Table of Contents

9. Halves and Quarters

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Mintu cat and Mottu cat were friends. Once they stole a chapati from Malini's kitchen. I will take it — said Mintu. No, I will take it — said Mottu. While they were quarrelling, there came Tittu Monkey. Hi! What is the problem? why are you quarrelling? — he asked. "We don't know how to divide this chapati between us — the cats said. OK! don't worry. I will divide the chapati equally for both of you — he said. Clever Tittu divided the chapati like this:

Monkey showing two pieces of Chapati to the two cats.

These are not equal, the left part is bigger — Mintu and Mottu said. Oh, no problem, I will make it equal — Tittu said. He then cut a part of the left piece and ate it.

Monkey showing two pieces of Chapati to the two cats. Monkey saying, "Now is it equal?"

Oh! Now the right part is bigger — the cats cried. I am sorry — said Tittu. He cut a part from the bigger piece and ate it. When there was only a small piece remaining, he said — This is my share for the work. Tittu then quickly ate the last piece and climbed the tree.

Half-Half

Chapati. If the cats ask you to divide the chapati equally, how will you divide it?

  • If you do not cheat like Tittu, the cats will have these parts.

Cats looking at two equally divided pieces of chapati.

Half of Half

  • If two more cats come for food how will you divide one chapati equally for four cats?

A girl is dividing chapati in four equal parts for four cats.
Each of us got a quarter of the chapati. You are a good 'divider'. Ha!

Half of Many Pieces

A chocolate.

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

  • Circle the portion that Reena got.

How many pieces of chocolate are there?

How many pieces were left with Rani?

Girl eating chocolate.
Ha! Half a chocolate is as tasty as a whole chocolate!

Many Shapes from a Half Sheet

Take a piece of paper. Cut the sheet into two equal triangles so that each triangle is equal to half of the sheet.

Shade the two triangles with different colours.

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

Shape drawn with two triangles.

Many Ways to Cut into Half

A boy talking about division of rectangle into parts.
I have made a rectangle into two equal parts like this. Each part is half .

We write it as ½ It means 1 part out of 2. You can check if these parts are equal Try keeping one on top of the other.

In how many different ways can you cut a rectangle into half ?

  • Draw 5 different ways .

 

5 rectangles.

Can you check if they are equal?

Many Ways to Make Quarters

A boy talking about four parts of a rectangle.
I make our arts like this. Each part is a quarter.
And I can write it as ¼.
It means 1 part out of 4.

  • In how many different ways can you cut a rectangle into four equal parts? Draw 5 different ways.

5 rectangles.

Can you check if they are equal?

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.

A girl is cutting cake with her family members.

  • Colour each share with different colours.

  • How much does each get? _______________

Four circular shaped cakes divided in four equal parts each.

  • Father gave his share of cake to Rajni. Now colour the total part that Rajni will get.

  • Out of 4 parts Rajni will get ___ parts, which is equal to half of the cake. So she can write it as  /4 or ½ .

Four circular shaped cakes divided in four equal parts each.

Before Rajni's father gave his share to Rajni, she had  ½ of 'half the cake', which was ¼ of the total cake.

  • Colour the share Raju got.

Four circular shaped cakes divided in four equal parts each.


  • 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 ¾ .

Four circular shaped cakes divided in four equal parts each.

Greedy Kundu

Kundu is a greedy man. Whenever he goes to the market, he wants to get more and more but doesn't want to spend much money.

One day he wants to eat pumpkin halwa (sweet dish) He tries to buy a big pumpkin with only ₹10. He asks the first pumpkin seller the price of a big pumpkin.

First pumpkin-seller— ¼ of this pumpkin is for ₹ 10.

  • This full pumpkin will cost ₹__________________ 

.

Kundu—Eh! For ₹ 10, you should give me ½ of this pumpkin.

First pumpkin seller — Then you go to the next seller, he can give you ½ of such a big pumpkin for ₹ 10. I keep only good quality pumpkins.

A lady selling pumpkin to a man.

Kundu walks to the next seller and looks for a pumpkin of the same size.

Kundu—How much of this pumpkin will I get for ₹10?

Second pumpkin seller—Half

  • This full pumpkin will cost ₹____________________ 

Kundu—Eh! Why not give me ¾?  

A man and pumpkin are falling from the roof of a house.

Second pumpkin-seller — Run away! Go, get your pumpkin from that man. He sells such bad vegetables that he will even give you a full pumpkin of this size for ₹ 10.

The greedy Kundu walks to the next pumpkin seller. He looks at a pumpkin of the same size and asks him —will you give me this big one for ₹ 10?

Third pumpkin-seller — Why don't you climb the roof of that house? You can get pumpkins free from the plant itself!

Kundu is very happy. He climbs the roof of that house and then...................

Using a Price List

  1. How much does ½ kg of tomatoes cost?
  2. Which costs more – ½ kg of onions or ¼   kg of carrots?
  3. What is the price of ¾   kg of potatoes?
  4. Keerthi is going for shopping. She has only ₹ 20 with her. Can she buy all the things in her shopping list?
  5. Make two questions yourself from the price list.

1.

2.

A girl is holding a paper in her hand. It is written ,"potato-1/2kg, pumpkin-2kg and carrot-1/4kg" on the paper.

Item

Price in ₹

(per kg)

Tomato

8

Potato

12

Onion

10

Carrot

16

Pumpkin

4

        

Practice Time

  1. What part of the whole is coloured? Write below each shape.

Two rectangles. First rectangle is divided diagonally with half side coloured and second rectangle has four parts with bottom 2 parts coloured.

  1. Colour that part of the shape which is written below.

Six geometrical figures are given with fraction written below them.

  1. Cut in half.

Draw a line which divides these shapes into half.

Picture of a bird, star and a pumpkin.

  1. Colour half the number of shapes as shown here.

First picture has 8 rectangles and 4 are coloured. Second picture has 18 circles. Third picture has 10 flowers.

  1. Colour ¼ of these shapes.

First picture has 4 zig-zag shaped figures. Second picture has 8 drops of water. Third picture has 4 cubes.

  1. Match the coloured part as shown.

An 8-sided figure divided in 4 equal parts is shown in 4 styles. First figure has two parts coloured. Second figure has 1 part coloured. Third figure has all parts coloured and fourth figure has 3 parts coloured.

  1. Make the other half

½   of the picture is drawn here. Can you complete the picture by drawing the other half?

Half picture of a flower, butterfly and an insect is shown.

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

A picture has only a quarter made showing the Sun.

Half and Quarter of a Metre

Using your metre scale, cut a string of one metre.

  • On this string, mark the length ½ metre, ¼ metre and ¾   metre.
  • Using your string, draw a line of length ½   metre on the floor. How many centimetres long is the line?

A girl is measuring a string with a meter scale.
Remember, 1 metre = 100 cm

So

½   metre=......... cm

¼   metre=......... cm

¾   metre=......... cm

Can you see that when we add i and i we get f?

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 ¼   litre of milk.

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

5 bottles.

Remember, 1 litre=1000 millilitres

  • How many millilitres of milk does each bottle have?.

2 bottles.

Shan poured 1 litre of milk into two bottles so that the first bottle holds ¾ litre and the other holds ¼   litre.

  • Shade the level of milk in each bottle.
  • How many millilitres of milk does each bottle hold?

Balance the Weight

Picture has a weight of 1kg, 2 weights of 500g, 3 weights of 250g, 2 weights of 200g, 1 weight of 100g and 1 weight of 50g.

A balance scale with 2 kg weight on one side.

  • Choose from the weights above to make the two pans equal. In how many ways can you do it?
  1. Draw the weights in the empty pan.

Remember, 1kg =1000 g

A balance scale with 3/4 kg weight on one side.

  1. In how many different ways can you balance this weight of ¾ kg?

  1. .............
  2. …………
  3. …………

Why is It Wrong?

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

Rectangle is divided into 1 big coloured rectangle and 3 small rectangles. Triangle is divided into 1 big and 1 small coloured triangle. Below the rectangle 1/4 is crossed and below the triangle 1/2 is crossed.

Practice Time

  • There are 60 mangoes. ½   of them are ripe. How many mangoes are ripe?
  • There are 32 children. ½   of them are girls. How many children are boys?
  • There are 20 stars. A quarter of them are red. How many stars are red?

      How many are not red?

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

A child is writing and there are three 2 rupee coins, three 1 rupee coins, three 50 paise coins and four 25paise coins.