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Math-Magic Solutions for Class-5, Chapter-4: Parts and Wholes

The chapter Parts and Wholes focuses on dealing with fractions and wholes. It covers the concept of how fractions work and how to add and subtract them. It helps the students to understand how to operate with fractions.

Download the NCERT Solutions for Parts and Wholes in PDF

Parts and Wholes

Question 1 :

a) Draw a rectangle of length 9 cm and width 6 cm. Divide it into three equal parts and complete the flag.
b) The top one-third of our flag is saffron (or orange). What is the colour of the middle one-third of the flag?
c) Where will you draw the Ashoka chakra?
d) How much of the flag will you colour green?
e) Is the white colour now less than 1 3 of the flag? Why?

Answer :

a) The complete flag is shown below.

b) The middle one-third of the flag is coloured in white.
c) The Ashoka chakra is in the middle of the white part.
d) One-third portion the flag is coloured in green.
e) The flag is divided into 3 equal parts. Each of the three colours is 1/3 of the flag. But in the white portion the Ashok chakra has been draw. So, the white colour is less than 1/3 of the flag.


Question 2 :

a) Now look at this flag. How much of it is black?

b) The green part of the flag can be written as.........
c) Is red less than one-third of the flag? Why?

 
Answer :

a) The flag is divided into three equal parts. Each part is one-third of the flag. Therefore, the one-third of the flag is black.
b) Since each part is one-third of the flag, the green part of the flag is one-third of the flag.
c) There is a white emblem in the red coloured portion. Therefore, the red colour is less than one-third of the fag.


Question 3 :

This is the flag of Myanmar, our neighbour.

a) Is blue more than one-fourth of the flag or less?
b) Guess how much of the flag is red. Is it more than 1/2 ? Is it more than three-fourths?

Answer :

c) Observe the given flag, the blue portion is less than one-fourth of the flag.
d) The blue portion is less than one-fourth of the flag. Therefore, the red portion of the flag is more than 1/2 ,even it is more than three- fourths..


Practice Time

Question 1 :

B) Colour the hats

a) Colour 1/3 of the hats red. Colour three-fifth hats blue.
b) How many hats did you colour red?
c) How many hats did you colour blue?
d) What part of the hats are not coloured?

Answer :

a) There are 15 hats in the given picture. Therefore,
1/3 of 15 = 1/3 X 15 = 5
Three-fifth of 15 = 3/5 X 15 =3X15/5 =9
So, colour 5 hats in red, and 9 hats in blue

b) Five hats are coloured in red.
c) Nine hats are coloured in blue.
d) One out of fifteen hats is not coloured. Therefore,1/15 hats are not coloured.


Question 2 :

A) Chocolate bar
a) 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?

b) What part of the chocolate did Manju eat?

Answer :

a) The chocolate is divided into 12 equal pieces.
Step 1: Since Raji got one-fourth of the whole chocolate, multiply 1/4by 12 to find the share of Raji.
1/4 X 12 = 12/4 = 3
Therefore, Raji got 3 pieces of the chocolate.
Step 2: Since Sugandha got one-third of the whole chocolate, multiply 1/3 by 12 to find the share of Sugandha.
1/3 X 12 = 12/4 = 4
Therefore, Sugandha got 4 pieces of the chocolate.
Step 3: Since Sheela got one-sixth of the whole chocolate, multiply 1/6 by 12 to find the share of Sheela.
1/6 X 12 = 12/6 = 2
Therefore, Sheela got 2 pieces of the chocolate.
Step 4: Since Manju ate the remaining part, add the shares of each of her friends and then subtract the result from 12 to find the share of Manju.
4 + 3 + 2 = 9 12 – 9 = 3 Therefore, Manju got 3 pieces of the chocolate.
b) Since Manju got 3 pieces out of 12 pieces of the chocolate, divide 3 by 12 to find the portion of the whole chocolate that Manju ate.
3/12 = 1/4
Therefore, Manju got one-fourth of the chocolate.


Patterns in Parts

Question 1 :

Look at grid A again. Is the grid coloured:
a) 1/2 Blue ,1/2 white?
b) 2/4 Blue ,2/4 white?
c) 3/8 Blue ,3/8 white?
d) 4/8 Blue ,4/8 white?
Mark (❌) on the wrong answer.

Answer :

Observe the grid A, it is coloured 8/16 blue, and 8/16 white.
Express 8/16 as equivalent fractions by dividing the numerator and denominator with the same number.
8/16 = 8#8/ 16#8 = 1/2
8/16 = 8#4/ 16#4 = 2/4
8/16 = 8#2/ 16#2 = 4/8 
Therefore, the wrong answer is:
c) 3/8 Blue , 3/8 White (❌)


Question 2 :

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 :

Do as directed. Answers may vary. A sample answer is:


Question 3 :

Draw grids of 16 squares and make patterns with
a) 2/8 red,1/2 yellow, 1/4 green
b) 3/16 red,5/16 yellow, 1/2 green

 
Answer :

a) Find the number of squares to be coloured in red, yellow, and green.
Number of red-coloured squares = 2/8 X 16 = 4
Number of yellow-coloured squares = 1/4 X 16 = 8
Number of green-coloured squares = 1/4 X 16 = 4
Therefore, draw a grid of 16 squares and colour 4 squares in the red, 8 squares in the yellow, and 4 squares in the green.

b) Find the number of squares to be coloured in blue, red, and green.
Number of blue-coloured squares = 3/16 X 16 = 3
Number of red-coloured squares = 5/16 X 16 = 5
Number of green-coloured squares = 1/2 X16 =8
Therefore, draw a grid of 16 squares and colour 3 squares in the blue, 5 squares in the red, and 8 squares in the green.


Ramu’s vegetable field

Question 1 :

Ramu’s vegetable field has 9 equal parts. What vegetables does he grow?
1) Which vegetable grows in the biggest part of his field? What part?
2) On what part of the field does he grow potatoes?
3) What part of the field is used to grow spinach? What part is used for brinjals?
4) Now you write some questions by looking at this picture.

Answer :

Observe the given picture. Ramu grows chillies, brinjals, tomatoes, spinach, and potatoes.
1) Observe the given picture. Out of 9 parts, tomatoes are in 3 parts. That is
3/9 = 1/3
Therefore, Ramu grows tomatoes in the biggest part of his field. That is one-third of the field.
2) The potatoes are in 2 out of 9 parts. That is 2/9 of the field.
Therefore, he grows potatoes in the two-ninth part of the field.
3) Spinach is in 1 out of 9 parts. Therefore, he grows spinach in the one-ninth part of the field.
Brinjals are in 2 out of 9 parts. Therefore, he grows brinjals in the two-ninth part of the field.
4) Do it by yourself. Answers may vary. A sample question is: Which vegetable grows in the smallest part of his field? What part?


Question 2 :

Ramu wanted to give these vegetables to his friends. He gave Aboobacker one-fifth of these tomatoes and 1/3 of the potatoes. Srija got 2/5 of the tomatoes and 3/6 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

Answer :

There are 18 potatoes and 20 tomatoes in the given picture. See the given figure.
Step 1: Find the Aboobacker’s share as:
One-fifth of the tomatoes =1/5 X 20 = 20/5 = 4tomatoes.
1/3 of the potatoes = 1/3 X 18 =18/3 = 6 potatoes
Step 2: Find Srija’s share as:
2/5 of the tomatoes = 2/5 X 20 = 2 X 20/5 = 8 tomatoes
3/6 of the potatoes = 3/6 X 18 = 3 X 18/6 = 9 potatoes
Now, circle Aboobacker’s share in blue, and Srija’s share in yellow.
 Since Nancy got the rest of the vegetables, count the vegetables that are not circled to find the share of Nacy.
Therefore, Nancy got 3 potatoes and 8 tomatoes.


Guess and Check

Question 1 :

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