NCERT Solutions Class 4 Maths Chapter 5 Sharing and Measuring

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C L A S S 4 · M AT H S

NCERT Solutions

One Half

NCERT Textbook — Math Mela

BOOK PAGES SECTIONS QUESTIONS MEDIUM

62 – 79 21 66 English

Solutions, notes, sample papers & more at 103 pages

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

CLASS 4 · MATHS · MATH MELA

NCERT Solutions — Chapter 5: Sharing and Measuring
This chapter is about sharing a thing equally. When we cut a whole into equal parts we get halves,
quarters, thirds and more, and we learn to write each part as a fraction like 1/2, 1/4 or 1/5.

TEXTBOOK BOOK PAGES

Math Mela (Class 4) 62 – 79

SECTIONS QUESTIONS

21 66

MEDIUM

English

Let Us Discuss — Page 62
Parts and Wholes

DISCUSSION

Q1 Which part of the paper you would have chosen—one half or two quarters? Why?

Either one, because they are exactly the same size.

One Quarter

One Half

One Quarter

Page 1 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Ikra’s drawing sheet. The left part is one half. The right part is cut once more into two quarters.

Paper cut into 2 equal parts → each part is one half

Each half cut again into 2 → the paper now has 4 quarters

1 quarter + 1 quarter = 2 quarters = one half

Why it happens: Two quarters are the two pieces of one half, so putting them back
together gives that half again.

Try This: Fold a sheet in half. Cut along the fold. Now fold one half again and cut.
Place the two small pieces on top of the other half — they cover it exactly.

Q2 Do you think Ikra shared the paper equally? Why? Try with a paper.

Yes, Ikra shared the paper equally.

One Quarter

One Half

One Quarter

The sheet after Ikra’s cuts: one half on the left, two quarters on the right.

Page 2 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Samina gets two quarters. That is 1/4 + 1/4 = 2/4.
Ikra keeps one half, which is 1/2.
Two quarters cover one half exactly, so both girls get the same amount of paper.

Why it happens: Ikra first cut the sheet into two equal halves. She only cut one half
into two smaller equal pieces. Cutting a piece does not make it bigger or smaller.

Check it yourself: Cut a sheet the same way. Put Samina’s two pieces on top of Ikra’s
piece. They fit exactly.

Q3 How do you know that the paper has been divided equally?

We know it because the parts fit exactly on top of one another.

One Quarter

One Half

One Quarter

The drawing sheet after it is cut. The dotted lines show where the cuts were made.

1. Cut the sheet along the lines shown.
2. Place one piece on top of the other piece.
3. If no piece sticks out anywhere, the parts are equal.

Page 3 of 103

as e
Class 4 Maths Chapter 5 Sharing and Measuring
a g l AglaSem · NCERT Solutions

co m
m.
Why it happens: Equal parts have the same size and shape, so one part covers the

m as e
l
other completely with nothing left over.

m .co a g
l a se
a g
Q4 Why do you think Samina chose two quarters of the paper?

com
m . ag
l a se
agthe word ‘two’ sounded bigger than ‘one’.
Samina chose two quarters because

m
She heard “two quarters” and “one half”.
co
m.
She looked only at the numbers 2 and 1, not at the size of the pieces.

m as e
.co g l
But a quarter is a smaller piece than a half, so two quarters are only the same as one half.
a
se m
g l a
a
m a s
m.co agl
l a se
ag One Quarter
co m
m .
m One Half as e
.co a g l
se m
g l a
a One Quarter
se m
com g l a
m . a
ase
agl

co m
One half on the left; the same amount of paper cut as two quarters on the right.

m .
o m l a se
m ag on how many equal
.cWhy it happens: In a fraction, the size of each piece depends
l a se
ag parts the whole was cut into. More pieces means smaller pieces.

.c
s e m
m a
e m . co agl
as
Let Us Do — Page 63
a g l

co m
m .
m ase
.co


a g l Page 4 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Parts and Wholes

Q1 Samina has divided some figures into two parts. Colour the figures that are divided
into halves correctly. How did you get the answer?

(a) (b) (c) (d) (e)

Samina’s five figures. The red dotted line shows where each figure has been cut into two
parts.

Colour figures (a), (b) and (d).

(a) (b) (c) (d) (e)

Five figures. The red dotted line shows where each figure has been cut into two parts.

Page 5 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

FIGURE IS IT CUT INTO REASON
HALVES?

(a) Yes The cut goes straight down the middle. Fold along it and the two
sides match.

(b) Yes The cut goes down the middle of the house shape. Both sides
match.

(c) No The line is low down. The top piece is much bigger than the bottom
piece.

(d) Yes The cut passes through the centre and also cuts the missing corner
in half. Fold along it and the two pieces match.

(e) No The slanting line leaves 2 star points on one side and 3 on the other
side.

(a) (b) (c) (d) (e)

The three figures that are cut into halves correctly are coloured.

Why it happens: A figure is cut into halves only when the two pieces are the same
size. The easy test is to fold along the cut — if the two pieces cover each other, they
are halves.

Check it yourself: Trace figure (d) on paper, cut it out and fold along the dotted line.
The two pieces sit exactly on top of each other.

Page 6 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Q2 Divide the shapes into halves by drawing a line.

(a) (b) (c) (d)

The four shapes to be divided, as printed in the book.

Draw the line through the middle of each shape, as shown.

(a) (b) (c) (d)

The four shapes as printed in the book.

(a) (b) (c) (d)

One way to cut each shape into two halves.

(a) Four-petal flower: draw a line straight down between the left two petals and the right two
petals.
(b) Five-petal flower: draw a line down through the middle of the top petal and the gap
below it.
(c) Parallelogram: join the middle of the left slanting side to the middle of the right slanting
side.

Page 7 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

(d) Six-pointed star: draw a line from the top point straight down to the bottom point.

Why it happens: Each of these shapes has a line down which the two sides match. A
cut along that line makes two pieces of the same size.

Tip: There is more than one right answer. For the star you can also join the left point
to the right point.

Let Us Do — Page 64
Parts and Wholes

THINK

Q1 Divide these shapes into 4 equal parts/quarters.

(b)
(a)
(c)

(d) (e)

The five shapes to be divided, as printed in the book.

Cut each shape with two lines through its middle, or with three cuts of the same width.

(b)
(a)

(c)

(d) (e)

Page 8 of 103

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Class 4 Maths Chapter 5 Sharing and Measuring
a g l AglaSem · NCERT Solutions

The five shapes as printed in the book.
co m
e m.
m l as
m .co a g
l a se
ag
(b)
co m
(a)
e m . ag
g l as
a
(c)

co m
em.
m l as
m .co (d) (e)
a g
l a se
a g One way to cut each shape into four equal parts.

om a s
. c agl
(a) Rhombus: draw both of its diagonals. They make 4 equal triangles.
(b) Long thin rectangle: make 3 cuts m
a s e across it, all the same distance apart. This gives 4 equal

agl
small rectangles.
(c) Oval: draw one line down the middle and one line across the middle.
(d) Rectangle: draw one line down the middle and one line across the middle. This gives 4
co m
m .
e
equal small rectangles.

coa m g l as
(e) Step-shape: it matches itself top to bottom and left to right, so a line down the middle

m . a
s e
and line across the middle give 4 equal parts.
a
agl
Each shape is now in 4 equal parts
se m
om
Each part is one quarter = 1/4 of the cshape g l a
. a
a s em
agl
Why it happens: A line through the middle makes two halves. Cutting each half in
half again gives four pieces of the same size.
co m
m .
m as e
.co a g l
a s emQ2
gl
Think: How would we write the fraction for each part if we divided an object into 5
a c
.
equal parts?

s e m
m a
em . co agl
g l as
Each part would be written as 1/5. We read it as one-fifth.
a

com
m .
m ase
.co


a g l Page 9 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

A roti cut into 5 equal parts. One part is coloured.

2 equal parts → each part is 1/2 (one half)
4 equal parts → each part is 1/4 (one quarter)

5 equal parts → each part is 1/5 (one-fifth)

Why it happens: The number below the line tells how many equal parts the whole
was cut into. The 1 above the line tells that we are taking 1 of those parts.

Page 10 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Try This: In the same way, 3 equal parts give 1/3, 6 equal parts give 1/6 and 10 equal
parts give 1/10.

Let Us Try — Pages 64–65
Many Ways to Make Halves and Quarters

ACTIVITY

Q1 In how many different ways can you fold/cut a rectangular paper in two equal
parts? Try it with a rectangular paper.

There are very many ways. Here are four easy ones to try.

(1) (2)

(3) (4)
Four ways to cut a rectangle into two equal parts.

1. Fold the paper left onto right. The fold is a line down the middle.
2. Fold the paper top down onto the bottom. The fold is a line across the middle.

Page 11 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

3. Cut along one slanting corner-to-corner line.
4. Cut along the other corner-to-corner line.

Why it happens: Every one of these cuts passes through the centre point of the
rectangle. Any straight cut through that centre point makes two equal parts, so
there are many, many ways.

Check it yourself: Mark the centre of a rectangle. Draw any slanting line through
that point and cut. Turn one piece round — it fits exactly on the other.

Q2 Now try to draw and show five different ways in which we can fold/cut a rectangle
into four equal parts (1/4 or quarter).

Here are five ways. In each one all four pieces are the same size.

(1) (2) (3)

(4) (5)

Five different ways of cutting a rectangle into four equal parts.

1. Three cuts down the paper → 4 tall strips.
2. Three cuts across the paper → 4 wide strips.
3. One cut down the middle and one cut across the middle → 4 small rectangles.
4. Both corner-to-corner lines → 4 triangles.
5. One cut down the middle, then a corner-to-corner cut in each half → 4 triangles.

Page 12 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Why it happens: In every picture the paper is shared into four pieces of the same
size, so each piece is 1/4 of the paper, even though the pieces have different shapes.

Tip: Fold instead of cutting. Fold in half, then fold in half again, and open it out. The
fold lines show the four equal parts.

Q3 Match the following parts with their corresponding wholes.

A 1

I am 1/2 of

B
2

I am 1/2 of

C
3
I am 1/2 of

D
4
I am 1/4 of

Four parts on the left and four whole shapes on the right.

Match each piece with the shape it came from.

Page 13 of 103

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Class 4 Maths Chapter 5 Sharing and Measuring
a g l AglaSem · NCERT Solutions

. com1
A
e m
m l as
m .co a g
l a se I am 1/2 of

a g
B
m
.co
2

em ag
l a s
g
I am 1/2 of
a

co m
m.
C

a se
com
3

.
I am 1/2 of
ag l
m
ase
agl
D

omof a s
agl
4
I am.c1/4

a sem
agl

co m
m .
e
Four parts on the left and four whole shapes on the right.

m l as
m .co a g
a s ePART
gl
WHOLE WHY
a A — two triangles 4 — the square Draw both corner-to-corner lines in the square. Two opposite
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joined at a point
com
triangles make this shape, and they are half the square.
g l a
m . a
e
as Cut that rectangle along one corner-to-corner line. Each piece
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B — the big triangle 1 — the small
rectangle is this triangle, so it is half.

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C — the half-circle 2 — the circle Cut the circle straight through the middle and you get two
half-circles.
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m as e
.co
D — the long thin 3 — the wide
a g l
Cut that rectangle into 4 strips of the same width. Each strip is

a s em strip rectangle one quarter.

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s e m
m a
em . co agl
g l as
a

co m
m .
m as e
.co


a g l Page 14 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

A 1

I am 1/2 of

B
2

I am 1/2 of

C
3
I am 1/2 of

D
4
I am 1/4 of

The matching pairs joined by dotted lines.

Why it happens: A half must fit into its whole exactly twice, and a quarter must fit
exactly four times. Checking how many times a part fits is the safest way to match.

In-text Questions — Page 68
Ding Dong Bell!!

Q1 How much dhokla does Sumedha get now?

Sumedha now gets 2/5 (two-fifths) of the dhokla.

Page 15 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

The dhokla is cut into 5 equal parts. The two coloured parts are Sumedha’s own share and Idha’s
share.

5 people share the dhokla → each share is 1/5

Sumedha’s own share = 1/5

Idha gives her share = 1/5

1/5 + 1/5 = 2/5

Why it happens: Two pieces of the same size joined together make two of those
pieces, so we simply count the pieces she now has: 2 pieces out of 5.

Page 16 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Let Us Discuss — Page 68
Ding Dong Bell!!

DISCUSSION

Q1 What is Sumedha observing about her share as each guest comes in?

She sees that her share keeps getting smaller every time a new guest comes.

2 people 3 people 4 people 5 people

1/2 1/3 1/4 1/5

The same dhokla shared by 2, 3, 4 and 5 people. The coloured slice is Sumedha’s share each time.

2 people (Sumedha, Vinayak) → 1/2

3 people (Kumar comes) → 1/3

4 people (Paridhi comes) → 1/4

5 people (Idha comes) → 1/5

Why it happens: The dhokla stays the same size. When it is shared among more
people, it is cut into more equal parts, so each part becomes smaller.

Q2 In which situation will Sumedha get to eat more dhokla: when shared among 9
people or 11 people?

She gets more when it is shared among 9 people.

Page 17 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

9 people → 1/9

11 people → 1/11

The same dhokla cut into 9 equal parts and into 11 equal parts.

9 people → each share = 1/9

11 people → each share = 1/11

1/9 is bigger than 1/11

Page 18 of 103

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Class 4 Maths Chapter 5 Sharing and Measuring
a g l AglaSem · NCERT Solutions

co m
m.
Why it happens: Cutting the same dhokla into 11 parts makes thinner slices than

m as e
l
cutting it into 9 parts. Fewer people means a bigger piece for each one.

m .co a g
l a se
a g
Q3 How many pieces of 1/6 would make a complete dhokla?

com
m . ag
l a se
g
6 pieces of 1/6 make one completeadhokla.

co m
em.
m l as
m .co a g
l a se
a g
m a s
m.co agl
l a se
ag

co m
m .
m as e
.co a g l
se m
g l a
a
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
. co agl
A dhokla cut into 6 equal pieces. All six pieces together make the whole dhokla.

e m
g l as
a

co m
m .
m ase
.co


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Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6

= 6 pieces of one-sixth

= 1 whole dhokla

Why it happens: 1/6 means the dhokla was cut into 6 equal parts. Putting all 6 parts
back gives the dhokla we started with.

Tip: In the same way, 5 pieces of 1/5 and 8 pieces of 1/8 each make one whole.

Q4 What would be Sumedha's share, if Idha and Vinayak both give their share of
dhokla to her?

Her share would be 3/5 (three-fifths) of the dhokla.

Page 20 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

The dhokla in 5 equal parts. The three coloured parts are Sumedha’s share, Idha’s share and Vinayak’s
share.

Everyone’s share = 1/5 (5 people)

Sumedha’s own share ……… 1/5

Idha’s share ………………… 1/5

Vinayak’s share …………… 1/5

1/5 + 1/5 + 1/5 = 3/5

Page 21 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Why it happens: She now holds 3 of the 5 equal pieces, so we write 3 above and 5
below.

Let Us Do — Pages 68–69
Ding Dong Bell!!

Q1 How much dhokla would each person get if it was shared equally among 6 people?
Try also with 8 people. Who will get the bigger pieces of dhokla? Draw and explain.

Among 6 people each gets 1/6. Among 8 people each gets 1/8. The 6 people get the bigger
pieces.

Page 22 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

6 people → 1/6 each

8 people → 1/8 each

The same dhokla cut into 6 equal pieces and into 8 equal pieces. One share is coloured in each.

6 people → 6 equal pieces → each piece = 1/6

8 people → 8 equal pieces → each piece = 1/8

1/6 is bigger than 1/8

Why it happens: The dhokla is the same size both times. Making 8 cuts of the same
dhokla gives thinner pieces than making 6, so each of the 8 people gets less.

Page 23 of 103

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Class 4 Maths Chapter 5 Sharing and Measuring
a g l AglaSem · NCERT Solutions

co m
m.
Check it yourself: Cut two paper circles of the same size. Fold one into 6 equal slices

m as e
l
and the other into 8. Put one slice from each side by side.

m .co a g
l a se
a g
Q2 Shade a portion of the dhokla to represent the fraction Sumedha would get when

co m
ag
the dhokla is shared equally among the given number of people. Discuss why the

m .
e
fractions get smaller.

g l as
ANSWER a
Colour one slice in each circle. The share is 1/2, 1/3, 1/4, 1/5, 1/8 and 1/9.
co m
se m.
m l a
m .co2 people ag 4 people
ase
3 people
agl
m a s
m .co agl
l a se
ag

co m
Half One-third
m .
m as e
.co a g l
a s em 5 people 8 people 9 people
agl
se m
com g l a
m . a
ase
agl

co m
m .
o m l a se
g to be coloured in each one.
.c The dhokla cut for 2, 3, 4, 5, 8 and 9 people. Sumedha’s shareahas
se m
g l a
a c
m .
m a s e
e m . co agl
g l as
a

co m
m .
m ase
.co


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Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

PEOPLE SUMEDHA’S SHARE IN WORDS

2 1/2 Half

3 1/3 One-third

4 1/4 One-fourth

5 1/5 One-fifth

8 1/8 One-eighth

9 1/9 One-ninth

2 people 3 people 4 people

1/2 — Half 1/3 — One-third 1/4 — One-fourth

5 people 8 people 9 people

1/5 — One-fifth 1/8 — One-eighth 1/9 — One-ninth

The completed picture with one slice coloured in each dhokla.

Why it happens: The fractions get smaller because the dhokla does not grow. More
people means more cuts, and more cuts make every slice thinner.

Page 25 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Let Us Discuss — Page 69
Using the fraction kit

DISCUSSION

Q1 Share your observations about the different pieces and the whole.

Here is what the fraction kit shows.

1
1/2 1/2
1/3 1/3 1/3
1/4 1/4 1/4 1/4
1/5 1/5 1/5 1/5 1/5
1/6 1/6 1/6 1/6 1/6 1/6
1/7 1/7 1/7 1/7 1/7 1/7 1/7
1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8
1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9 1/9
1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10 1/10

The fraction kit laid out in rows, from the whole down to tenths.

All the pieces in one row are of the same size.
Every row, put together, covers the whole strip exactly.
The 1/2 piece is the biggest piece; the 1/10 piece is the smallest.
As we go down, the pieces become more in number and smaller in size.

2 pieces of 1/2 = 1 whole

4 pieces of 1/4 = 1 whole

10 pieces of 1/10 = 1 whole

Why it happens: Each row is the same whole cut into a different number of equal
parts, so more parts always means smaller parts.

Page 26 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Q2 Take any two different pieces of the fraction kit and compare them. Discuss which
one is smaller and why.

Sample answer: Take the 1/4 piece and the 1/8 piece. The 1/8 piece is smaller.

1/4

1/8 1/8

The 1/4 piece placed above two 1/8 pieces.

Put the 1/8 piece on the 1/4 piece

It covers only part of it

In fact 2 pieces of 1/8 cover 1 piece of 1/4

Why it happens: For 1/8 the whole was cut into 8 equal parts and for 1/4 into only 4.
Cutting the same whole into more parts makes each part smaller.

Try This: Compare 1/3 with 1/6, and 1/5 with 1/10. Each time the piece with the
bigger number below the line is the smaller piece.

Q3 Sumedha noticed that when a whole is equally divided in a larger number of parts,
each part gets smaller. Do you agree with Sumedha?

Yes, Sumedha is right.

Page 27 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

1/2

1/4

Page 28 of 103

as e
Class 4 Maths Chapter 5 Sharing and Measuring
a g l AglaSem · NCERT Solutions

co m
e m.
m l as
m .co a g
l a se
a g

co m
e m . ag
g l as
a

co m
em.
m l as
m .co a g
l a se 1/8
a g
The same roti cut into 2, 4 and 8 equal parts. One part is coloured each time.

m a s
m .co agl
l a se
g
Same roti, 2 parts → each part = 1/2

Same roti, 4 parts → each part = 1/4
a

co m
.
Same roti, 8 parts → each part = 1/8 — the smallest
e m
m l as
.co
m it happens: The whole never changes. If it has to be shared among more parts,a g
a s eWhy
agl every part must take less.
se m
com g l a
m . a
ase
agl
Q4 Sumedha says, “When I join 5 pieces of 1/5, it makes a whole dhokla.” Try to do it
yourself with your fraction kit.

co m
m .
m as e
.co l
Sumedha is right. Five pieces of 1/5 make one whole.
a g
se m
g l a
a c
1/5 1/5 1/5 1/5
m .
m a s e
e m . co 1 whole agl
g l as
a

co m
m .
m ase
.co


a g l Page 29 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Four of the five one-fifth pieces are drawn above the whole strip; the fifth one completes it.

1. Take out all five 1/5 pieces from your kit.
2. Place them end to end in a line.
3. Put the whole strip below them.
4. The five pieces cover the whole strip exactly, with nothing sticking out.

1/5 + 1/5 + 1/5 + 1/5 + 1/5 = 1 whole

Why it happens: 1/5 means the whole was cut into 5 equal parts, so putting all 5
parts back gives the whole again.

Q5 Sumedha says that this part is one-third of the complete whole. Why is she saying
so?

Because the whole dhokla was cut into 3 equal pieces and she is holding 1 of them.

hole dhokla, cut into 3 equalthe
pieces
piece Sumedha is holding
The whole dhokla cut into three equal pieces, and one single piece beside it.

Dhokla cut into 3 equal pieces

Sumedha holds 1 piece

1 out of 3 equal pieces = 1/3 (one-third)

Page 30 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Why it happens: The number below the line counts the equal pieces of the whole,
and the number above counts how many we have taken.

Check it yourself: The two pieces left on the plate are also 1/3 each. All three pieces
together make the whole dhokla.

In-text Questions — Page 70
Let us try to fill in the blanks

Q1 ________ is greater than ________ ( 1/5 , 1/4 ).

1/4 is greater than 1/5.

1/4 1/4

1/5 1/5

A one-fourth strip drawn above a one-fifth strip of the same whole.

1/4 → the whole is cut into 4 equal parts

1/5 → the whole is cut into 5 equal parts

Fewer parts means bigger parts, so 1/4 > 1/5

Why it happens: Both fractions come from the same whole. Cutting it into 5 pieces
makes each piece thinner than cutting it into 4.

Q2 ________ > ________ (1/9, 1/6).

1/6 > 1/9

Page 31 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

1/6 1/6

1/9 1/9

A one-sixth strip drawn above a one-ninth strip of the same whole.

1/6 → whole cut into 6 equal parts

1/9 → whole cut into 9 equal parts

9 parts are thinner than 6 parts, so 1/6 > 1/9

Why it happens: The more equal parts we make from one whole, the smaller each
part becomes.

Q3 1/6 _____ 1/8.

Put the sign > in the blank: 1/6 > 1/8.

1/6 1/6

1/8 1/8

A one-sixth strip drawn above a one-eighth strip of the same whole.

Same whole → 6 equal parts or 8 equal parts

8 parts → each part is thinner

So 1/6 is greater than 1/8

Page 32 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Why it happens: Look at the fraction chart: the 1/6 strip is clearly longer than the
1/8 strip.

Q4 ________ is smaller than ________ ( ____ , ____ ).

You may write any two fractions of the same whole. Sample answer: 1/10 is smaller than 1/7 (
1/10 , 1/7 ).

1/7 1/7

1/10 1/10

A one-seventh strip drawn above a one-tenth strip of the same whole.

1/10 → whole cut into 10 equal parts

1/7 → whole cut into 7 equal parts

10 parts are thinner than 7, so 1/10 is smaller than 1/7

Why it happens: When the number above the line is 1, the fraction with the bigger
number below the line is always the smaller piece.

Try This: 1/9 is smaller than 1/3. 1/8 is smaller than 1/2. Check each pair on the
fraction chart on page 77.

My Flower Garden — Pages 70–71

Page 33 of 103

as e
Class 4 Maths Chapter 5 Sharing and Measuring
a g l AglaSem · NCERT Solutions

Idha’s garden
co m
e m.
m l as
Q1
.co
Marigold in _____________ part of the garden.
m a g
l a se
ag

m
Marigold is in 1/5 (one-fifth) part of the garden.

. co ag
e m
g l as
a
Rose Mogra Rose Marigold m
co
Jasmine
m .
m a s e
e m . co agl
g l as Idha’s revised plan. The garden is in 5 equal strips.
a
m a s
The garden has 5 equal strips
m .co agl
l a se
g
Marigold is planted in 1 strip

1 strip out of 5 = 1/5
a

co m
m .
as e
comgarden. g l
Why it happens: All five strips are the same size, so one strip is one-fifth of the

m . a
ase
whole

agl
se m
com g l a
. a
Jasmine in _____________ part of the garden.
m
Q2

ase
ANSWER agl
m
Jasmine is in 1/5 (one-fifth) part of the garden.

. co
e m
m l as
m .co a g
l a se
ag Rose Mogra Rose Marigold Jasmine
.c
s e m
m a
e m . co agl
g l as
Idha’s revised plan. The garden is in 5 equal strips.

a

co m
m .
m as e
.co


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Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

5 equal strips in all

Jasmine is in 1 strip

So Jasmine has 1/5 of the garden

Why it happens: Jasmine, Mogra and Marigold each take one strip, so each of them
has one-fifth. Rose takes two strips, which is 2/5.

Check it yourself: 1/5 + 1/5 + 1/5 + 2/5 = 5/5, the whole garden.

Q3 Mogra in _____________ part.

Mogra is in 1/5 (one-fifth) part of the garden.

Rose Mogra Rose Marigold Rose

The garden now has Rose in three strips.

The garden still has 5 equal strips

Mogra is in 1 strip → 1/5

Why it happens: Even though Rose has spread to three strips, the garden is still cut
into the same five equal strips, so one strip is still one-fifth.

Q4 Marigold in _____________ part.

Marigold is in 1/5 (one-fifth) part of the garden.

Page 35 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Rose Mogra Rose Marigold Rose

The garden with Rose in three strips, Mogra in one and Marigold in one.

Mogra ……… 1/5

Marigold …… 1/5

Rose ………… 1/5 + 1/5 + 1/5 = 3/5

1/5 + 1/5 + 3/5 = 5/5 = the whole garden

Why it happens: Every strip is one-fifth, so we just count how many strips each
flower has.

Q5 Marigold in _____________ part.

Marigold is in 1/5 (one-fifth) part of the garden.

Rose Rose Rose Marigold Rose

The garden with Rose in four strips and Marigold in one strip.

Rose …… 1/5 + 1/5 + 1/5 + 1/5 = 4/5

Marigold … 1/5

4/5 + 1/5 = 5/5 = the whole garden

Page 36 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Rose Rose Rose Rose Rose

In the last picture Rose fills all five strips, which is 5/5 — the complete garden.

Why it happens: When all five of the five equal strips are used, we write 5/5, and
that is one whole garden.

Let Us Do — Page 71
My Flower Garden

ACTIVITY

Q1 Make a flower garden with seven flowering seeds—Mogra, Marigold, Jasmine, Rose,
Lily, Hibiscus, and Periwinkle? a) Marigold in one-seventh (1/7) and Rose and
Hibiscus in three-sevenths (3/7) part each.

Cut the garden into 7 equal strips and fill them like this.

The garden strip is divided into 7 equal parts.

Marigold …… 1 strip = 1/7
Rose ………… 3 strips = 3/7

Hibiscus ……… 3 strips = 3/7

1 + 3 + 3 = 7 strips = the whole garden

Page 37 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Marigold Rose Rose Rose Hibiscus Hibiscus Hibiscus

One way to plant the garden: 1 strip of Marigold, 3 of Rose and 3 of Hibiscus.

Why it happens: Each strip is one-seventh of the garden, so 3 strips together make
3/7. All seven strips fill the garden exactly.

Tip: The strips of one flower need not be next to each other. Any arrangement is
right as long as the counts are 1, 3 and 3.

Q2 Make a flower garden with seven flowering seeds—Mogra, Marigold, Jasmine, Rose,
Lily, Hibiscus, and Periwinkle? b) Lily in three-sevenths (3/7), Marigold in two-
sevenths (2/7) and Periwinkle in another two-sevenths (2/7).

Again cut the garden into 7 equal strips.

The garden strip is divided into 7 equal parts.

Lily …………… 3 strips = 3/7

Marigold ……… 2 strips = 2/7

Periwinkle …… 2 strips = 2/7

3 + 2 + 2 = 7 strips = the whole garden

Page 38 of 103

ase
Class 4 Maths Chapter 5 Sharing and Measuring
a g l AglaSem · NCERT Solutions

co m
e m.
m l as
Lily
m .co Lily Lily Marigold
a g
Marigold Periwinkle Periwinkle

l a se
a g
One way to plant this garden: 3 strips of Lily, 2 of Marigold and 2 of Periwinkle.

co m
em . ag
g l as
Why it happens: Two strips out of seven equal strips is written as 2/7, because we
have taken 2 of the 7 equal parts. a

co m
e m.
m l as
.co a
Make a flower garden with seven flowering seeds—Mogra, Marigold, Jasmine, Rose,
g
em
Q3

a s Lily, Hibiscus, and Periwinkle? c) Mogra in five-sevenths (5/7) part and Hibiscus in

a gl two-sevenths (2/7).

om a s
. c agl

a s emwith Hibiscus.
Fill five strips with Mogra and two strips

agl

co m
m .
m as e
.co a g l
se m
g l a
a The garden strip is divided into 7 equal parts.

se m
com g l a
m . a
ase
agl
Mogra ……… 5 strips = 5/7

Hibiscus …… 2 strips = 2/7

5 + 2 = 7 strips = the whole garden
co m
m .
m as e
.co a g l
se m
g l a
a c
Mogra Mogra Mogra Mogra Mogra Hibiscus Hibiscus
m .
m a s e
em . co agl
l as
One way to plant this garden: 5 strips of Mogra and 2 strips of Hibiscus.
g
a

co m
m .
m as e
.co


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Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Why it happens: 5/7 and 2/7 together make 7/7, and 7/7 is one whole garden.

Check it yourself: In all three gardens the strip counts add up to 7. If they do not,
some part of the garden has been left empty or used twice.

Do It Yourself — Page 73
Dream Dosa Designer!!

Q1 Write the fractions for each of the toppings in the following dosas. 1) Chilli paneer =
2) Classic potato =

Chilli paneer = 4/6 and Classic potato = 2/6.

Page 40 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

2 1

1 1

1 2

This dosa is cut into 6 equal parts. Topping 1 is chilli paneer and topping 2 is classic potato.

Total parts of the dosa = 6

Parts marked 1 (chilli paneer) = 4 → 4/6

Parts marked 2 (classic potato) = 2 → 2/6

Check: 4/6 + 2/6 = 6/6 = the whole dosa

Why it happens: The dosa is cut into 6 equal slices, so each slice is 1/6. We only
count how many slices carry each topping.

Page 41 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Q2 Write the fractions for each of the toppings in the following dosas. 1) Tangy tomato
= 2) Classic potato = 3) Spicy onion =

Tangy tomato = 2/6, Classic potato = 2/6, Spicy onion = 2/6.

1 3

1 2

2 3

This dosa is cut into 6 equal parts. Topping 1 is tangy tomato, 2 is classic potato and 3 is spicy onion.

Page 42 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Total parts = 6

Marked 1 → 2 slices → 2/6

Marked 2 → 2 slices → 2/6

Marked 3 → 2 slices → 2/6

Check: 2/6 + 2/6 + 2/6 = 6/6

Why it happens: All three toppings have the same number of slices, so all three
fractions are the same.

Did you know? 2/6 is the same as 1/3, because 2 slices of one-sixth cover one-third
of the dosa.

Q3 Write the fractions for each of the toppings in the following dosas. 1) Spicy onion =
2) Tangy tomato =

Spicy onion = 4/8 and Tangy tomato = 4/8.

Page 43 of 103

as e
Class 4 Maths Chapter 5 Sharing and Measuring
a g l AglaSem · NCERT Solutions

co m
e m.
m l as
m .co a g
l a se
a g

com
. ag
a g2e
l as
m
1
m
1 2 lase m.
co m

. co ag
e m
g l as
a
2 com
1 a s
m . agl
ase
agl 1 2
co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
.
This dosa is cut into 8 equal parts. Topping 1 is spicy onion and topping 2 is tangy tomato.
m a
ase
agl
Total parts = 8

co m
Marked 1 (spicy onion) → 4 slices → 4/8
m .
m as e
.co
Marked 2 (tangy tomato) → 4 slices → 4/8
a g l
se m Check: 4/8 + 4/8 = 8/8 = the whole dosa
g l a
a c
m .
m a s e
co agl
Why it happens: The two toppings share the dosa equally, so each one covers half
m .
of it. 4/8 is the same as 1/2.
as e
a g l

co m
m .
m ase
.co


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Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Q4 Write the fractions for each of the toppings in the following dosas. 1) Tangy tomato
= 2) Classic potato = 3) Spicy onion =

Tangy tomato = 1/6, Classic potato = 2/6, Spicy onion = 3/6.

1 2

3 2

3 3

This dosa is cut into 6 equal parts. Topping 1 is tangy tomato, 2 is classic potato and 3 is spicy onion.

Page 45 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Total parts = 6

Marked 1 → 1 slice → 1/6

Marked 2 → 2 slices → 2/6
Marked 3 → 3 slices → 3/6

Check: 1/6 + 2/6 + 3/6 = 6/6

Why it happens: Spicy onion has 3 of the 6 slices, which is half the dosa. Tangy
tomato has only 1 slice, the smallest share.

Let Us Explore — Page 73
Dream Dosa Designer!!

TRY THIS

Q1 Make a dosa with 2/3 topping of Spicy onion, 1/3 of Classic potato.

Cut the dosa into 3 equal slices. Put spicy onion on 2 slices and classic potato on 1 slice.

Page 46 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

An empty dosa cut into 3 equal parts.

3 equal slices in all

Spicy onion ……… 2 slices = 2/3

Classic potato … 1 slice = 1/3

2/3 + 1/3 = 3/3 = the whole dosa

Page 47 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

potato onion

onion

The finished dosa: two slices of spicy onion and one slice of classic potato.

Why it happens: The number below the line, 3, tells us how many equal slices to cut.
The number above tells us how many slices get that topping.

Q2 Make a dosa with 3/8 of Classic potato, 1/8 of Chilly paneer and 4/8 of Tangy tomato
mix.

Cut the dosa into 8 equal slices and share them 3, 1 and 4.

Page 48 of 103

as e
Class 4 Maths Chapter 5 Sharing and Measuring
a g l AglaSem · NCERT Solutions

co m
e m.
m l as
m .co a g
l a se
a g

co m
e m . ag
g l as
a

co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
ag

co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
.
An empty dosa cut into 8 equal parts.
m a
ase
agl
8 equal slices in all

co m
Classic potato … 3 slices = 3/8
m .
m as e
.co
Chilly paneer …… 1 slice = 1/8
a g l
se m Tangy tomato …… 4 slices = 4/8
g l a
a c
3 + 1 + 4 = 8 slices = the whole dosa
m .
m a s e
e m . co agl
g l as
a

com
m .
m ase
.co


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Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

3 1
3 1
3 1
3 2

The finished dosa. 1 = classic potato (3 slices), 2 = chilly paneer (1 slice), 3 = tangy tomato (4 slices).

Why it happens: All the fractions have 8 below the line, so all of them count the
same eighth-size slices. The slice counts must add up to 8.

Q3 Meena has 8 diyas. Colour 1/4 of her diyas red. To find 1/4, let us divide the number
of diyas into 4 equal parts. Can you see how to divide the diyas into 4 equal parts?
Now colour 2 diyas red.

Put the 8 diyas into 4 equal groups of 2. One group is 2 diyas, so 1/4 of 8 is 2 diyas.

Page 50 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Meena’s 8 diyas. The red dotted lines split them into 4 equal groups.

8 diyas shared into 4 equal groups

8=2+2+2+2

Each group has 2 diyas

So 1/4 of 8 = 2 diyas

Page 51 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Two diyas — one group out of the four — are coloured red.

Why it happens: A fraction of a group works just like a fraction of a roti. We first
make equal groups, then take as many groups as the fraction asks for.

Try This: In the same way, 1/2 of 8 diyas is 4 diyas, and 1/8 of 8 diyas is 1 diya.

Let Us Do — Page 74
Finding fractions of a group

Q1 There are 12 cookies. What fraction of cookies will each get if the number of
children are as follows: a) 3 children b) 6 children c) 2 children d) 4 children

Share the 12 cookies into equal groups, one group for each child.

The 12 cookies.

Page 52 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

CHILDREN COOKIES FOR EACH CHILD FRACTION OF ALL THE COOKIES

a) 3 children 12 = 4 + 4 + 4, so 4 cookies 1/3

b) 6 children 12 = 2 + 2 + 2 + 2 + 2 + 2, so 2 cookies 1/6

c) 2 children 12 = 6 + 6, so 6 cookies 1/2

d) 4 children 12 = 3 + 3 + 3 + 3, so 3 cookies 1/4

For 3 children: circle 4 cookies for one child. That circled part is 1/3 of all the cookies.

Why it happens: Each child gets one of the equal groups. If there are 3 groups, one
group is 1/3 of the whole lot; if there are 6 groups, one group is 1/6.

Check it yourself: More children, fewer cookies each — just like the dhokla story.

Page 53 of 103

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Class 4 Maths Chapter 5 Sharing and Measuring
a g l AglaSem · NCERT Solutions

co m
m.
Simran calls her school friends for her birthday party. 1/3 of her friends receive a
e
Q2

m l as
.co
hairband as their return gift. Place hairbands on 1/3 of her friends.

a g
se m
g l a
a

Simran has 9 friends. 1/3 of 9 is 3 friends, so draw hairbands on 3 of them.

co m
e m . ag
g l as
a

co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
ag

co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
m . a
ase
agl

co m
m .
m as e
.co Simran’s 9 friends.
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 .
m ase
.co


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Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Count the friends = 9

Share them into 3 equal groups: 9 = 3 + 3 + 3

Each group has 3 friends

1/3 of 9 = 3 friends

Hairbands drawn on 3 of the 9 friends.

Why it happens: One-third means one group out of three equal groups, so we take
just one of the groups of 3.

Page 55 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Q3 Draw flowers in 1/5 of the given number of pots.

There are 15 pots. 1/5 of 15 is 3 pots, so draw flowers in 3 pots.

The 15 pots given in the book.

Count the pots = 15

Share them into 5 equal groups: 15 = 3 + 3 + 3 + 3 + 3

Each group has 3 pots

1/5 of 15 = 3 pots

Page 56 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

Flowers drawn in 3 of the 15 pots.

Why it happens: One-fifth means one group out of five equal groups. Skip-counting
in 3s five times gives 15, so each group is 3 pots.

Let Us Find Fractions in Our Surroundings — Page 75
Kadamba’s examples

Q1 Yesterday Mummy asked to divide a box of barfis into four equal parts. There are 16
barfis in the box. Draw a picture of 16 barfis and find 1/4 of the whole. How many
barfis are in each part?

There are 4 barfis in each part.

Page 57 of 103

Class 4 Maths Chapter 5 Sharing and Measuring AglaSem · NCERT Solutions

A box of 16 barfis, drawn in 4 rows of 4.

16 barfis shared into 4 equal parts
16 = 4 + 4 + 4 + 4

Each part has 4 barfis

So 1/4 of 16 = 4 barfis

Page 58 of 103

as e
Class 4 Maths Chapter 5 Sharing and Measuring
a g l AglaSem · NCERT Solutions

co m
e m.
m l as
m .co a g
l a se
a g

co m
e m . ag
g l as
a

co m
em.
m l as
m .co a g
l a se
a g
m a s
m .co agl
l a se
ag

co m
m .
m as e
.co a g l
se m
g l a
a
se m
com g l a
.
The 16 barfis split into 4 equal rows. Each row is one-fourth of the box.
m a
gl ase
a
Why it happens: Making 4 equal rows of the 16 barfis is the same as cutting the box
into quarters. One row is one quarter.
co m
m .
m as e
.co a g l
m
Try This: 1/2 of 16 barfis is 8 barfis, and 1/8 of 16 barfis is 2 barfis.

l a se
ag
.c
s e m
m a
e m . co agl
g l as
a

co m
m .
m ase
.co


a g l Page 59 of 103