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**Half-Half**

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

**Solution:**

**Half of Half**

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

**Solution:**

**Half of Many Pieces**

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? _______

**Solution:**

There are 6 pieces of chocolate.

Rani gave half of her chocolate to her friend Reena. Rani was left with the remaining half, that is, 3 pieces.

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

**Solution:**

**Disclaimer:** The answer may vary from student to student, based on his/her observation. The answer provided here is for reference only.

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

• Draw 5 different ways.

Can you check if they are equal?

**Solution:**

Yes, they are equal.

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

Can you check if they are equal?

**Solution:**

Yes, 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.

• Colour each share with different colours.

• How much does each get? ________

**Solution:**

- Each of them gets $\frac{1}{4}$ of the cake.

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

**Solution:**

Out of 4 parts Rajni will get _________ parts, which is equal to half of the cake. So she can write it as $\overline{)4}$ or $\frac{1}{2}$.

**Solution:**

Out of 4 parts Rajni will get __ 2 __ parts, which is equal to half of the cake. So she can write it as $\frac{2}{4}$ or $\frac{1}{2}$.

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 $\frac{3}{4}$.

**Solution:**

Rajni and Raju together get $\frac{3}{4}$ of the total cake.

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

First pumpkin-seller— $\frac{1}{4}$ of this pumpkin is for Rs 10.

• This full pumpkin will cost Rs __________.

**Solution:**

Cost of $\frac{1}{4}$ of the pumpkin = Rs 10

∴ Cost of 1 full pumpkin = $4\times $Rs 10 = Rs 40

This full pumpkin will cost Rs __40__.

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 Rs 10?

Second pumpkin-seller — Half.

• This full pumpkin will cost Rs _________.

**Solution:**

Cost of $\frac{1}{2}$ of the pumpkin = Rs 10

∴ Cost of the full pumpkin = 2$\times $Rs 10 = Rs 20

This full pumpkin will cost Rs __20__.

**Using a Price List**

Item | Price in Rs (per kg) |

Tomato Potato Onion Carrot Pumpkin |
8 12 10 16 4 |

(b) Which costs more – $\frac{1}{2}$ kg of onions or $\frac{1}{4}$ kg of carrots?

(c) What is the price of $\frac{3}{4}$ kg of potatoes?

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

shopping list?

(e) Make two questions yourself from the price list.

1.

2.

**Solution:**

(a) Cost of 1 kg tomatoes = Rs 8

∴ Cost of $\frac{1}{2}$ kg tomatoes = Rs 8 ÷ 2

= Rs 4

(b) Cost of 1 kg onions = Rs 10

Cost of 1 kg carrots = Rs 16

∴ Cost of $\frac{1}{2}$ kg onions = Rs 10 ÷ 2

= Rs 5

And,

Cost of $\frac{1}{4}$ kg carrots = Rs 16 ÷ 4

= Rs 4

The cost of $\frac{1}{2}$ kg onions is more than the cost of $\frac{1}{4}$ kg carrots.

(c) Cost of 1 kg potatoes = Rs 12

Cost of $\frac{1}{4}$ kg carrots = Rs 12 ÷ 4

= Rs 3

∴ Cost of $\frac{3}{4}$ kg potatoes = Rs 3 × 3

= Rs 9

(d) Keerthi has Rs 20.

Her shopping list includes $\frac{1}{2}$ kg potatoes, 2 kg pumpkins and $\frac{1}{4}$ kg carrots.

Cost of $\frac{1}{2}$ kg potatoes = Rs 12 ÷ 2

= Rs 6

Cost of 2 kg pumpkins = Rs 2$\times $4

= Rs 8

Cost of $\frac{1}{4}$ kg carrots = Rs 16 ÷ 4

= Rs 4

Total cost of all vegetables = Rs 6 + Rs 8 + Rs 4 = Rs 18

Keerthi can purchase all the vegetables in her shopping list, as she has Rs 20.

(e)* *

1. How much pumpkin can she buy with the total money?

2. What will be the cost of 2 kg onions?

**Disclaimer:** It is highly recommended that the students prepare the sample questions on their own.

**Practice Time**

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

**Solution:**

__$\overline{)\frac{1}{2}}$__ __$\overline{)\frac{2}{4}}$__

**Make the other half**

$\frac{1}{2}$ of the picture is drawn here. Can you complete the picture by drawing the other half?

**Solution:**

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

**Solution:**

Three more quarters are required to complete the picture.

**Half and Quarter of a Metre**

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

• On this string, mark the length $\frac{1}{2}$ metre, $\frac{1}{4}$ metre and $\frac{3}{4}$ metre.

• Using your string, draw a line of length $\frac{1}{2}$ metre on the floor.

How many centimetres long is the line? ___________

Remember, 1 metre = 100 cm

So

$\frac{1}{2}$ metre = ....... cm

$\frac{1}{4}$ metre = ....... cm

$\frac{3}{4}$ metre = ....... cm

Can you see that when we add $\frac{1}{2}$ and $\frac{1}{4}$ we get $\frac{3}{4}$ ?

**Solution:**

1 m = 100 cm

Line of $\frac{1}{2}$ m on the floor = 100 cm ÷ 2 = 50 cm

So, a line of $\frac{1}{2}$ m on the floor is 50 cm long.

$\frac{1}{2}$ m = 100 cm ÷ 2 = 50 cm

$\frac{1}{4}$ m = 100 cm ÷ 4 = 25 cm

$\frac{3}{4}$ m = 25 cm × 3 = 75 cm

**Disclaimer:** Students are advised to do the activity by themselves.

**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 $\frac{1}{4}$ litre of milk.

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

Remember, 1 litre = 1000 millilitres

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

**Solution:**

- 1 litre = 1000 millilitres

Thus,

Quantity of milk in each bottle = 1000 mL ÷ 4 = 250 mL

Thus, each bottle contains 250 mL milk.

**Sharing Milk**

Shan poured 1 litre of milk into two bottles so that the first bottle holds $\frac{3}{4}$ litre and the other holds $\frac{1}{4}$ litre.

• Shade the level of milk in each bottle.

• How many millilitres of milk does each bottle hold?

**Solution:**

- 1 litre = 1000 millilitres

Thus,

Quantity of milk = 1000 mL ÷ 4 = 250 mL

Another bottle holds $\frac{3}{4}$ L milk.

Thus,

Quantity of milk = 250 mL × 3 = 750 mL

**Balance the Weight**

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

(a) Draw the weights in the empty pan.

Remember, 1kg = 1000 g

**Solution:**

We know

1 kg = 1000 g

Thus,

2 kg = 2$\times $1000 g = 2000 g

Following are the different ways in which we can make the two weights equal.

1) 1 kg + 500 g + 500 g = 2000 g

2) 1 kg + 500 g + 250 g + 250 g = 2000 g

3) 1 kg + 500 g + 250 g + 200 g + 50 g = 2000 g

4) 1 kg + 500 g + 200 g + 200 g + 100 g = 2000 g

5) 1 kg + 250 g + 250 g + 250 g + 200 g + 50 g = 2000 g

We can make five different combinations to get 2 kg weight.

**Disclaimer:** The answer may vary from student to student. The answer provided here is for reference only.

**Balance the Weight**

In how many different ways can you balance this weight of $\frac{3}{4}$kg?

(1) .....................

(2) .....................

(3) .....................

**Solution:**

We know

1 kg = 1000 g

Thus,

$\frac{1}{4}$ kg = $1000\xf74=250\mathrm{g}$

$\frac{3}{4}$ kg = $250\mathrm{g}\times 3=750\mathrm{g}$

Following are the different ways in which we can balance the weight of $\frac{3}{4}$ kg:

1) 500 g + 200 g + 50 g = 750 g

2) 250 g + 250 g + 250 g = 750 g

3) 250 g + 250 g + 200 g + 50 g = 750 g

**Practice Time**

• There are 60 mangoes. $\frac{1}{2}$ of them are ripe. How many mangoes are ripe?

• There are 32 children. $\frac{1}{2}$ 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 Rs 2. He gives a one-rupee coin, one half-rupee coin and one quarter-rupee coin. Is it enough?

**Solution:**

- Total mangoes = 60

Number of ripe mangoes = 60 ÷ 2 = 30

30 out of 60 mangoes are ripe.

- Total children = 32

So, $\frac{1}{2}$ of them are boys.

Number of boys = 32 ÷ 2

= 16

16 out of 32 children are boys.

- Total stars = 20

Number of stars that are red = 20 ÷ 4 = 5

5 out of 20 stars are red.

Number of stars that are not red = 20 − 5

= 15

- Cost of a pencil = Rs 2

But, the pencil is for Rs 2.

Money required = Rs (2.00 − 1.75) = Rs 0.25

Ravi did not give enough money to buy the pencil. Rs 0.25 more is required to buy the pencil.