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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 3 · M AT H S
NCERT Solutions
Chapter 8: Fair Share
NCERT Textbook — Maths Mela
BOOK PAGES SECTIONS QUESTIONS MEDIUM
107 – 116 13 44 English
Every question Step by step Exam ready
Activities, in-text questions The working shown, not Written to match how
and all exercises. just the final answer. marks are awarded.
Solutions, notes, sample papers & more at 44 pages
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l h h e i h e A aS m · NCERT So ut ons
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C L A SS 3 · M AT H S · M AT H S M E L A
NCERT So ut ons — C apt r 8: Fa r S ar
l i h e i h e
This chapter is all about sharing things fairly. You learn what a half and a quarter are, how to check that
parts are really equal, and what double means.
T E XT B OOK B OOK PAGE S
Ma h Mela Cla
t s ss 3 107 116
S EC T I ONS QU E ST I ONS
13 44
M EDI UM
English
In-text Questions — Page 107
Shabnam and Mukta share their lunch
Q1 How do you think they are going to share the chocolate and the paratha equally?
One whole chocolate bar and one whole paratha .
They will cut each thing into two equal parts.
Break the chocolate along its middle line.
Fold the paratha in half and cut on the fold.
Shabnam takes one part and Mukta takes the other.
Why Two equal parts give both girls the same amount
: .
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Q2 Think about a strategy that you can use to check whether the two pieces are equal or
not.
1 2
The chocolate has been broken into two pieces and
, 1 2.
Put one piece on top of the other piece.
Place piece 2 exactly over piece 1.
If they cover each other fully, the pieces are equal.
If one piece sticks out, they are not equal.
Why Equal parts are the same size so one sits exactly on the other
: , .
Let us iscuss — Page 107
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Sharing objects equally
L E T US DI S C USS
Q1 How do you share objects equally?
6 sweets
p at 1
l e p at 2
l e
Six sweets and two empty plates .
Give one object to each person, turn by turn.
One sweet to plate 1, one sweet to plate 2.
Keep going until no sweet is left.
Count both plates. Here each plate gets 3.
Why Giving one at a time makes both shares grow together so they stay equal
: , .
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co m
m.
Q2 Why is Shabnam folding the paratha over itself ?
m ase
.co a g l
se m
g l a
a
co m
em . ag
g l as
a
co m
em.
.co
m A whole paratha, and the same paratha after it is fg
a lasover.
olded
m
ase
agl
s
She folds it to find the middle of the parat.hcao. m a
em agl
asother.
The two sides sit exactly on ealch
g
Cutting on the fold gives twoa equal parts.
Why When both sides match the fold is exactly in the middle m.com
as e
: , .
m l
m.co a g
l a se
g
a n-text Questions — Page 108
I
se m
com g l a
m . a
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
co m
m .
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.co
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Half
Q1 Tick the paratha that has been cut equally.
Three parathas each with one cut line
, .
Tick the third paratha.
Its cut line goes right through the middle.
Both parts are the same size.
In the first two, the line is not in the middle.
Why A cut through the middle makes two halves Any other cut makes one part
: .
bigger.
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Q2 How many halves make one whole? Check with some halves.
Ha lf Ha lf
One whole card cut into two equal parts each marked Half
, .
Two halves make one whole.
Take two halves of a chapati.
Join them along the cut side.
You get back one full chapati.
Why The whole was cut into equal parts so those parts join back into whole
: 2 , 2 1 .
Let us o — Pages 108–109
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Half
L E T US D O
Q1 Circle the shapes where half of the whole is coloured.
Five objects. Part of each one is coloured.
Circle the kite, the apple and the orange rectangle.
In these, the coloured part and the white part match.
Pizza: 2 of its 3 equal parts are coloured. That is more than half.
The bottle is not cut into two equal parts.
The three shapes to circle.
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Q2 Draw a line to show one-half of the whole.
A tile, a piece of sugarcane, a carrom board and a paratha.
Draw one line through the middle of each object.
Tile — a line down the middle.
Sugarcane — a line across the middle.
Carrom board — join two opposite corners.
Paratha — a line through the centre.
The blue dashed lines .
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co m
m.
Q3 Shabnam has eaten some chikki from 3 sides. Tick how much chikki is left? (a) less
m
than half (b) more than Half (c) half
ase
.co a g l
se m
g l a
a
co m
em . ag
g l as
a
co m
em.
m l as
m.co a g
l a se
a g
m a s
em
.co agl
a s
aTghel orange squares are the chikki still left .
co m
m .
m as e
Tick (.cc)ohalf a g l
s em
.
gl a
a
m
Whole chikki = 6 × 4 = 24 small squares
a se
Orange squares left = 4 + 3 + 3 + 2 = 12
. com ag l
m
ase
agl
12 + 12 = 24, so 12 is half of 24
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a
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m .
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Q4 Show by colouring half a chikki that has been eaten from 2 sides.
A whole chikki made of small equal squares.
Colour 12 of the 24 small squares.
Whole chikki = 6 × 4 = 24 squares
Half of 24 = 12 squares
Here 6 + 4 + 1 + 1 = 12
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The 12 coloured squares show half.
Colouring the 12 eaten squares instead is also right.
Q5 Draw lines to show different ways of making a half.
Four equal hexagons drawn on a dot grid.
Draw one line through the centre of each hexagon.
Left corner to right corner.
Middle of the top side to middle of the bottom side.
Top-right corner to bottom-left corner.
Top-left corner to bottom-right corner.
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Four different ways of making a half.
Q6 Complete the whole picture by drawing the other half.
Three pictures each drawn only on one side
, .
Draw the same lines on the other side, like a mirror.
Count the dots and draw the same number on the other side.
Picture 1 becomes a triangle, picture 2 a diamond with a small triangle below, picture 3 a
square.
Red lines the other half
: .
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Let us xplore — Page 110
E
Folding paper to make a half
L E T US E XPLOR E
Q1 Take a rectangular sheet of paper and fold it in half. Find all the different ways to make
a half.
square sheet rectangular sheet
A square sheet of paper and a rectangular sheet of paper.
A rectangular sheet folds in half in 2 ways.
Fold the left side onto the right side.
Fold the top side onto the bottom side.
2 ways 4 ways
Red dashed lines show the folds .
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Why A corner to corner fold does not work the two parts do not sit on e.acchomother
m
:
se
- - : .
com g l a
m . a
ase
aQ2gl Take a square piece of paper and fold it in half. Find all the different ways to make a
half.
co m
em . ag
g l as
a
co m
em.
m l as
m .co a g
l a se
a g
square sheet
m rectangular sheet
a s
A square sheeet om .co agl
as f paper and a rectangular sheet of paper.
agl
co m
.
e m
c o m
A square sheet folds in half in 4 ways.
g l as
m . a
s e Left side onto right side
la Top side onto bottom side
.
ag
.
m
Along one corner-to-corner line.
a se
com l
Along the other corner-to-corner line.
. ag
m
ase
agl
co m
m .
m as e
.co a g l
se m
g l a
a c
m .
m a s e
2 ways m . co 4 ways agl
l a se
ag Red dashed lines show the folds .
co m
m .
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.co
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Why All four sides of a square are equal
: .
Let us iscuss — Page 110
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The old man and his two sons
L E T US DI S C USS
Q1 Is this a fair way of sharing? Is there another way to share it fairly?
man o trg ee so ar amp
l l woo n an tlle bl ke
The three things the old man gave to his two sons .
No, it is not fair.
Amit gets all the mangoes.
Bala gets the lamp in the day, when no one needs it.
Bala gets the blanket in summer, when no one needs it.
A fair way: Share the mangoes equally Use the lamp and the blanket by turns night by night
. , .
Let us o — Page 110
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Sharing mangoes
L E T US D O
Q1 Here are some mangoes. Share them equally between the two children.
One bowl of mangoes and two empty bowls one for each child
, .
There are 6 mangoes. Give them out one by one.
Put 1 mango in each childʼs bowl, again and again.
Stop when the first bowl is empty.
3 + 3 = 6, so each child gets 3 mangoes
The mangoes after sharing .
H alf and ouble — Page 111
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Fill in the blanks using double or half
Q1 4 marbles are ______ of 8 marbles.
4 8
Two plates of marbles .
The blank is half.
4+4=8
Why The smaller number is half of the bigger one Adding the smaller number
: .
twice gives the bigger number .
Q2 8 marbles are ______ of 4 marbles.
4 8
Two plates of marbles .
The blank is double.
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4+4=8
Why The bigger number is double of the smaller one Adding the smaller number
: .
twice gives the bigger number .
Q3 10 marbles are ______ of 5 marbles.
10 5
Two plates of marbles .
The blank is double.
5 + 5 = 10
Why The bigger number is double of the smaller one Adding the smaller number
: .
twice gives the bigger number .
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Q4 5 marbles are ______ of 10 marbles.
m as e
.co a g l
se m
g l a
a
co m
em . ag
g l as
a
10 5
Two plates of marbles
m
.
co
e m.
m l as
A NSW E R .co a g
a s em
agl
The blank is half .
m a s
.co agl
5 + 5 = 10
a s em
l
Why The smaller numberaisghalf of the bigger one Adding the smaller number
: .
twice gives the bigger number
com
.
.
m a s em
. co a gl
as em 6 marbles are
l
Q5 of 12 marbles.
g
______
a
se m
com g l a
m . a
ase
agl
co m
12
m .6
m as e
.co
Two plates of marbles
a g l
m
.
l a se
ag
.c
s e m
m a
The blank is half.
e m . co agl
g l as
6 + 6 = 12 a
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m .
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.co
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Why The smaller number is half of the bigger one Adding the smaller number
: .
twice gives the bigger number .
Q6 12 marbles are ______ of 6 marbles.
12 6
Two plates of marbles .
The blank is double.
6 + 6 = 12
Why The bigger number is double of the smaller one Adding the smaller number
: .
twice gives the bigger number .
Q7 On a number line, how far is 13 from the double of 7?
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
A number line from 0 to 17.
The answer is 1.
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Double of 7 = 7 + 7 = 14
From 13 to 14 is 1 step
1
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
The jump drawn on the number line .
Why : 13 and 14 are next to each other on the number line, so the gap is one step.
Q8 How far is 5 from half of 14?
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
A number line from 0 to 17.
The answer is 2.
Half of 14: 7 + 7 = 14, so half of 14 = 7
From 5 to 7 is 5 → 6 → 7 = 2 steps
2
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
The jump drawn on the number line .
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G uess Who am I? — Page 112
Use the clues to find the right number of marbles
PUZZL E
Q1 I have less than the double of 3 marbles. I have more than the half of 8 marbles. (a) 4
Marbles (b) 5 Marbles (c) 6 Marbles
(a) b
( ) c
( )
4 Mar bles 5 Mar bles 6 Mar bles
Three plates of marbles to choose from .
Tick (b) 5 Marbles.
Double of 3 = 3 + 3 = 6, so I have less than 6
Half of 8 = 4, because 4 + 4 = 8, so I have more than 4
The only number between 4 and 6 is 5
(a) b
( ) c
( )
4 Mar bles 5 Mar bles 6 Mar bles
The plate that has been circled.
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Q2 I have less than the double of 4 marbles. I have more than the half of 10 marbles. (a) 8
Marbles (b) 6 Marbles (c) 3 Marbles
(a) b
( ) c
( )
8 Mar bles 6 Mar bles 3 Mar bles
Three plates of marbles to choose from .
Tick (b) 6 Marbles.
Double of 4 = 4 + 4 = 8, so I have less than 8
Half of 10 = 5, because 5 + 5 = 10, so I have more than 5
Only 6 is less than 8 and more than 5
(a) b
( ) c
( )
8 Mar bles 6 Mar bles 3 Mar bles
The plate that has been circled.
In-text Questions — Page 112
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Quarter
co m
em.
m l as
Q1 .co
What part of the chikki did they get?
m a g
l a se
a g
com
e m . ag
g l as
a
co m
e m.
m l as
m .co a g
l a se
a g
a s
com
4 child
agl
ren shared it
.
em cut into four parts of the same size
One whoaleschikki
agl
.
co m
m .
as e
omgot one quarter of the chikki.
.c
Each child
a g l
m
se The chikki was cut into parts of the same size
a
agl It was shared equally among children
4 .
4 .
So one share is one quarter.
se m
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m . a
ase
agl
co m
m .
m as e
.co a g l
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m .
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Q2 How many quarters in a whole?
4 children shared it
One whole chikki cut into four parts of the same size
.
4 quarters m ake one whole.
1 quarter + 1 quarter + 1 quarter + 1 quarter = 1 whole
Why The whole was cut into equal parts so all parts join back into whole
: 4 , 4 1 .
Tip: 2 quarters together are the same as one half.
Let us o — Page 113
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Quarter
L E T US D O
Q1 Tick the objects that show quarters.
Four objects that have been cut into parts.
Tick the chikki and the chocolate bar.
Each of them is cut into 4 pieces of the same size.
The round roti has 4 pieces, but they are not the same size.
The orange is cut into only 2 pieces, so those are halves.
Q2 Draw lines to make a quarter of the whole.
A square tile, a roti, a flower and a rhombus, each still whole.
Draw two lines through the middle of each shape.
Square — one line down and one across.
Roti and flower — two lines through the centre, like a plus sign.
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Rhombus — join the opposite corners.
Two red lines make 4 equal parts.
Q3 Draw the remaining three quarters and complete the whole.
(a) b
( )
Each picture shows one part only.
Each picture is one quarter. Draw 3 more parts of the same size.
(a) Draw 3 more fan parts to make a full circle.
(b) Draw 3 more mats: 1 beside it and 2 below.
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(a) b
( )
The red parts complete each whole .
Q4 Draw the remaining quarters to complete the whole.
(a) b
( )
Each picture is made of three equal squares.
Each picture already has 3 equal squares, so draw 1 more.
Look for the empty corner.
Draw one square of the same size there.
The picture becomes a big square made of 4 quarters.
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co m
e m.
m l as
m.co a g
l a se
a g (a) b
( )
co m
em . ag
g l as
a
The square drawn in red fills the empty corner
co m
m.
.
m as e
.co a g l
m
se Quarter? — Page 114
aglflaor
a
H
Tick the right word for each blank
om a s
e m . c agl
s
Q1 Shabnam has coloured half/a qu arter of the birds.
a
agl
co m
m .
m as e
.co a g l
se m
g l a
a
se m
Shabnam
com
Mukta
g l a
s S. ome birds are coloured and some are left white
The two bird caredm a
a s
agl
. .
co m
.
em
m as
Tick half.
.co a g l
se m
g l a
a
Birds on Shabnam’s card = 8
.c
Coloured birds = 4
s e m
m a
4 + 4 = 8, so 4 is half of 8
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g l as
a
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m .
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Why Half means one of two equal groups
: . 4 and 4 make the 8 birds.
Q2 Mukta has coloured half/a quarter of the birds.
Shabnam Mukta
The two bird cards Some birds are coloured and some are left white
. .
Tick a quarter.
Birds on Mukta’s card = 8
Coloured birds = 2
2 + 2 + 2 + 2 = 8, so 2 is a quarter of 8
Why A quarter means one of four equal groups Four groups of make
: . 2 8.
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Q3 Shabnam has coloured half/double the number of birds that Mukta has coloured.
Shabnam Mukta
The two bird cards Some birds are coloured and some are left white
. .
Tick double.
Shabnam coloured 4 birds
Mukta coloured 2 birds
2 + 2 = 4, so 4 is double of 2
Why Double means the same number added again
: .
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Q4 Lakshanya tied half/a quarter of her flowers.
Lakshanya Peehu
Each girl has 16 flowers. The rest are still in her bowl.
Tick a quarter.
Lakshanya has 16 flowers
Flowers on her string = 4
4 + 4 + 4 + 4 = 16, so 4 is a quarter of 16
Why Four equal groups of make
: 4 16, so is one quarter of
4 16.
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Q5 Peehu tied half/a quarter of her flowers.
Lakshanya Peehu
Each girl has 16 flowers. The rest are still in her bowl.
Tick half.
Peehu has 16 flowers
Flowers on her garland = 8
8 + 8 = 16, so 8 is half of 16
Why Two equal groups of make
: 8 16, so is half of
8 16.
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co m
m.
Q6 Lakshanya tied half/double the number of flowers that Peehu tied.
m ase
.co a g l
se m
a
Lakshanya Peehu
a g l
co m
em . ag
g l as
a
co m
flowers The rest are still in her bowl m.
se
Each girl has 16
m l a
. .
. co ag
se m
l a
agA NSW E R
Tick half.
m a s
m .co agl
l a se
Lakshanya tied 4 flowers
a g
Peehu tied 8 flowers
co m
4 + 4 = 8, so 4 is half of 8
m .
m l a se
m .co a g
aseW hy La k s ha nya t ied fewer flowers so her number is t he h alf not the double
agl
: , , .
se m
com g l a
Let us o — Pages 115–116 em. a
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a
agl
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Quarters and whole
L E T US D O
Q1 Tick the shapes below that show three-quarters.
Eight shapes. Part of each shape is coloured.
Tick four shapes.
The green bar 3 of its 4 parts are green.
The triangle 3 of its 4 small triangles are coloured.
The orange rectangle 3 of its 4 parts are orange.
The red strip 3 of its 4 parts are red.
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The four shapes to tick .
− Exp anat on
l i
Three-quarters means 3 of the 4 equal parts are coloured. The other shapes do not show
it: the pink strip and the big yellow circle show 2 quarters (half), the blue triangle shows
half, and the small circle shows 1 quarter. The bookʼs Quarters and Whole box shows the
same idea:
1 quarter 2 quarters (half) 3 quarters 4 quarters (whole)
One quarter two quarters three quarters and four quarters of a circle
, , .
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Q2 Colour the shapes below to show the fractions as instructed.
2 quarters 1 quarter 3 quarters
3 quarters
4 quarters 1 quarter
Six shapes each already divided into four equal parts with its instruction
, , .
Each shape already has 4 equal parts. Colour as many as the words say.
Square 2 parts. Circle 1 part. Kite 3 parts.
Hexagon — all 4 parts. Strip 3 parts. Star 1 part.
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2 quarters 1 quarter 3 quarters
3 quarters
4 quarters 1 quarter
The six shapes after colouring .
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Draw lines and colour the shapes below to show the fractions as instructed.c.om
m
Q3
a se
. com ag l
m
ase
agl
co m
e m . ag
g l as
2 quarters a 1 quarter 3 quarters
co m
em.
m l as
m.co a g
l a se
a g
4 quarters
1 quarter
a s
com
3 quarters
Six plaeinmsh.apes each with its instruction agl
las
, .
ag
co m
.
se m
o m
First draw lines to make 4 equal parts, then colour.
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Dr.acw one line across the middle and one line down the middle
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Colour 2, 1, 3, 4, 3 and 1 parts, as the words say.
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l h h e i h e A aS m · NCERT So ut ons
gl e l i
2 quarters 1 quarter 3 quarters
4 quarters
3 quarters 1 quarter
The lines and the coloured parts .
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Page 42
l h h e i h e A aS m · NCERT So ut ons
gl e l i
Q4 Here is a rectangle which shows quarters. Discuss how.
A rectangle of 16 small squares, painted in four colours.
The rectangle has 16 small squares.
Each colour (green, purple, red, yellow) fills 4 squares
4 + 4 + 4 + 4 = 16
So each colour covers one quarter of the rectangle, even though the shapes look different.
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l h h e i h e A aS m · NCERT So ut ons
gl e l i
Q5 Show quarters and halves in different ways in the grids given below.
Four empty grids. Each grid has 5 squares across and 4 squares down.
Squares in one grid = 5 × 4 = 20
Half of 20 = 10 squares
One quarter of 20 = 5 squares
Colour 10 squares for half and 5 squares for a quarter, in a different pattern in each grid.
half half one quarter one quarter
Half in two ways, a quarter in two ways.
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l h h e i h e A aS m · NCERT So ut ons
gl e l i
Q6 Use the fraction cards from your book to form a whole.
two halves four quarters
Cut-out pieces like the ones on the sheet at the back of the book.
Take the cut-out pieces from the back of your book.
Join 2 halves — you get one whole.
Join 4 quarters — you also get one whole.
1 half and 2 quarters also make one whole.
Put one piece on another to check that the pieces are the same size.
C hapter at a glance
When 1 whole is shared equally between 2 people, each share is called a half.
When 1 whole is shared equally among 4 people, each share is called a quarter.
2 halves make one whole. 4 quarters make one whole. 2 quarters make one half.
Double means adding the same number again: double of 7 is 14.
Parts are equal only when they are the same size. Fold or place one on the other to check.
Equal parts can look different, as long as each one has the same amount.
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l h h e i h e
a g l A aS m · NCERT So ut ons
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WORD HOW MANY MAKE A
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WHOLE CHAPTER
Whole The full thing, not cut 1 whole One full paratha
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1 whole shared equally 2 h lves
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Quarter 1 whole shared equally
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4 qu rters A quarter of 8 birds is 2
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Two quarters a Half asecim
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The same as one half 2 more qu rters needed rcle
Threesem. a a
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3 equal parts out of 4 1 more qu rter needed 3 of 4 squ res coloured
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Four quarters Already a whole A fully coloured hexagon
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The complete whole
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Double The same number added Double of 7 is 14
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Equal parts Parts of the same size — They match when placed on
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