NCERT Solutions for Class 5 Maths (Math Magic) Chapter 4 Parts and Wholes

NCERT
SOLUTIONS
CLASS - 5th

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Class : 5th
Subject : Maths
Chapter : 4
Chapter Name : Parts And Wholes

Q1 Draw a rectangle of length 8 cm and width 6 cm. Divide it into three equal parts and complete
the ag. The top one – third of our ag is saffron (or orange). What is the colour of the middle-
one – third of the ag? Where will you draw the Ashoka chakra? How much of the ag will you
colour green?

Answer.

The colour of middle one-third of the ag is white. The Ashoka chakra is drawn at the centre of
the ag. One-third of the ag is coloured green.

Page : 50 , Block Name : Our Flag

Q2 Now look at this ag. How much of it is black? ________
The green part of the ag can be written as ________
Is red less than one - third of the ag? Why?

Answer. Total number of parts of the ag = 3 Now, we see that out of three equal parts, only one
part of the ag is black. Thus, 13 of the ag is black. We can also see that out of three parts of the
ag, only one part is green. Thus, green part of the ag is 13 of the ag.The red portion of the ag

is less than 13 of the ag, because a white emblem is also present in the red portion of the ag.

Page : 50 , Block Name : Our Flag

Q3

This is the ag of Myanmar, our neighbour. Is blue more than one-fourth of the ag or less? Guess
how much of the ag is red. Is it more than 12? Is it more than three-fourths?

Answer. The blue colour is present in less than one-fourth of the ag. I think, red colour is
present in more than three-fourth of the ag.

Page : 50 , Block Name : Our Flag

Q1 Collect as many ags as you can.

Answer. Malaysia

USA

Canada

Kuwait

Page : 51 , Block Name : Find out

Q2 How many ags have three colours? Are all the coloured parts equal in these ags?

Answer. The ag of Ghana, Azerbaijan, Malaysia,and Venezuela have three color.

Page : 51 , Block Name : Find out

Q1 Chocolate bar Manju had a chocolate. She gave one-fourth of it to Raji, one-third to Sugatha
and one-sixth to Sheela. She ate the remaining part. How many pieces of chocolate did each get?

What part of the chocolate did Manju eat?

Answer. Total number of pieces in the chocolate bar = 12
Manju gives one-fourth of the chocolate to Raji.
Number of pieces of chocolate given to Raji = 12 ÷ 4 = 3 Thus, Raji got 3 pieces of chocolate. Now,
Manju gives one-third of the chocolate to Sugatha.

Number of pieces of chocolate given to Sugatha = 12 ÷ 3 = 4 Thus, Sugatha got 4 pieces of
chocolate. Now, Manju gives one-sixth of the chocolate to Sheela.
Number of pieces of chocolate given to Sheela = 12 ÷ 6 = 2 Thus, Sheela got 2 pieces of chocolate.
Total number of pieces of chocolate given to Raji, Sugatha and Sheela = 3 + 4 + 2 = 9 Total number
of pieces of chocolate left in the bar = 12 − 9 = 3 As Manju ate the remaining part of the chocolate,
she will get 3 pieces of chocolate. Part of the chocolate eaten by Manju = 14

Page : 52 , Block Name : Practice Time

Q2 Colour the hats Colour 13 of the hats red. Colour three- fth hats blue. How many hats did you
colour red? How many hats did you colour blue? What part of the hats are not coloured?

Answer.

Total number of hats = 15 It is given that we have to colour 13 of hats in red. Number of red
coloured hats = 15 ÷ 3 = 5 It is given that we have to colour 35 of the total hats in blue. One- fth
of the total hats = 15 ÷ 5 = 3 Number of blue coloured hats = 3 × 3 = 9 Number of hats that are not
coloured = 1 Thus, part of hats that are not coloured = 115
Page : 53 , Block Name : Practice Time

Q1 Greedy Gatekeepers Remember Birbal, the clever minister of King Akbar? Do you know how he
became a minister? Birbal was then a young boy living in a village. He was very clever and could
write poetry. He thought he would try his luck in the King’s court. So he took some of his poems
and set off for the city. When he reached the outer gate of the palace, he was stopped by the
gatekeeper. “Hey! Stop there! Where are you going?”, shouted the gatekeeper. “I am a poet. I want
to see King Akbar and show my poems to him”, replied the poet. “Oh, you are a poet! The king is
kind, he will surely give you a prize. I will let you in if you give me 110 of your prize”.
Young Birbal agreed since he had no other way. When he went in, the gatekeeper calculated “If he
gets 100 gold coins I will get _________ gold coins”. The poet came to a second gatekeeper. This
gatekeeper also said, “I will let you in if you give me two- fth of your prize”. The poet agreed. The
gatekeeper happily calculated, “The poet will get at least 100 gold coins so I will get ___________
gold coins!” The poet reached the last gate. The gatekeeper said, “I will allow you to see the king
only if you give me half of the prize that you get”. The poet had no other way. He agreed and went
inside. The gatekeeper thought, “Today is a great day. If he gets 100 gold coins I will get __________
gold coins. But if he gets 1000 coins - wow! I will get ____________”. The king was very happy with
the poems and said, “Your work is very good. You can ask anything as your prize”. “My Lord, I
want 100 slaps”. “What! 100 slaps? ___________”. The king was shocked -

What happened after that? Complete the story. What part of the prize did the poet get?

Answer. The rst gatekeeper thought that the king would give 100 gold coins to Birbal as a prize.
The rst gatekeeper demanded 110 of the prize that he would get from the king. So, number of
gold coins that would be received by rst gatekeeper = 100 ÷ 10 = 10 The second gatekeeper
demanded 25 of the prize that Birbal would receive from the king. One- fth of 100 = 100 ÷ 5 = 20
So, number of gold coins that would be received by second gatekeeper = 20 × 2 = 40 The third
gatekeeper demanded half of the prize that Birbal would receive from the king. So, number of gold
coins that would be received by third gatekeeper = 100 ÷ 2 = 50 After listening to his poems, the
king became happy. Then, Birbal requested the king to give him 100 slaps as a prize. Hence, the
third gatekeeper got 50 slaps, second gatekeeper got 40 slaps, and the rst gatekeeper got 10
slaps. The poet got 0 slaps.

Page : 56 , Block Name : Greedy Gatekeepers

Q1 Make different patterns by colouring some squares in the grids B, C, D. What part of the grid
did you colour? What part of the grid remained white? Write.

Answer.

Page : 57 , Block Name : Patterns In Parts

Q2 Look at grid A again. Is the grid coloured.
(a) 12 blue, 12 white?
(b) 24 blue, 24 white?
(c) 38 blue, 58 white?
(d) 48 blue, 48 white?
Mark (X) on the wrong answer.
Answer. Total number of squares in grid A = 16
Number of squares that are blue-coloured = 8
Number of squares that are white-coloured = 8
Fraction of grid A that is blue-coloured = 12
Fraction of grid A that is white-coloured = 12
So, 12 of the grid A is blue and 12 of the grid A is white.
12=24=48

Page : 57 , Block Name : Pattern In Parts

Q3 Draw grids of 16 squares and make patterns with
(a) 28 red, 12 yellow, 14 green (b) 316 blue, 516 red, 12 yellow

Answer.

Page : 57 , Block Name : Pattern In Parts

Q1 Ramu’s vegetable eld has 9 equal parts. What vegetables does he grow?

(1) Which vegetable grows in the biggest part of his eld? What part?
(2) On what part of the eld does he grow potatoes?
(3) What part of the eld is used to grow spinach? What part is used for brinjals?
(4) Now you write some questions by looking at this picture.

Answer. Ramu grows capsicum, brinjal, tomatoes, spinach and potatoes in his eld.

1) Total number of parts of the vegetable eld= 9 Ramu grows tomatoes in the biggest part of his
eld. Part of eld used for growing tomatoes = 3 Part of eld used for growing tomatoes = 39 = 13.
Ramu grows tomatoes in one-third of the eld.

2) Part of eld used for growing potatoes = 2 Total number of parts of the vegetable eld=9 Part of
the eld used for growing potatoes =29 So, Ramu grows potatoes in two-ninth part of the eld.

3) Total number of parts of the vegetable eld = 9 Number of parts used for growing spinach = 1
So, part of the eld used for growing spinach = 19 Number of parts of eld used for growing
brinjals = 2 So, part of the eld used for growing brinjals = 29 Thus, Ramu grows spinach and

brinjals in one-ninth and two-ninth part of the eld respectively.
4) Missing

Page : 58 , Block Name : Ramu’s Vegetable Field

Q1 Ramu wanted to give below vegetables to his friends. He gave Aboobacker one- fth of these
tomatoes and 13 of the potatoes. Srija got 25 of the tomatoes and 36 of the potatoes. Nancy got
the rest of these vegetables. Circle Aboobacker’s share in blue. Circle Srija’s share in yellow.

How many potatoes and tomatoes did Nancy get?

Answer. Total number of tomatoes = 20 Total number of potatoes = 18 Aboobacker got one- fth of
the tomatoes, and one-third of the potatoes. Number of tomatoes with Aboobacker = 20 ÷ 5 = 4
Number of potatoes with Aboobacker = 18 ÷ 3 = 6 So, we will circle 4 tomatoes and 6 potatoes in
blue to show Aboobacker’s share. Srija got two- fth of the tomatoes and three-sixth of the
potatoes. Number of tomatoes with Srija = 2 × 4 = 8 One-sixth of 18 = 3 Number of potatoes with
Srija = 3 × 3 = 9

Thus, Ramu gave 4 tomatoes to Aboobacker and 8 tomatoes to Srija. So, he gave a total of 12
tomatoes to Aboobacker and Srija. Now, Ramu gave 6 potatoes to Aboobacker and 9 potatoes to

Srija. So, he gave a total of 15 potatoes to Aboobacker and Srija. Number of tomatoes left = 20 − 12
= 8 Number of potatoes left = 18 − 15 = 3 Thus, Nancy got 8 tomatoes and 3 potatoes.

Page : 59 , Block Name : Ramu’s Vegetable Field

Q1 The Card Puzzle

(1) Divide the white area in square A into two equal parts. Got the answer? Was that easy? Now do
the second question.
(2) Divide the white area in square B into three equal parts! That too is easy, isn’t it? Now see the
third question.
(3) Divide the white area in square C into four equal parts!! Is it a bit dif cult? Don’t worry, take
your time. Only if you have given up, look for the answer. Here comes the last question.
(4) Divide the white area in square D into seven equal parts!!!! The world record for this is 7
seconds. But you can take minutes! Tired of thinking? Look for the answer on page 68. So was that
dif cult?

Answer.

Page : 61 , Block Name : The Card Puzzle

Q1 What part of each shape is coloured? First guess the answer, then check.

Answer. Following are the guesses :
1) One-eighth of the shape is coloured.
2) One-sixth of the shape is coloured.
3) Two-ninth of the shape is coloured.
4) Four- fteenth of the shape is coloured.
To cross-check our guess, we will divide each of the given shapes into equal parts of size of the
coloured part as shown below :

On cross-checking, we now nd that our guess is correct.

Page : 61 , Block Name : Guess And Check

Q1 Look at the small triangle. What part of the square is it? How will you nd this out?

Answer. We will divide the whole square into small triangles as shown in the adjoining gure.

We will get 16 such triangles.
Total number of triangles = 16
Number of coloured triangles = 1
Fraction of square coloured = 116
Thus, the coloured small triangle is one-sixteenth of the square.

Page : 62 , Block Name : Guess And Check

Q1 Complete these
(1)

This circle is divided into two equal parts. Out of _________ equal parts one part is coloured blue.

(2)

Here the circle is divided into _________ equal parts. Out of ________ equal parts, ________ parts are
coloured blue.
(3)

Answer. (1) The circle is divided into two equal parts. Out of two equal parts, one part is blue in
colour.
(2) Here, the circle is divided into four equal parts. Out of four equal parts, two parts are blue-
coloured.
(3) Here, the circle is divided into six equal parts. Out of six equal parts, three parts are blue-
coloured.
(4) Here, the circle is divided into eight equal parts. Out of eight equal parts, four parts are blue-
coloured.
So, we can say that,
12 = 24 = 36 = 48

Page : 62 , Block Name : Coloured Parts

Q1 Ramesh bought a piece of halwa for his children Ammu and Anu.
He divided it equally for them.
• Each will get __________ part of halwa.
“This piece is too big. We can’t eat it”, they said.
So he divided the pieces into half again. Now how many pieces will Ammu get? ________
• What part of the halwa is it? _________
“Make it even smaller, Dad” they asked. So he again cut the halwa into smaller pieces.
“Ok, thank you, Dad.”
• Now how many pieces will each get?
• What part of the halwa is each piece now?
• If Ramesh had cut the halwa into 6 equal parts how many pieces would each have got? Look at
your answers for questions 1 to 4 and write --

= ____ =______=____= ______
1
= −
2

Answer. When Ramesh divides the piece of halwa in two parts,then each child will get half part of
halwa. Each will get 12 part of halwa.

• When each of the two pieces of halwa is divided into 2 equal parts, then there will be a total of 4
pieces of halwa. Now, each of the child gets 2 pieces of halwa.
Thus, Ammu will get 2 pieces of halwa. Total number of pieces of halwa = 4
Number of pieces with Ammu = 2
Part of halwa that Ammu gets = 24=12
Thus, Ammu will get half part of the halwa.

• When each of the 4 pieces cut again into halves, then we have a total of 8 pieces of halwa. Now,
each child will get 4 pieces of halwa.

• As one whole piece of halwa is now divided into 8 equal halves, each piece is 18 part of the
whole piece.

• When Ramesh divides the halwa into 6 equal parts, then each of the 2 child gets 3 pieces of
halwa.
12 = 24 = 36 = 48 = 510 = 612

Page : 64 , Block Name : Cutting The Halwa

Q1 Look at the picture. Write what part of the strip is each green piece. Write the part for a piece
of each colour.

How many one-fourths will make a half?
How many will make ?
1

8
1

4

How many 1

8
are in 1

2
?
Now ask your friends some questions on the same picture.

Answer.
The green strip is divided into 4 equal parts. Thus, each part is 14 of the whole green strip. Two
one-fourths will make a half.
1/4 + 1/4 = 1/2 .
Two one-eighths will make 1/4 = 1/8 + 1/8 = ¼

Page : 64 , Block Name : Parts Of The Strip

Q2 Look at this square.
What part is coloured blue?
What part is green?

Answer. We will draw a grid to nd the portion of each colour in the following square.

Total number of small squares in the grid = 16
Number of small blue coloured squares = 2
Fraction of blue shaded square = 216 = 18.
Thus, one-eighth of the square is shaded blue.
Number of green shaded squares = 1 Fraction of green shaded square =116
Thus, one-sixteenth of the square is shaded green.

Page : 64 , Block Name : Patterns

Q3 Ammini says half of half and one-third of three-quarters are equal. Do you agree? How will
you show this?

Answer. We can show the above with the help of gures.

So, half of half is equal to one-quarter, and one-third of three-quarters is equal to one-quarter.
Thus, we can say that half of half is equal to one-third of three quarters.

Page : 64 , Block Name : Puzzle: Is It Equal

Q1 This show 1/5 petals of a ower. Complete the ower by drawing the other petals.

Answer.

Page : 65 , Block Name : From A Part To The Whole

Q2 The picture shows one-third of the blades of a fan. Complete the picture by drawing the other
blades.

Answer.

Page : 65 , Block Name : From A Part To The Whole

Q3 Half of the blades of another fan are shown here. Complete the picture by drawing the other
half. How many blades have you drawn?

Answer. We have drawn two more blades to complete the picture.

Page : 65 , Block Name : From A Part To The Whole

Q1 How many

will make one rupee? Is 50 paise half of one rupee? How many

will make one rupee?
25 paise is _________ part of one rupee 20 paise is _________ part of one rupee How many 10 paise
will make one rupee? So 10 paise is ________ part of one rupee.

Answer. We know that,
One rupee = 100 paise Number of 50 paise coins in one rupee = 100 ÷ 50 = 2
So, two 50 paise coin will make one rupee.
There are two 50 paise coin in one rupee. So, 50 paise is half of one rupee.
We know that, 100 paise = Re 1 Number of 25 paise in one rupee = 100 ÷ 25 = 4
So, four 25 paise coins will make 1 rupee.
We know that, four 25 paise coins will make 1 rupee.
So,25 paise is one-fourth part of one rupee.
Number of 20 paise coin in one rupee = 100 ÷ 20 = 5 There are ve 20 paise coin in one rupee.
So, 20 paise is one- fth part of one rupee.
Number of 10 paise coin in one rupee = 100 ÷ 10 = 10 Ten 10 paise coin will make one rupee.
So 10 paise is one-tenth part of one rupee.

Page : 65 , Block Name : Rupees And Paise

Q1 My eldest daughter will get half of my camels. My second daughter will get one fourth of my
camels. My third daughter will get one fth of my camels. How did this happen? Discuss.

Answer. Total number of camels = 20
First daughter will get × 20 = 10
1

2

Second daughter will get
1
× 20 = 5
4

Third daughter will get \frac{1}{5} \times 20=4\)

Page : 66 , Block Name : An Old Woman’s Will

Q1 How many hours does Arun take for?

Answer. Sleeping : 8 Hours.
Studying : 6 Hours
Playing : 3 Hours

Page : 67 , Block Name : Arun’s Time Table

Q1 A school has decided to bring out a magazine every quarter of the year. How many magazines
will they have in a year? If they want to print it at the end of each quarter of a year, which are the
months for printing? Mark the number of those months.

Answer. They will have 4 magazines in a year, and he magazines will be printed in March, June,
September and December.

Page : 68 , Block Name : School Magazine

Q1 Most people sleep about 8 hours a day. Then what part of a day is it? _____

Answer. It is 8

24
=
1

3
part of the day.

Page : 68 , Block Name : Sleeping Beauty

Q2 So what part of a year do they sleep? A person 60-year-old must have slept ______ years.

Answer. An old person must have slept years.
1
× 60 = 20
3

Page : 68 , Block Name : Sleeping Beauty

Q1 How much does 2kg of tomato cost?

Answer. 2kg = 2X12 = Rs.24

Page : 69 , Block Name : Keerti’s Shopping List

Q2 How much does 1

2
kg of tomato cost?

Answer.
1 1
kg = X12 = Rs.6
2 2

Page : 69 , Block Name : Keerti’s Shopping List

Q3 Kiran wants 2 1
kg of tomato. How much will cost?
2

1
= 2 × 12
Answer. Cost of 2 tomato = = Rs.30
1 2
kg
2 5
= × 12
2

Page : 69 , Block Name : Keerti’s Shopping List

Q4 How much does 3 potato cost?
1
kg
2

1
= 3 × 10
2

Answer. Cost of 3 potato =
1 7
kg × 10
2 2

Rs. 35

Page : 69 , Block Name : Keerti’s Shopping List

Q5 What is the price of 1 1
kg of carrot?
4

1
= 1 × 18
4

Answer. Cost of 1 kg carrot =
1 5
× 18
4 4

Rs. 22.50

Page : 69 , Block Name : Keerti’s Shopping List

Q6 He bought a gourd of weight 4 and its costs?
3
kg
4

3
= 4 × 8
4

Answer. Cost of 4 gourd = =
3 48
kg × 8
4 4

Rs. 96

Page : 69 , Block Name : Keerti’s Shopping List

Q1 What time is the train expected to come today?

Answer. The right time of train = 6:45

The train is 30 min late
The correct time of arrival = :45 + 0.30 = 7:15

Page : 70 , Block Name : Practice Time

Q2 Nazia gets off at a station after 2 hours from this station. What time will she get off?
1

2

Answer. Nazia’s time after = 7:15 +2:30 = 9:45

Page : 70 , Block Name : Practice Time

Q3 Shazi will take 5 hours to reach Ernakulam by this train. At what time will he reach there?

Answer. Shaji’s time after 5h = 7:15 + 5:00 = 12:15

Page : 70 , Block Name : Practice Time