ase
.co


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Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

36 mm = 30 mm + 6 mm = 3 cm 6 mm

67 mm = 60 mm + 7 mm = 6 cm 7 mm

Sample answer for the class discussion: "I did not count 36 small marks, because I would lose
count. I saw that 36 mm has 3 tens in it, and every ten millimetres is one centimetre. So I went
straight to the 3 cm mark and then counted only 6 small marks. For 67 mm I went to 6 cm and
counted 7 small marks."

Why splitting the number works: The tens digit of a millimetre number is the
number of whole centimetres, and the ones digit is the millimetres left over. This is
the same idea as reading 36 as 3 tens and 6 ones.

Let Us Do — Pages 63–64
Relationships between Different Units — 10 mm = 1 cm, 100 cm = 1 m, 1,000 m = 1 km

LET US DO

Q1 Fill in the blanks appropriately in the double number lines given below. (a) top: 1
cm, 7 cm, 15 cm, ___ cm, ___ cm, ___ cm, 50 cm; bottom: 10 mm, ___ mm, ___ mm, 250
mm, 320 mm, 450 mm, ___ ; and the multiplier boxes ×7, ×10, ×__, ×__. (b) top: 1 m, 4
m, 10 m, ___ m, ___ m, ___ m, 21 m; bottom: ___ cm, ___ cm, ___ cm, 1,200 cm, 1,400 cm,
1,700 cm, ___ cm; boxes ×4, ×100, ×__, ×__. (c) top: 1 km, 9 km, 25 km, ___ km, ___ km, ___
km, 82 km; bottom: 1,000 m, ___ m, ___ m, 41,000 m, 55,000 m, 67,000 m, ___ m; boxes
×9, ×1,000, ×__, ×__.

On a double number line, the two lines are lined up tick for tick. Going down or up between the
lines changes the unit. Going sideways along a line changes the length.

(a) centimetres and millimetres — 1 cm = 10 mm

Page 25 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

×7

1 cm 7 cm 15 cm 25 cm 32 cm 45 cm 50 cm

×10 ×10

10 mm 70 mm 150 mm 250 mm 320 mm 450 mm 500 mm

×7
(a) filled in. Red is what you write. Both empty boxes are ×10 and ×7.

7 cm = 7 × 10 = 70 mm · 15 cm = 150 mm

250 mm = 250 ÷ 10 = 25 cm · 320 mm = 32 cm · 450 mm = 45 cm
50 cm = 50 × 10 = 500 mm

Empty boxes: the one below 7 cm is ×10, the bottom one is ×7

A misprint to know about: The very last label on the bottom line of (a) is printed as
"____ m". It should be "____ mm", because that whole line is in millimetres. The
answer is 500 mm. (500 mm is only half a metre, so "m" cannot be right.)

(b) metres and centimetres — 1 m = 100 cm

TOP LINE (M) 1m 4m 10 m 12 m 14 m 17 m 21 m

BOTTOM LINE (CM) 100 cm 400 cm 1,000 cm 1,200 cm 1,400 cm 1,700 cm 2,100 cm

Both empty boxes: the one under 4 m is ×100, the bottom one is ×4

1 m = 1 × 100 = 100 cm · 4 m = 400 cm · 10 m = 1,000 cm

1,200 cm = 1,200 ÷ 100 = 12 m · 1,400 cm = 14 m · 1,700 cm = 17 m

21 m = 21 × 100 = 2,100 cm

(c) kilometres and metres — 1 km = 1,000 m

Page 26 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

TOP LINE (KM) 1 km 9 km 25 km 41 km 55 km 67 km 82 km

BOTTOM LINE 1,000 m 9,000 m 25,000 m 41,000 m 55,000 m 67,000 m 82,000 m
(M)

Both empty boxes: the one under 9 km is ×1,000, the bottom one is ×9

9 km = 9 × 1,000 = 9,000 m · 25 km = 25,000 m

41,000 m = 41,000 ÷ 1,000 = 41 km · 55,000 m = 55 km · 67,000 m = 67 km

82 km = 82,000 m

The one idea behind all three: Going down to the smaller unit means multiplying —
by 10 for cm to mm, by 100 for m to cm, by 1,000 for km to m. Going up to the
bigger unit means dividing by the same number. The smaller the unit, the more of
them you need, so the number gets bigger.

Quick trick with zeros: ×10 adds one zero, ×100 adds two zeros, ×1,000 adds three
zeros. 82 km → 82,000 m. And going the other way, take the zeros off: 25,000 m →
25 km.

Q2 Use your understanding from above to fill in the blanks appropriately. (a) 4 cm 5
mm = ____ mm (b) 89 mm = ____ cm ____ mm (c) 234 cm = ____ mm (d) 514 mm = ____ cm
____ mm (e) 6 m 34 cm = ____ cm (f) 20 m 12 cm = ____ cm (g) 397 m = ____ cm (h) 5,792
cm = ____ m ____ cm (i) 9,108 cm = ____ m ____ cm (j) 34 km = ____ m (k) 6,870 m = ____ km
____ m (l) 10,552 m = ____ km ____ m (m) 29 km 30 m = ____ m (n) 32 km 359 m = ____ m

Keep three facts in front of you: 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1,000 m.

Page 27 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

PART ANSWER WORKING

(a) 4 cm 5 mm 45 mm 4 cm = 40 mm; 40 + 5 = 45

(b) 89 mm 8 cm 9 mm 89 = 80 + 9; 80 mm = 8 cm

(c) 234 cm 2,340 mm 234 × 10 = 2,340

(d) 514 mm 51 cm 4 mm 514 = 510 + 4; 510 mm = 51 cm

(e) 6 m 34 cm 634 cm 6 m = 600 cm; 600 + 34 = 634

(f) 20 m 12 cm 2,012 cm 20 m = 2,000 cm; 2,000 + 12 = 2,012

(g) 397 m 39,700 cm 397 × 100 = 39,700

(h) 5,792 cm 57 m 92 cm 5,792 = 5,700 + 92; 5,700 cm = 57 m

(i) 9,108 cm 91 m 8 cm 9,108 = 9,100 + 8; 9,100 cm = 91 m

(j) 34 km 34,000 m 34 × 1,000 = 34,000

(k) 6,870 m 6 km 870 m 6,870 = 6,000 + 870

(l) 10,552 m 10 km 552 m 10,552 = 10,000 + 552

(m) 29 km 30 m 29,030 m 29 km = 29,000 m; 29,000 + 30

(n) 32 km 359 m 32,359 m 32 km = 32,000 m; 32,000 + 359

There are only two kinds of question here, and each has its own recipe.
Recipe 1 — big unit into small unit (parts a, c, e, f, g, j, m, n):

1. Change the big part by multiplying (×10, ×100 or ×1,000).
2. Add the small part that was already there.

Recipe 2 — small unit into big unit (parts b, d, h, i, k, l):

1. Split the number into a round part and a leftover: 5,792 = 5,700 + 92.
2. The round part changes into whole big units: 5,700 cm = 57 m.
3. The leftover stays as it is: 92 cm.

Why the split works: 5,700 cm is exactly 57 hundreds of centimetres, and each
hundred is one metre. The 92 left over is not enough to make another whole metre,
so it stays in centimetres.

Page 28 of 50

as e
Class 5 Maths Chapter 5 Far and Near
a g l AglaSem · NCERT Solutions

co m
m.
Watch part (i): 9,108 cm = 91 m 8 cm, not 91 m 80 cm. Look at the last two digits —

m as e
l
they are 0 and 8, which is eight, not eighty.
.co a g
a s em
gl any answer by going back: Part (l) says 10,552 m = 10 km 552 m. Check: 10
aCheck
km = 10,000 m, and 10,000 + 552 = 10,552 ✓

co m
m . ag
l a se
ag — Pages 64–65
Adding and Subtracting Lengths

m
Saji's walk and the electricians' cable

co
em.
as
ADDING AND SUBTRACTING LENGTHS

m l
.co a g
a s em
l
Saji saw on his smartphone that he walked 3 km 450 m in the morning and another
g
Q1

a 4 km 650 m in the evening. How much did he walk in the whole day? How would you
solve this problem? Share your thoughts in class.
m a s
em
.co agl
a s

agl day.
Saji walked 8 km 100 m in the whole
There are two good ways. Both give the same answer — use whichever you like.

co m
Way 1 — add like units together.
m .
o m l a se
.c the metres. 450 m + 650 m = 1,100 m. g
1. Add the kilometres. 3 km + 4 km = 7 km.
2. m
e a
las3. 1,100 m is more than a kilometre, so change it: 1,100 m = 1 km 100 m.
Add

ag
m
4. Put the pieces together. 7 km + 1 km 100 m = 8 km 100 m.

a se
Way 2 — change everything into metres first.
. com a g l
m
ase
agl
1. 3 km 450 m = 3,000 + 450 = 3,450 m.
2. 4 km 650 m = 4,000 + 650 = 4,650 m.
3. Add. 3,450 + 4,650 = 8,100 m.

co m
4. Change back. 8,100 m = 8,000 m + 100 m = 8 km 100 m.
m .
m as e
c o
.Way 1: 7 km + 1,100 m = 7 km + 1 km 100 m = 8 km 100 mag l
se m
g l a
a Way 2: 3,450 m + 4,650 m = 8,100 m = 8 km 100 m
c
m .
Both ways agree ✓
m a s e
e m . co agl
g l as
a

com
m .
m ase
.co


a g l Page 29 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

Morning walk
3 km 450 m

Evening walk Whole day: 8 km 100 m
4 km 650 m

The two walks joined end to end make the whole day's walking.

Adding two lengths means laying them end to end.

Why 1,100 m had to be changed: We do not leave an answer as "7 km 1,100 m",
just as we do not leave 15 rupees as "1 ten and 5 ones and 10 more ones". Once the
metres reach 1,000 they make a whole kilometre, and that kilometre joins the
kilometre column.

Sample answer for the class discussion: "I liked Way 2 better, because once
everything is in metres it is just an ordinary addition sum like 3,450 + 4,650. Way 1 is
quicker in the head when the metres add up to less than 1,000."

Q2 Electricians are changing the cables in a house. They need 63 m of cable for this
purpose. They used 16 m 75 cm cable in the first room. What is the length of the
cable left?

46 m 25 cm of cable is left.
We must find what is left, so we subtract. First name the two quantities.

Cable they started with: 63 m
Cable already used: 16 m 75 cm

Change both into centimetres, then subtract.

1. 63 m = 63 × 100 = 6,300 cm.
2. 16 m 75 cm = 1,600 + 75 = 1,675 cm.
3. Subtract. 6,300 − 1,675 = 4,625 cm.
4. Change back into metres. 4,625 = 4,600 + 25, and 4,600 cm = 46 m. So the answer is 46 m
25 cm.

Page 30 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

6,300 cm

− 1,675 cm

———————————

4,625 cm

4,625 cm = 4,600 cm + 25 cm = 46 m 25 cm

You can also subtract in two columns, metres and centimetres, exactly as the book shows.
Because 0 cm is less than 75 cm, borrow one metre and turn it into 100 cm.

M CM

Start with 63 → 62 00 → 100

Take away 16 75

Left 46 25

Why we borrow 100 and not 10: When we borrow in ordinary subtraction, one ten
becomes 10 ones. Here, one metre becomes 100 centimetres — because that is how
many centimetres a metre holds. The borrowing rule always follows the unit.

Check it yourself: Add back. 46 m 25 cm + 16 m 75 cm = 62 m and 100 cm = 63 m ✓
That is exactly the cable they started with.

Let Us Do — Page 66
Word problems on adding and subtracting lengths

LET US DO

Q1 Rani has two red-coloured ribbon rolls, one of length 3 m 75 cm and another 2 m 25
cm long. How much ribbon does she have?

Rani has 6 m of ribbon.
We must find the total length, so we add the two rolls.

Page 31 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

1. Add the metres. 3 m + 2 m = 5 m.
2. Add the centimetres. 75 cm + 25 cm = 100 cm.
3. 100 cm is a whole metre, so change it: 100 cm = 1 m.
4. Join them. 5 m + 1 m = 6 m.

3 m 75 cm + 2 m 25 cm

= 5 m + 100 cm

=5m+1m

= 6 m of ribbon

Check it the other way: 3 m 75 cm = 375 cm and 2 m 25 cm = 225 cm. 375 + 225 =
600 cm = 6 m ✓

Why the answer is so neat: 75 and 25 are partners that make 100. Look for such
pairs — 40 and 60, 30 and 70, 90 and 10 — they turn a messy addition into an easy
one.

Q2 The distance from Bhopal to Sanchi is 48 km 700 m. Bhadbhada Ghat waterfall is on
the way, and 17 km 900 m away from Bhopal. How far is Sanchi from the waterfall?

Sanchi is 30 km 800 m from the waterfall.
Name the quantities first. Bhopal, the waterfall and Sanchi lie on one road, in that order.

Bhopal Bhadbhada Ghat Sanchi

17 km 900 m 30 km?800 m
Whole road Bhopal → Sanchi = 48 km 700 m
The waterfall is on the way, so the two smaller pieces make up the whole road.

1. Change both distances into metres. 48 km 700 m = 48,700 m. 17 km 900 m = 17,900 m.
2. Subtract, because we want the leftover piece of road. 48,700 − 17,900 = 30,800 m.
3. Change back. 30,800 m = 30,000 + 800 = 30 km 800 m.

Page 32 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

48,700 m

− 17,900 m

—————————————

30,800 m = 30 km 800 m

Check it yourself: 17 km 900 m + 30 km 800 m = 47 km 1,700 m = 48 km 700 m ✓
That is the full Bhopal–Sanchi road.

Did you know? Sanchi in Madhya Pradesh has the Great Stupa, built more than two
thousand years ago in the time of Emperor Ashoka.

Q3 Gulmarg Gondola in Gulmarg, Kashmir is the second longest and second highest
cable car in the world. It is divided into two sections. The first section covers 2 km
300 m and the second section covers 2 km 650 m. What is the total distance covered
by the cable car?

The cable car covers 4 km 950 m in all.
We want the total, so we add the two sections.

1. Add the kilometres. 2 km + 2 km = 4 km.
2. Add the metres. 300 m + 650 m = 950 m.
3. 950 m is less than 1,000 m, so it stays as it is. No carrying needed.

2 km 300 m + 2 km 650 m

= 4 km 950 m

= 4 km 950 m (= 4,950 m)

Why nothing was carried here: A kilometre is only made when the metres reach
1,000. Here they reached only 950, which is 50 short. So the metres stay in the metre
place.

Check it yourself: 2,300 m + 2,650 m = 4,950 m ✓ And 4,950 m = 4 km 950 m.

Page 33 of 50

as e
Class 5 Maths Chapter 5 Far and Near
a g l AglaSem · NCERT Solutions

co m
m.
Circle the bigger length and find the difference. (a) 11 mm and 1 cm (b) 26 mm and 2
e
Q4

m 1,480 m and 7 km 479 m
c6okm
cm (c) 20 cm and 201 mm (d) 1,020 mm and 1 m (e) 2 m and 245 cm (f) 5,678 m and 6
g l as
. a
em
km (g)

a s
agl

m
The one rule: change both lengths into the same unit first, then compare and subtract.
. co ag
em
PART
UNIT agl
as
BOTH IN ONE BIGGER LENGTH (CIRCLE
THIS)
DIFFERENCE

com
(a) 11 mm and 1 cm 11 mm and 10 mm 11 mm 1 mm

.
m 6 mm
as e
com l
(b) 26 mm and 2 cm 26 mm and 20 mm 26 mm

. a g
m
ase
agl(d) 1,020 mm and 1 m
(c) 20 cm and 201 mm 200 mm and 201 mm 201 mm 1 mm

1,020 mm and 1,000 1,020 mm 20 mm = 2 cm
mm
om a s
e
. c
mcm 245 cm agl
a s
(e) 2 m and 245 cm 200 cm and 245 45 cm

(f) 5,678 m and 6 km agl
5,678 m and 6,000 m 6 km 322 m

m
.co
(g) 6 km 1,480 m and 7 km 7,480 m and 7,479 m 6 km 1,480 m 1m
479 m
se m
com g l a
m . a
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The working, one part at a time.

agl
(a) 1 cm = 10 mm. 11 − 10 = 1 mm
se m
(b) 2 cm = 20 mm. 26 − 20 = 6 mm .com g l a
em a
a s
agl
(c) 20 cm = 200 mm. 201 − 200 = 1 mm

(d) 1 m = 1,000 mm. 1,020 − 1,000 = 20 mm, which is 2 cm

co m
(e) 2 m = 200 cm. 245 − 200 = 45 cm
m .
m as e
.co
(f) 6 km = 6,000 m. 6,000 − 5,678 = 322 m
a g l
se m (g) 6 km 1,480 m = 6,000 + 1,480 = 7,480 m
g l a
a c
7 km 479 m = 7,000 + 479 = 7,479 m
m .
m a s e
co agl
7,480 − 7,479 = 1 m
m .
ase
a g l

com
m .
m ase
.co


a g l Page 34 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

Part (g) is the tricky one. At first glance 7 km 479 m looks bigger, because 7 is
bigger than 6. But 6 km 1,480 m has 1,480 metres in it — more than a whole
kilometre extra. Once you change both into metres the trap disappears: 7,480 m
against 7,479 m. Never compare only the first number.

Tip: Parts (a) and (c) show how close two lengths can be — just 1 mm apart. That is
why millimetre marks matter on a ruler.

Multiplying and Dividing Lengths — Pages 66–67
Shirts, cloth for bags, a sari border and a new road

MULTIPLYING AND DIVIDING LENGTHS

Q1 We need a 1 m 80 cm cloth to make a shirt for a 10-year old child. How much cloth
will be needed to make shirts for 20 such children?

36 m of cloth is needed.
We need cloth for 20 shirts, and each shirt takes the same amount. So we multiply.

1. Break the length into its two parts: 1 m and 80 cm.
2. Multiply each part by 20. 20 × 1 m = 20 m. 20 × 80 cm = 1,600 cm.
3. Change the centimetres into metres. 1,600 cm = 1,600 ÷ 100 = 16 m.
4. Add the two answers. 20 m + 16 m = 36 m.

20 × 1 m 80 cm

= (20 × 1 m) + (20 × 80 cm)

= 20 m + 1,600 cm
= 20 m + 16 m

= 36 m of cloth

The other way — change into centimetres first.

Page 35 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

1 m 80 cm = 180 cm

20 × 180 = 3,600 cm

3,600 cm = 3,600 ÷ 100 = 36 m ✓ same answer

Why breaking the length up is allowed: Twenty shirts each needing 1 metre plus
80 centimetres is the same as twenty whole metres plus twenty lots of 80
centimetres. You are only grouping the cloth differently — the total does not change.

Check it yourself: Go backwards. 36 m ÷ 20 = 3,600 cm ÷ 20 = 180 cm = 1 m 80 cm,
which is exactly one shirt ✓

Q2 A shop sells cloth for making bags at ₹100 for 5 m. How much money is needed to
buy a 1 m cloth? Now, use the double number line to find the cost of the cloth or the
length of cloth that we can buy at a particular cost. (Top line: 5 m, 10 m, 20 m, 40 m,
___ m. Bottom line: ₹100, ₹___, ₹___, ₹___, ₹2000. Boxes: ×__, ×__, ×__.)

× ___

5m 10 m 20 m 40 m ____ m

× ___

₹100 ₹____ ₹____ ₹____ ₹2000

× ___

The double number line printed on page 67.

1 m of cloth costs ₹20.

5 m costs ₹100

1 m costs 100 ÷ 5 = ₹20

Page 36 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

Now fill the double number line. Every metre costs ₹20, so to go from the top line to the bottom
line you multiply by 20.

×2

5m 10 m 20 m 40 m 100 m

×20

₹100 ₹200 ₹400 ₹800 ₹2000

×2
Metres on top, rupees below. Down the arrow is ×20; across the top from 5 m to 10 m is ×2.

LENGTH OF CLOTH 5m 10 m 20 m 40 m 100 m

COST ₹100 ₹200 ₹400 ₹800 ₹2000

10 m: 10 × 20 = ₹200

20 m: 20 × 20 = ₹400

40 m: 40 × 20 = ₹800

₹2000: 2000 ÷ 20 = 100 m

The three empty boxes are ×2 (5 m to 10 m), ×20 (metres to rupees) and ×2 (₹100 to ₹200).

Why the two lines move together: Double the cloth, double the money. From 5 m
to 10 m the length doubles, and from ₹100 to ₹200 the money doubles too. That is
why one arrow labelled ×2 works for both lines.

Check it yourself: 100 m × ₹20 = ₹2,000 ✓ And ₹800 ÷ ₹20 = 40 m ✓

Page 37 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

Q3 Anita is making an embroidery on the border of a sari. She needs a 1 m long thread
to embroider a 50 cm sari. How much thread would she need for a 5 m sari border?
A 1 m long thread costs ₹50. How much money will be needed to buy the thread?

She needs 10 m of thread, and it will cost ₹500.
Name the quantities first. Every 50 cm of border eats up 1 m of thread. The border is 5 m long.

1. Put the border into centimetres. 5 m = 5 × 100 = 500 cm.
2. Find how many 50 cm pieces are in the border. 500 ÷ 50 = 10 pieces.
3. Each piece needs 1 m of thread. So 10 pieces need 10 × 1 m = 10 m of thread.
4. Now the money. 1 m of thread costs ₹50, so 10 m cost 10 × 50 = ₹500.

Border = 5 m = 500 cm

500 ÷ 50 = 10 parts

Thread needed = 10 × 1 m = 10 m

Cost = 10 × ₹50 = ₹500

The 5 m border, cut into ten 50 cm pieces

each piece = 50 cm

Each piece needs 1 m of thread → 10 pieces need 10 m of thread
10 m of thread × ₹50 for each metre = ₹500

Ten equal pieces of border, and one metre of thread for each of them.

Why the thread is longer than the border: Embroidery thread goes up and down
through the cloth again and again, so it uses more thread than the plain length of
the border. Here it uses twice as much — 1 m of thread for every 50 cm of border.

Check it yourself: If 50 cm needs 1 m, then 1 m of border needs 2 m of thread. So 5
m of border needs 5 × 2 = 10 m ✓ Same answer by a second route.

Page 38 of 50

as e
Class 5 Maths Chapter 5 Far and Near
a g l AglaSem · NCERT Solutions

co m
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A road 12 km 600 m long is being laid in a town. The workers lay an equal length of
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road each day, and complete the work in 6 days. How much road-laying work is
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2 km 100 m of road is laid each day.
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The whole road is shared equally over 6 days, so we divide.
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1. Change the road into metres. 12 km 600 m = 12,000 + 600 = 12,600 m.
2. Divide by the number of days. 12,600 ÷ 6 = 2,100 m.
3. Change the answer back. 2,100 m = 2,000 + 100 = 2 km 100 m.
co m
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12 km 600 m = 12,600 m

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2,100 m = 2 km 100 m each day
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Let Us Estimate — Page 68
m a s e
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g l as
a

co m
m .
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Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

Guessing heights and depths using a reference

LET US ESTIMATE

Q1 The height of the tallest building in your neighbourhood. What did you use as a
reference to estimate the height?

Use something whose height you already know as a measuring stick. That known thing is
called a reference.
The book gives you two good references on this very page.

A single-storeyed house is about 3 m tall.
An electric pole is about 8 m to 9 m tall.

1. Stand where you can see the whole building.
2. Count its floors. Each floor of a house is about 3 m.
3. Multiply. Floors × 3 m gives the height.
4. Check with the pole. If the building looks about as tall as one and a half electric poles, that
is about 13 m — which should match your first answer roughly.

Sample answer: "The tallest building near my house is the four-storeyed hospital. Each storey is
about 3 m, so 4 × 3 m = 12 m. I used a single-storeyed house as my reference, because the
hospital looked exactly four of those stacked up. It also looked a little taller than the electric
pole in front of it, which fits, because the pole is about 9 m."

4 floors × 3 m for each floor = about 12 m

Why an estimate is useful: Nobody can climb up with a tape measure. But if you
know one height for sure, you can compare everything else to it. That is what
estimating means — a sensible near answer, not a wild guess.

Say "about": An estimate should be written as "about 12 m", not "12 m". Saying
"about" is honest, and it is the mark of a careful measurer.

Q2 The height of the tallest tree in your neighbourhood. What did you use as a
reference?

Use the electric pole, or a person, as your reference.

Page 40 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

1. Find a pole or a person standing near the tree.
2. See how many of them would stack up to the top of the tree. Hold your thumb up at
arm's length to help you compare.
3. Multiply. If the tree is about one and a half poles high, and a pole is about 9 m, the tree is
about 13 m or 14 m.

Sample answer: "The tallest tree near my home is an old neem tree in the temple courtyard. My
father is about 1 m 70 cm tall, and I counted that about eight of him would reach the top. So the
tree is roughly 8 × 1 m 70 cm, which is about 13 m or 14 m. I used my father's height as the
reference because he was standing right at the trunk."

8 × 1 m 70 cm
= 8 × 170 cm

= 1,360 cm

= about 13 m 60 cm

Try this on a sunny day: Stand a 1 m stick upright and measure its shadow. Then
measure the tree's shadow. If the stick's shadow is 2 m and the tree's shadow is 26
m, the tree is 13 m — because the tree's shadow is 13 times the stick's shadow, so
the tree is 13 times the stick.

Q3 The depth of a well or swimming pool in your neighbourhood. How did you find out?

Depth cannot be seen, so measure it with a rope and a stone.

1. Tie a small stone to the end of a long rope.
2. Lower it slowly until the stone touches the bottom.
3. Pinch the rope at the place where it meets the top of the well.
4. Pull the rope out and measure from the stone up to your pinch, using a long tape.

For a swimming pool it is even easier: the depth is usually painted on the side, in metres, at the
shallow end and the deep end.
Sample answer: "The well in our village is about 12 m deep. I tied a stone to a rope and lowered
it until it touched the bottom. When I pulled the rope out and measured it with a long tape, it
was 12 m. The swimming pool at the sports ground has 1 m painted at the shallow end and 2 m
at the deep end."

Page 41 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

Why the rope works: The rope takes the shape of the depth. Once it is out of the
well it is just a straight length lying on the ground, and a straight length is easy to
measure. This is the same trick as using a thread to measure a curved sprout.

Safety first: Never lean over a well. Ask an adult to lower the rope while you hold
the tape.

Let Us Explore — Page 68
Feet and inches — the units we use for height

LET US EXPLORE

Q1 In daily life, we use other units of measuring length as well. Height is usually
measured in feet and inches. Look at your ruler to see if inches are also marked on
it. Find out how many cm and mm equal 1 inch.

1 inch = 2 cm 5 mm, which is 25 mm. And 1 foot = 12 inches, about 30 cm.
Look at your ruler. Many rulers have centimetres along one long edge and inches along the
other.

1. Turn the ruler to the inch side. The numbers there are much further apart than the
centimetre numbers.
2. Line up the 0 of the inch side with the 0 of the centimetre side.
3. Look at where the 1 inch mark falls on the centimetre side. It lands a little past the
halfway point between 2 and 3.
4. Read it: 2 cm and about 5 small marks more — that is 2 cm 5 mm.

centimetres

1 2 3 4

1 inch

1 inch reaches past 2 cm and 5 small marks more.
So 1 inch = 2 cm 5 mm = 25 mm.

Page 42 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

One inch measured against the centimetre scale.

1 inch = 2 cm 5 mm = 25 mm

1 foot = 12 inches

1 foot = 12 × 2 cm 5 mm = 12 × 25 mm = 300 mm = 30 cm

Why 12 inches make about 30 cm: Each inch is 25 mm. Twelve of them are 12 × 25
= 300 mm. And 300 mm = 30 cm, because 10 mm make 1 cm. So a foot is about
three tenths of a metre.

Did you know? If you measure very carefully, one inch is 2 cm 5 mm and a tiny bit
more (2.54 cm). Books for your class round it to 2 cm 5 mm, which is close enough
for everyday work.

Try This: Measure your school desk in centimetres and then in inches. Divide the cm
number by 25 mm — you should get roughly the inch number.

Measure Your Height — Page 69
Measuring heights in feet and inches

MEASURE YOUR HEIGHT

Q1 Stand against a wall and mark your height. Measure the distance between the floor
and the marked point in feet and inches. Similarly, other students in the class can
also measure their heights. Find out who is the tallest student in your class. What is
his or her height in feet and inches?

Here is how to do it properly, and then a sample answer.

1. Take off your shoes and stand with your back flat against the wall. Heels touching the wall,
head straight, eyes looking forward.
2. Ask a friend to lay a book flat on your head, touching the wall. Make a light pencil mark on
the wall under the book.
3. Step away. Measure from the floor up to the mark with a measuring tape.
4. Read it in feet and inches if the tape has them, or read it in centimetres and change it:
divide by 30 to get feet, and change what is left over into inches by dividing by 2 cm 5 mm.

Page 43 of 50

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Class 5 Maths Chapter 5 Far and Near
a g l AglaSem · NCERT Solutions

5. Write everyone's height in a class table. Then look for the biggest number — that is the
co m
tallest student.
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Suppose your height is 130 cm.
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10 cm = 100 mm; 100 ÷ 25 = 4 → 4 inches
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NAME HEIGHT IN CM HEIGHT IN FEET AND INCHES

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Meera 128 cm about 4 ft 2 in

aglArjun 133 cm about 4 ft 4 in

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Fatima 136 cm about 4 ft 6 in

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Ravi (tallest) 142 cm
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In this sample class the tallest student is Ravi, whose height is about 4 feet 8 inches.

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Try This — Page 69
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m a s e
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g l as
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co m
m .
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Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

The operation-sign puzzle

TRY THIS

Q1 Put appropriate operation sign (+, –, ×, ÷) such that each row and column and each 4
× 4 box should not repeat the sign. (The grid is given with ÷ in row 1 column 1, + in
row 1 column 4, × in row 2 column 2, + in row 3 column 3, and – in row 4 column 4.)

÷ +

×

+

−

The 4 × 4 grid printed on page 69, with five signs already filled in.

Here is the completed grid. Every row has all four signs, and so does every column.

Page 45 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

COLUMN 1 COLUMN 2 COLUMN 3 COLUMN 4

ROW 1 ÷ – × +

ROW 2 + × – ÷

ROW 3 – ÷ + ×

ROW 4 × + ÷ –

÷ – × +

+ × – ÷

– ÷ + ×

× + ÷ –

Black signs were printed in the book. Red signs are the ones you work out.

How to find them, one clue at a time.

1. Row 1 already has ÷ and +. So the two empty places must hold – and ×, in some order.

Page 46 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

2. Look down column 2. Row 2 already has ×. So row 1 column 2 cannot be ×; it must be –. That
leaves × for row 1 column 3.
3. Look down column 4. It has + at the top and – at the bottom, so the two middle places take
× and ÷. Row 2 already has ×, so row 2 column 4 must be ÷, and row 3 column 4 must be ×.
4. Row 2 now has ×, ÷. The two left places take + and –. Column 3 already has × and + in it, so
row 2 column 3 must be –. That leaves + for row 2 column 1.
5. Column 1 has ÷ and +. Row 3 column 1 must be – or ÷, and ÷ is already used in that column,
so it is –. Then row 3 column 2 is ÷, and row 4 column 1 is ×.
6. Row 4 now has × and –. Column 2 already has –, ×, ÷, so row 4 column 2 is +, and row 4
column 3 is ÷.

The one idea behind the whole puzzle: Every time, ask "which signs are already
used in this row and in this column?" Cross those out. If only one sign is left, you
have found the answer. This is how every Sudoku-style puzzle is solved — never by
guessing.

Check it yourself: Read each of the four rows aloud, and then each of the four
columns. Every one should contain +, –, × and ÷ exactly once. Row 3, for example, is
–, ÷, +, × ✓

About the wording: The book says "each 4 × 4 box", but the whole grid is the only 4
× 4 box there is. The real conditions are the ones we used — no sign twice in any
row, and none twice in any column. More than one filling is possible; the one above
is a correct answer.

Chapter at a glance
Choose the unit that fits the thing. A handkerchief is about 40 cm long. India Gate is
about 42 m tall. Both use the number 40-something, but one needs centimetres and the
other needs metres. Ask yourself: is this thing about as big as my hand, my classroom, or
my village? Small things take cm, room-sized things take m, far-away places take km.
1 m = 100 cm. So a metre is a hundred centimetres joined in a line. To change metres into
centimetres, multiply by 100. 6 m = 6 × 100 = 600 cm. To change centimetres into metres,
see how many hundreds are inside. 540 cm = 500 cm + 40 cm = 5 m 40 cm.
1 km = 1,000 m. Kilo means thousand. When you walk 1,000 m, you have walked 1 km. This
is the unit for long distances — the road to the next town, a train journey, a race. 34 km = 34
× 1,000 = 34,000 m.

Page 47 of 50

Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

1 cm = 10 mm. Look at your ruler. Between the 1 and the 2 there are nine small lines, which
cut that centimetre into ten equal parts. Each tiny part is one millimetre. Millimetres let us
measure small things — a sprout, a screw, a nail. 89 mm = 80 mm + 9 mm = 8 cm 9 mm.
The same length can be written in two ways. 750 cm and 6 m 150 cm look different but
they are the same length, because 6 m 150 cm = 600 cm + 150 cm = 750 cm. Before you
compare two lengths, always change both into the same unit. Then compare like ordinary
numbers.
A double number line shows two units together. One line is marked in cm, the line below
it in mm, and the two lines are lined up tick for tick. Jumping from the top line to the bottom
line means multiplying by 10. Jumping sideways along a line means multiplying by 7, or 4, or
whatever the step is. It is a picture of a conversion.
Adding and subtracting lengths. There are two safe ways. Way 1 — add the same units
together: 3 km + 4 km = 7 km, and 450 m + 650 m = 1,100 m, which is 1 km 100 m, so the
total is 8 km 100 m. Way 2 — change everything into the smaller unit first: 3,450 m + 4,650
m = 8,100 m = 8 km 100 m. Both give the same answer.
Multiplying and dividing lengths. Break the length into its two parts and work on each. 20
shirts × 1 m 80 cm = (20 × 1 m) + (20 × 80 cm) = 20 m + 1,600 cm = 20 m + 16 m = 36 m. For
dividing, change into the smaller unit: 12 km 600 m ÷ 6 = 12,600 m ÷ 6 = 2,100 m = 2 km 100
m each day.
Feet and inches are also used every day. Height is usually told in feet and inches. On a
ruler, 1 inch is a little more than two and a half centimetres — the book takes 1 inch = 2 cm 5
mm. And 1 foot = 12 inches, about 30 cm.

Page 48 of 50

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Class 5 Maths Chapter 5 Far and Near
a g l AglaSem · NCERT Solutions

co m
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Quick revision
m l a se
m .co WHAT IT MEANS ag EXAMPLE
ase
WORD WHERE IT

agl
APPEARS

Length How long a thing is from end to end Page 57, first A handkerchief is 40 cm

m
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paragraph long

a s em
agl
Distance How far apart two places are Chapter title Far Dibrugarh to
and Near, page 57 Kanniyakumari is 4,187
km

. com
m 13 cm long
Centimetre (cm) A small standard unit; the numbered Let Us Find, page A mobile phone is

com l ase
marks on your ruler 57 about

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Metre (m) 100 centimetres joined in a line Let Us Find, page A well can be 50 m

a g l 57 deep

a s
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Millimetre (mm) One of the ten equal parts of a centimetre The World of Small 1 cm = 10 mm

. agl
Things, page 61

e m
forslong distances
1,000 metres; used a
Kilometre (km)
a g l Let Us Explore,
page 59
3-km race = 3,000 m

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Kilo A word meaning thousand Page 59 Kilometre = thousand

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metres

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Double.number 63gand
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Two number lines drawn one below the 1 cm on top, 10 mm

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other, lined up, showing the same 67 below it

a lengths in two units

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A very long measuring tape used on a Measuring Long Used to mark 100 m
g l a
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playground

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Rodometer
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A wheel you push along the ground; it Measuring Long Used to measure a
(measuring wheel) counts how far it has rolled Distances, page 59 road

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Distances, pagem
Rangefinder / Laser Tools that measure a distance without Measuring Long

m
distance meter walking it
a s e 59 across a field
e m . c o aglof Small Millimetre marks add
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Precision The World
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How exact a measurement is

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Things, page 61 precision

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Inch A unit used for height; a little more than Let Us Explore, 1 inch = 2 cm 5 mm
s e m
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2½ cm page 68

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Foot
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12 inches, about 30 cm Let Us Explore, A child may be 4 ft 2 in
a page 68 tall

co m
m .
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.co


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Class 5 Maths Chapter 5 Far and Near AglaSem · NCERT Solutions

WORD WHAT IT MEANS WHERE IT EXAMPLE
APPEARS

Reference A thing whose size you already know, Let Us Estimate, A one-storeyed house
used to guess another size page 68 is about 3 m

Page 50 of 50