** 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.