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Updated 6 August 2026

NCERT Solutions

Sharing and Measuring

CBSE · Class 4 · Mathematics

NCERT Solutions for Sharing and Measuring — CBSE Class 4 Mathematics.

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Parts and Wholes — Let Us Discuss

1Which part of the paper you would have chosen—one half or two quarters? Why?Show solution

Given: A sheet of paper is to be shared between Ikra and Samina. The choices are one half (

\frac{1}{2}

) or two quarters (

\frac{2}{4}

).

Concept:

\frac{1}{2} = \frac{2}{4}

because when a whole is divided into 4 equal parts, two of those parts together equal one half.

Answer: Both choices give exactly the same amount of paper.

\frac{1}{2} = \frac{2}{4}

. So it does not matter which one you choose — you get the same area of paper either way. A student may say they would choose either one, as long as they understand both are equal.

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2Do you think Ikra shared the paper equally? Why? Try with a paper.Show solution

Given: Ikra offered Samina two quarters and kept one half for herself.

Concept:

\frac{2}{4} = \frac{1}{2}

. Two quarters of a whole equal one half of the same whole.

Working: If a paper is divided into 4 equal parts, each part is

\frac{1}{4}

. Two such parts =

\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}

.

Answer: Yes, Ikra shared the paper equally. Both sisters got exactly half the paper. Samina received two quarters (

\frac{2}{4}

) and Ikra kept one half (

\frac{1}{2}

), and these are equal.

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3How do you know that the paper has been divided equally?Show solution

Given: The paper is divided into two portions.

Concept: Equal division means both parts have the same area/size.

Answer: We can check equal division by folding one part over the other. If both parts overlap exactly (one covers the other completely), the paper has been divided equally. We can also measure the length or area of each part — if they are the same, the division is equal.

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4Why do you think Samina chose two quarters of the paper?Show solution

Given: Samina was offered a choice between 'one half' and 'two quarters'.

Reason: Samina is young and does not yet know that

\frac{2}{4} = \frac{1}{2}

. The phrase 'two quarters' sounds like a bigger amount because the number 2 is greater than 1, and 'quarters' sounds like more pieces. She thought she was getting more paper by choosing two quarters.

Answer: Samina chose two quarters because she thought two pieces would be more than one piece. She did not realise that

\frac{2}{4}

and

\frac{1}{2}

are equal amounts.

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Let Us Do — Halves and Quarters

1Samina has divided some figures into two parts. Colour the figures that are divided into halves correctly. How did you get the answer?Show solution

Given: Several figures divided into two parts.

Concept: A figure is divided into halves correctly only when both parts are exactly equal in size and shape.

Method: For each figure, check whether the dividing line creates two parts of equal area. If both parts are equal, the figure is divided into halves correctly and should be coloured.

Answer: Colour only those figures where the line divides the shape into two equal (congruent) parts. Figures where one part is larger than the other are NOT halves and should not be coloured. (Since the actual figures are in the textbook image, students should apply the above rule to each figure shown.)

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2Divide the shapes into halves by drawing a line.Show solution

Given: Various shapes (rectangle, circle, triangle, etc.).

Concept: To divide a shape into halves, draw a line that splits it into two equal parts.

Method:
- Rectangle: Draw a line through the middle either horizontally or vertically.
- Circle: Draw a line through the centre (diameter).
- Triangle: Draw a line from one vertex to the midpoint of the opposite side (median).
- Square: Draw a line through the centre horizontally, vertically, or diagonally.

Answer: Draw a straight line through the centre/middle of each shape so that both resulting parts are equal in size. (Students should draw the line on the shapes given in their textbook.)

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3Divide these shapes into 4 equal parts/quarters.Show solution

Given: Various shapes to be divided into 4 equal parts.

Concept: When a whole is divided into 4 equal parts, each part is called a quarter and is written as

\frac{1}{4}

.

Method:
- Rectangle/Square: Draw one horizontal and one vertical line through the centre, creating 4 equal parts.
- Circle: Draw two diameters perpendicular to each other.

Answer: Draw lines to divide each shape into 4 equal parts. Each part represents

\frac{1}{4}

of the whole. (Students should draw the lines on the shapes given in their textbook.)

Think answer: If an object is divided into 5 equal parts, each part is written as

\frac{1}{5}

(one-fifth). The denominator (bottom number) tells us the total number of equal parts, and the numerator (top number) tells us how many parts we are considering.

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Let Us Try — Many Ways to Make Halves and Quarters

1In how many different ways can you fold/cut a rectangular paper in two equal parts? Try it with a rectangular paper.Show solution

Given: A rectangular piece of paper.

Concept: A rectangle can be folded into two equal halves in multiple ways.

Different ways:
1. Fold along the horizontal centre line (landscape fold) — top half meets bottom half.
2. Fold along the vertical centre line (portrait fold) — left half meets right half.
3. Fold along one diagonal — creates two equal triangles.
4. Fold along the other diagonal — creates two equal triangles.

Answer: There are at least 4 different ways to fold/cut a rectangle into two equal halves. Each fold must result in two parts that are exactly equal in size.

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2Now try to draw and show five different ways in which we can fold/cut a rectangle into four equal parts (

\frac{1}{4}

or quarter).Show solution

Given: A rectangle to be divided into 4 equal parts.

Concept: Each of the 4 equal parts is

\frac{1}{4}

(one quarter) of the whole.

Five different ways:
1. Two horizontal lines dividing the rectangle into 4 equal horizontal strips.
2. Two vertical lines dividing the rectangle into 4 equal vertical strips.
3. One horizontal and one vertical line through the centre (making 4 equal rectangles).
4. One diagonal and one line perpendicular to it through the centre.
5. Fold into half vertically, then fold that half horizontally (or vice versa).

Answer: Draw 5 rectangles and show a different way of dividing each into 4 equal parts. Each part in every drawing should be

\frac{1}{4}

of the whole rectangle.

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3Match the following parts with their corresponding wholes.Show solution

Given: Parts of shapes and their corresponding wholes are shown in the textbook image.

Concept: A part of a shape, when repeated the correct number of times, makes the complete whole shape.

Method: Look at each part and identify which whole shape it belongs to by checking the shape, size, and the fraction it represents.

Answer: Match each part to the whole it belongs to by identifying the shape and checking that the part fits exactly into the whole the correct number of times. (Students should draw lines matching each part to its whole as shown in the textbook figures.)

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Ding Dong Bell — Let Us Discuss

1What is Sumedha observing about her share as each guest comes in?Show solution

Given: Each time a new guest arrives, the dhokla is shared equally among more people.

Observation: As more people share the dhokla, the number of equal parts increases, so each person's share becomes smaller.

Answer: Sumedha observes that as each new guest arrives and the dhokla is shared among more people, her share of the dhokla keeps getting smaller. More people sharing the same whole means each person gets a smaller fraction.

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2In which situation will Sumedha get to eat more dhokla: when shared among 9 people or 11 people?Show solution

Given: Dhokla shared among 9 people gives each person

\frac{1}{9}

; shared among 11 people gives each person

\frac{1}{11}

.

Concept: When the same whole is divided into more parts, each part is smaller. So

\frac{1}{9} > \frac{1}{11}

.

Answer: Sumedha will get more dhokla when it is shared among 9 people, because

\frac{1}{9}

is greater than

\frac{1}{11}

. Fewer people sharing means a bigger piece for each person.

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3How many pieces of

\frac{1}{6}

would make a complete dhokla?Show solution

Given: The dhokla is divided into 6 equal parts, each part =

\frac{1}{6}

.

Concept: The number of equal parts needed to make a whole equals the denominator.

Working:

\frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} + \frac{1}{6} = \frac{6}{6} = 1

(complete whole).

Answer: 6 pieces of

\frac{1}{6}

would make a complete dhokla.

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4What would be Sumedha's share, if Idha and Vinayak both give their share of dhokla to her?Show solution

Given: The dhokla is shared among 5 people (Sumedha, Vinayak, Kumar, Paridhi, Idha), so each person gets

\frac{1}{5}

. Idha and Vinayak give their shares to Sumedha.

Working: Sumedha's own share =

\frac{1}{5}

Idha's share =

\frac{1}{5}

Vinayak's share =

\frac{1}{5}

Total Sumedha gets =

\frac{1}{5} + \frac{1}{5} + \frac{1}{5} = \frac{3}{5}

Answer: Sumedha would get

\frac{3}{5}

(three-fifths) of the dhokla.

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Let Us Do — Dhokla Sharing

1How 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.Show solution

Given: One whole dhokla shared equally.

Case 1 — 6 people:
Each person gets

\frac{1}{6}

(one-sixth) of the dhokla.
Draw a circle divided into 6 equal parts; each part =

\frac{1}{6}

.

Case 2 — 8 people:
Each person gets

\frac{1}{8}

(one-eighth) of the dhokla.
Draw a circle divided into 8 equal parts; each part =

\frac{1}{8}

.

Comparison: Since 6 < 8, dividing among 6 people gives bigger pieces.

\frac{1}{6} > \frac{1}{8}

Answer: Each person gets

\frac{1}{6}

when shared among 6 people, and

\frac{1}{8}

when shared among 8 people. The people sharing among 6 will get bigger pieces because

\frac{1}{6} > \frac{1}{8}

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2Shade a portion of the dhokla to represent the fraction Sumedha would get when the dhokla is shared equally among the given number of people. Discuss why the fractions get smaller.Show solution

Given: Dhokla shared among different numbers of people.

Method: For each number of people

n

, Sumedha's share =

\frac{1}{n}

.
- 2 people: shade

\frac{1}{2}

of the circle
- 3 people: shade

\frac{1}{3}

of the circle
- 4 people: shade

\frac{1}{4}

of the circle
- 5 people: shade

\frac{1}{5}

of the circle, and so on.

Why fractions get smaller: The whole dhokla stays the same size. As we divide it among more people, each person's share becomes a smaller piece. The denominator (number of people) increases, making each fraction smaller.

Answer: Shade the appropriate sector in each circle diagram. The fractions get smaller because the same whole is being divided into more and more equal parts — more parts means each part is smaller.

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Let Us Discuss — Fraction Kit

1Share your observations about the different pieces and the whole.Show solution

Observations using the fraction kit:
- The whole (1) is the largest piece.
-

\frac{1}{2}

pieces are the next largest — 2 of them make the whole.
-

\frac{1}{3}

pieces are smaller than

\frac{1}{2}

— 3 of them make the whole.
- As the denominator increases (

\frac{1}{4}, \frac{1}{5}, \frac{1}{6}

, etc.), each piece gets progressively smaller.
- The piece with the largest denominator is the smallest piece.
- Any set of equal pieces with the same denominator, when combined to equal the denominator count, makes one whole.

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2Take any two different pieces of the fraction kit and compare them. Discuss which one is smaller and why.Show solution

Example: Compare

\frac{1}{4}

and

\frac{1}{6}

.

Place both pieces side by side. The

\frac{1}{6}

piece is shorter/smaller than the

\frac{1}{4}

piece.

Reason: Both fractions are parts of the same whole. The whole is divided into more parts for

\frac{1}{6}

(6 parts) than for

\frac{1}{4}

(4 parts). More parts from the same whole means each part is smaller.

Answer:

\frac{1}{6} < \frac{1}{4}

. The piece with the larger denominator is always smaller (when comparing unit fractions of the same whole).

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3Sumedha noticed that when a whole is equally divided in a larger number of parts, each part gets smaller. Do you agree with Sumedha?Show solution

Yes, I agree with Sumedha.

Explanation: When the same whole is divided into more equal parts, each part must be smaller because the total size stays the same but is shared among more pieces.

Example:

\frac{1}{2} > \frac{1}{3} > \frac{1}{4} > \frac{1}{5} > \frac{1}{6} > \frac{1}{7} > \frac{1}{8}

This can be verified with the fraction kit — the

\frac{1}{8}

strip is much smaller than the

\frac{1}{2}

strip, even though both are parts of the same whole.

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4Sumedha says, 'When I join 5 pieces of

\frac{1}{5}

, it makes a whole dhokla.' Try to do it yourself with your fraction kit.Show solution

Given: 5 pieces each of size

\frac{1}{5}

.

Working:

\frac{1}{5} + \frac{1}{5} + \frac{1}{5} + \frac{1}{5} + \frac{1}{5} = \frac{5}{5} = 1

(one whole)

Verification with fraction kit: Take 5 pieces of the

\frac{1}{5}

strip and place them together. They will exactly cover the whole strip.

Answer: Yes, Sumedha is correct. Joining 5 pieces of

\frac{1}{5}

makes exactly one whole.

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5Sumedha says that this part is one-third of the complete whole. Why is she saying so?Show solution

Given: A shape/strip where one part out of three equal parts is shown (refer to textbook image).

Concept: A fraction

\frac{1}{3}

means the whole is divided into 3 equal parts and we are considering 1 part.

Answer: Sumedha is saying the part is one-third (

\frac{1}{3}

) because the whole has been divided into 3 equal parts and the shaded/shown part is exactly 1 of those 3 equal parts. Since all 3 parts are equal in size and together they make the whole, each part is

\frac{1}{3}

of the whole.

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Fill in the Blanks — Comparing Fractions

1________ is greater than ________ (

\frac{1}{5}, \frac{1}{4}

).Show solution

Given: Two fractions

\frac{1}{4}

and

\frac{1}{5}

from the same whole.

Concept: For unit fractions (fractions with numerator 1), the one with the smaller denominator is greater.

Working: 4 < 5, so

\frac{1}{4} > \frac{1}{5}

.

Answer:

\frac{1}{4}

is greater than

\frac{1}{5}

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2________ > ________ (

\frac{1}{9}, \frac{1}{6}

).Show solution

Given: Two fractions

\frac{1}{9}

and

\frac{1}{6}

.

Concept: For unit fractions, smaller denominator means larger fraction.

Working: 6 < 9, so

\frac{1}{6} > \frac{1}{9}

.

Answer:

\frac{1}{6}

\frac{1}{9}

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\frac{1}{6}

\frac{1}{8}

(fill in > or <).Show solution

Given: Compare

\frac{1}{6}

and

\frac{1}{8}

.

Concept: For unit fractions, smaller denominator = larger fraction.

Working: 6 < 8, so

\frac{1}{6} > \frac{1}{8}

.

Answer:

\frac{1}{6}

\frac{1}{8}

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4________ is smaller than ________ (write your own pair of fractions).Show solution

Concept: For unit fractions, the one with the larger denominator is smaller.

Example answer:

\frac{1}{7}

is smaller than

\frac{1}{3}

.

Reason: 7 > 3, so when the whole is divided into 7 parts, each part is smaller than when divided into 3 parts. Therefore

\frac{1}{7} < \frac{1}{3}

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My Flower Garden

Q1Look at the garden (revised plan with 5 equal parts: Rose in 2 parts, Mogra, Marigold, Jasmine each in 1 part). Fill in: Marigold in ________ part of the garden. Jasmine in ________ part of the garden.Show solution

Given: The garden is divided into 5 equal parts. Rose occupies 2 parts (

\frac{2}{5}

), Mogra occupies 1 part (

\frac{1}{5}

), Marigold occupies 1 part, Jasmine occupies 1 part.

Answer:
Marigold in

\frac{1}{5}

(one-fifth) part of the garden.
Jasmine in

\frac{1}{5}

(one-fifth) part of the garden.

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Q2Look at the garden (Rose in 3 parts). Fill in: Mogra in ___________ part. Marigold in ___________ part.Show solution

Given: Garden divided into 5 equal parts. Rose occupies 3 parts =

\frac{3}{5}

. The remaining 2 parts are for Mogra and Marigold (1 each).

Answer:
Mogra in

\frac{1}{5}

part.
Marigold in

\frac{1}{5}

part.

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Q3Look at the garden (Rose in 4 parts). Fill in: Marigold in ___________ part.Show solution

Given: Garden divided into 5 equal parts. Rose occupies 4 parts =

\frac{4}{5}

. The remaining 1 part is for Marigold.

Answer: Marigold in

\frac{1}{5}

part.

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Let Us Do — Flower Garden with Seven Seeds

aMake a flower garden with seven flowering seeds. Marigold in one-seventh (

\frac{1}{7}

) and Rose and Hibiscus in three-sevenths (

\frac{3}{7}

) part each.

bLily in three-sevenths (

\frac{3}{7}

), Marigold in two-sevenths (

\frac{2}{7}

) and Periwinkle in another two-sevenths (

\frac{2}{7}

cMogra in five-sevenths (

\frac{5}{7}

) part and Hibiscus in two-sevenths (

\frac{2}{7}

Do It Yourself — Dream Dosa Designer

Dosa 1Write the fractions for each of the toppings in the first dosa. 1) Chilli paneer = 2) Classic potato =

Dosa 2Write the fractions for each of the toppings in the second dosa. 1) Tangy tomato = 2) Classic potato = 3) Spicy onion =

Dosa 3Write the fractions for each of the toppings in the third dosa. 1) Spicy onion = 2) Tangy tomato =

Dosa 4Write the fractions for each of the toppings in the fourth dosa. 1) Tangy tomato = 2) Classic potato = 3) Spicy onion =

Dosa Design 1Make a dosa with

\frac{2}{3}

topping of Spicy onion,

\frac{1}{3}

of Classic potato.

Dosa Design 2Make a dosa with

\frac{3}{8}

of Classic potato,

\frac{1}{8}

of Chilly paneer and

\frac{4}{8}

of Tangy tomato mix.

Let Us Do — Fractions of a Collection

1There 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

5Simran calls her school friends for her birthday party.

\frac{1}{3}

of her friends receive a hairband as their return gift. Place hairbands on

\frac{1}{3}

of her friends.

6Draw flowers in

\frac{1}{5}

of the given number of pots.

Let Us Find Fractions in Our Surroundings

1Yesterday 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

\frac{1}{4}

of the whole. How many barfis are in each part?

2Rohan has a piece of ribbon to decorate his notebook. Mohan's ribbon is one-fourth as long as Rohan's ribbon. How long will Rohan's ribbon be? Draw it. (Mohan's ribbon is shown.)

Let Us Do — Paper Folding Activity (Equivalent Fractions)

1-6Take a rectangular piece of paper, fold into three equal parts, colour one part, then fold in half repeatedly. Observe the coloured part. Fill in:

\frac{1}{3} = \frac{2}{6} = \_ = \_ = \_

Let Us Try — Halving Activity

1Take another piece of paper and try the same starting with two equal parts, and halving every time. Fill in:

\frac{1}{2} = \frac{2}{4} = \_ = \_ = \_

Let Us Discuss — Fraction Chart

1How many

\frac{1}{4}

s are equal to

\frac{1}{2}

2Is

\frac{2}{3}

less than or greater than

\frac{1}{2}

3Ten pieces of

\frac{1}{10}

make a complete whole. Is this statement true?

4Three pieces of

\frac{1}{6}

are equal to two pieces of

\frac{1}{8}

. Is this true?

5How many pieces of

\frac{1}{8}

make

\frac{1}{4}

6Find the pieces that you can put together to make another bigger piece.

Let Us Do — Squares and Fractions

1Bablu is playing with square shapes. He wants to cut them in such a way that each piece is equal in size. Circle the squares which have been cut into equal parts. Write the fraction for the shaded part, whenever possible.

2Check if the children's claim below about the shaded parts of each of the pictures is correct. Circle the ones which you think are correct, cross out the ones which are not correct. Ameena says:

\frac{1}{3}

; Kishore says:

\frac{1}{4}

; Perry says:

\frac{1}{6}

; Kunj says:

\frac{1}{3}

; Balu says:

\frac{1}{5}

; Gita says:

\frac{1}{4}

3Identify the fractions represented by the coloured parts in the given pictures.

4Identify the fraction of the whole that the blue parts make in each of the pictures given below.

5Divide the following into equal parts and shade the appropriate parts in each. a) Shade

\frac{2}{3}

b) Shade

\frac{4}{6}

c) Shade

\frac{1}{4}

(Can you also show

\frac{1}{8}

?) d) Shade

\frac{3}{4}

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Sharing and Measuring

Studying Sharing and Measuring? Get the full interactive chapter.

Parts and Wholes — Let Us Discuss

Let Us Do — Halves and Quarters

Let Us Try — Many Ways to Make Halves and Quarters

Ding Dong Bell — Let Us Discuss

Let Us Do — Dhokla Sharing

Let Us Discuss — Fraction Kit

Fill in the Blanks — Comparing Fractions

My Flower Garden

Let Us Do — Flower Garden with Seven Seeds

Do It Yourself — Dream Dosa Designer

Let Us Do — Fractions of a Collection

Let Us Find Fractions in Our Surroundings

Let Us Do — Paper Folding Activity (Equivalent Fractions)

Let Us Try — Halving Activity

Let Us Discuss — Fraction Chart

Let Us Do — Squares and Fractions

Frequently Asked Questions

Sources & Official References

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Practice Quiz

Important Questions

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Formula Sheet

Chapter Summary

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