Halves and Quarters

NCERT book Page No: 95

Half – Half

Question: 1

If the cat ask you to divide the chapati equally, how will you divide it?

Answer: I will fold the chapati into two equal halves and then break them from the creased line. Now, the chapati is half.

Half of Half

Question: 2

If two more cats come for food, how will you divide one chapatti equally for four cats?

Answer: First divide the chapati’s in two halves. Again divide it into further two halves. At last I will break the chapatti from the creased line as shown below

NCERT book Page No: 95-96

Half of Many Pieces

Rani got a chocolate. She divided it equally and gave half to her friend Reena.

Question: 3

(a) Circle the portion that Reena got.

Answer:

(b) How many pieces of chocolate are there?

Answer: The chocolate has totally six pieces.

(c) How many pieces were left with Rani?

Answer: Rani gave half of her chocolate to her friend Reena. So, now Rani was left with 3 pieces of chocolate.

NCERT book Page No: 96-97

Many Shapes from a Half Sheet

Question: 4

Draw different shapes using these triangles. One such shape is shown here.

Answer: Shapes using these triangles are shown below

Many Ways to Cut into Half

Question: 5

In how many different ways can you cut a rectangle into half? Draw 5 different ways. Can you check if they are equal?

Answer: The five different ways of a rectangle is shown below

Each part of a rectangle are equal as they exactly coincides with the other part.

Question: 6

In how many different ways can you cut a rectangle into four equal parts? Draw five different ways. Can you check if they are equal?

Answer: A rectangle divided into four equal parts are shown below. Yes, they are equal since each part exactly coincides with the remaining three parts.

NCERT book Page No: 98

Cutting the Cake

Rajni’s father brought a cake. She divided the cake into 4 equal parts – for herself, her brother Raju, her father and her mother.

Question: 7

Colour each share with different colours.

Answer:

Question: 8

How much does each get?

Answer: Each get 1/4 of the cake

Question: 9

Mother gave her share of cake to Rajni. Now colour the total part that Rajni will get.

Answer: Each person get 1/4 of the cake. So,

Cake that Rajni got = her share + her mother’s share

= 1/4 + 1/4

= 2 / 4

= 1 / 2

Hence, Rajni got 1/2 part of the cake.

Question: 10

Out of 4 parts Rajni will get ________ parts, which is equal to half of the cake.

So she can write it as ____ / 4 or 1/2

Answer: Rajni gets 2 parts of cake out of 4 parts. Hence, she can write it as 2/4 or ½

Question: 11

Colour the share Raju got.

Answer: The shaded part shows 1/4 part of the cake which Raju has got.

Question: 12

How much of the cake do Rajni and Raju together get? Colour their total share. Altogether they get 3 parts out of 4, so we can write it as 3/4

Answer: The total cake together Rajni and Raju got is 3/4

NCERT book Page No: 99

Question: 13

This full pumpkin will cost Rs _________

Answer: Cost of 1/4 pumpkin = Rs 10

Cost of one pumpkin = Rs 10 ÷ 1/4

= 10 × 4

= 40

Hence, cost of one pumpkin = Rs 40

Question: 14

Kundu how much of this pumpkin will I get for Rs 10? Second pumpkin seller-Half.

This full pumpkin will cost Rs _________

Answer: Cost of half pumkin = Rs 10

So, the cost of full pumpkin = Rs 10 + Rs 10

= Rs 20

Therefore, the cost of one full pumpkin is Rs 20

NCERT book Page No: 100

Using a Price List

Question: 15

(a) How much does 1/2 kg of tomatoes cost?

Answer: The cost of 1 kg tomato = Rs 8

Hence, the cost of 1/2 kg tomato = Rs 8 / 2

= Rs 4

Therefore, the cost of 1/2 kg tomatoes = Rs 4

(b) Which costs more – 1/2 kg of onions or 1/4 kg of carrots?

Answer: The cost of 1 kg onion = Rs 10

Therefore, the cost of 1/2 kg onion = 10 / 2

= Rs 5

The cost of 1 kg carrot = Rs 16

Hence, the cost of 1/4 kg carrot = 16 / 4

= Rs 4

Hence, the cost of 1/2 kg of onions is more than the cost of 1/4 kg of carrots

(c) What is the price of 3/4 kg of potatoes?

Answer: The cost of 1 kg of potatoes = Rs 12

The cost of 3/4 kg of potatoes = Rs 12 × 3/4

= Rs 36/4

= Rs 9

Therefore, the cost of 3/4 kg of potatoes = Rs 9

(d) Keerthi is going for shopping. She has only Rs 20 with her. Can she buy all the things in her shopping list?

Answer: Total money Keerthi has = Rs 20

Her shopping list includes = 1/2 kg potatoes, 2 kg pumpkin and 1/4 kg carrots.

Cost of 1 kg potatoes = Rs 12

Cost of 1/2 kg potatoes = Rs 12 / 2

= 6

Cost of 1 kg pumpkin = Rs 4

Cost of 2 kg pumpkin = Rs 4 × 2

= Rs 8

Cost of 1 kg carrot = Rs 16

Cost of 1/4 kg carrot = Rs 16/4

= Rs 4

Total cost of all the vegetables = 6 + 8 + 4

= Rs 18

Hence, Keerthi can buy all the vegetables in her shopping list.

NCERT book Page No: 101-103

Practice Time

Question: 16

(a) What part of the whole is coloured? Write below each shape.

Answer:

(b) Colour that part of the shape which is written below.

Answer:

(c) Cut in half

Draw a line which divides these shapes into half.

Answer:

(d) Colour half the number of shapes as shown here.

Answer:

(e) Colour 1/4 of these shapes.

Answer:

(f) Match the coloured part as shown.

Answer:

(g) Make the other half

1/2 of the picture is drawn here. Can you complete the picture by drawing the other half?

Answer:

(h) This is a quarter of a picture. Can you complete it? How many more quarters will you draw to complete it?

Answer:

To complete the picture, three more quarters are required.

• Half and Quarter of a Metre
• Using your metre scale, cut a string of one metre.
• On this string, mark the length 1/2 metre, 1/4 metre and 3/4 metre.
• Using your string, draw a line of length ½ metre on the floor.

Question: 17

How many centimetre long is the line?

Answer: We know

1 m = 100 cm

1/2 m on the floor = 100 cm ÷ 2

= 50 cm

Hence, 1/2 m on the floor = 50 cm long

Question: 18

So,

1/2 metre = ………….. cm

1/4 metre = ………….. cm

3/4 metre = ………….. cm

Can you see that when we add 1/2 and 1/4 we get 3/4?

Answer:

1/2 metre = 100 × 1/2

= 50 cm

1/4 metre = 100 × 1/4

= 25 cm

3/4 metre = 100 × 3/4

= 75 cm

Now, adding 1/2 and 1/4, we get

1/2 + 1/4 = (2 + 1)/4

= 3/4

Hence, on adding 1/2 and 1/4 we get 3/4

NCERT book Page No: 104

Sharing Milk

This bottle is full of milk and it holds one litre. The milk is put into 4 other bottles so that each bottle has 1/4 litre of milk.

Question: 19

Shade the bottles to show the level of milk in each.

Answer:

The shaded portion shows the level of milk marked in the figure given below

Question: 20

How many millilitres of milk does each bottle have?

Answer: We know

1 litre = 1000 millimetres

Each bottle contains = 1/4 litre of milk

Hence, each bottle contains = 1000 mL ÷ 4

= 250 mL of milk

Question: 21

Shan poured 1 litre of milk into two bottles so that the first bottle holds 3/4 litre and the other holds 1/4 litre.

(a) Shade the level of milk in each bottle.

(b) How many millilitres of milk does each bottle hold?

Answer:

(a) The level of milk marked is shown in below figure

(b) We know 1 litre = 1000 millilitres

Quantity of milk in first bottle = 750 mL of milk

Quantity of milk in second bottle = 250 mL of milk

NCERT book Page No: 105

Balance the Weight

Question: 22

Choose from the weights above to make the two pans equal. In how many ways can you do it?

Answer: There are many ways. Some of the ways are as follows

(i) 1 kg + 500 gm + 500 gm

(ii) 1 kg + 500 gm + 250 gm + 250 gm

(iii) 1 kg + 500 gm + 200 gm + 200 gm + 100 gm

(iv) 1 kg + 250 gm + 250 gm + 250 gm + 200 gm + 50 gm

(v) 1 kg + 200 gm + 200 gm + 100 gm + 500 gm

Question: 23

In how many different ways can you balance this weight of 3/4 kg?

1) ………..

2) ………..

3) …………

Answer:

3/4 kg = 1000 gm × 3/4

= 750 gm

1) 250 gm + 250 gm + 250 gm

2) 250 gm + 250 gm + 200 gm + 50 gm

3) 500 gm + 250 gm

NCERT book Page No: 106

Why is it Wrong?

Question: 24

Kannan shaded some parts as shown. But his friend Mini says that it is wrong. Explain why it is wrong.

Answer: Out of 5 parts of the rectangle, only 2 parts are coloured. Hence, it is 2/5 part which is coloured. In the triangle we cannot say how many parts of it is coloured, but it is clear that the coloured part is less than 1/2 part. Hence, 1/2 is wrong.

Practice Time

Question: 25

There are 60 mangoes, 1/2 of them are ripe. How many mangoes are ripe?

Answer: Total number of mangoes = 60 mangoes

Hence, number of mangoes which are ripe = 1/2 × 60

= 30 mangoes.

Therefore, 30 mangoes are ripe

Question: 26

There are 32 children. 1/2 of them are girls. How many children are boys?

Answer: Total number of children = 32

Half of them are girls, then remaining half will be obviously boys

Hence, half of 32 = 1/2 × 32 = 16

Therefore, the number of boys are 16

Question: 27

There are 20 stars. A quarter of them are red. How many stars are red? How many stars are not red?

Answer: Total number of stars = 20 stars

1/4 stars are red

Hence, the number of red stars = 1/4 × 20

= 5 stars

Therefore, number of stars which are red = 5 stars

Out of 20 stars, if 5 stars are red then obviously remaining 15 stars are not red.

Therefore, number of stars which are not red = 15 stars

Question: 28

Ravi wants a pencil. It costs Rs 2. He gives a one-rupee coin, one half-rupee coin and one quarter-rupee coin. Is it enough?

Answer: Total amount that Ravi gave = (1 + 0.50 + 0.25)

= Rs 1.75

But, the cost of the pencil = Rs 2

Money required to buy a pencil = Rs (2.00 – 1.75)

= Rs 0.25

Therefore, still Rs 0.25 is required to buy a pencil.

Hence, money given by Ravi is not enough.