Halves and Quarters
NCERT book Page No: 95
Half – Half
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
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.
(a) Circle the portion that Reena got.
(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
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
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.
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.
Colour each share with different colours.
How much does each get?
Answer: Each get 1/4 of the cake
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.
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
Colour the share Raju got.
Answer: The shaded part shows 1/4 part of the cake which Raju has got.
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
This full pumpkin will cost Rs _________
Answer: Cost of 1/4 pumpkin = Rs 10
Cost of one pumpkin = Rs 10 ÷ 1/4
= 10 × 4
Hence, cost of one pumpkin = Rs 40
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
(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
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
(a) What part of the whole is coloured? Write below each shape.
(b) Colour that part of the shape which is written below.
(c) Cut in half
Draw a line which divides these shapes into half.
(d) Colour half the number of shapes as shown here.
(e) Colour 1/4 of these shapes.
(f) Match the coloured part as shown.
(g) Make the other half
1/2 of the picture is drawn here. Can you complete the picture by drawing the other half?
(h) This is a quarter of a picture. Can you complete it? How many more quarters will you draw to complete it?
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.
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
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?
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
Hence, on adding 1/2 and 1/4 we get 3/4
NCERT book Page No: 104
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.
Shade the bottles to show the level of milk in each.
The shaded portion shows the level of milk marked in the figure given below
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
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?
(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
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
In how many different ways can you balance this weight of 3/4 kg?
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?
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.
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
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
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
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.