**Parts and Whole**

**Page: 50**

**1. Draw a rectangle of length 9 cm and width 6 cm. Divide it into three equal parts and complete the flag.**

**The top one-third of our flag is saffron (or orange).**

**(i) What is the colour of the middle one-third of the flag?**

**Solution:-**

The colour of the middle one-third of the flag is white.

**(ii) Where will you draw the Ashoka chakra?**

**Solution:-**

I will draw the Ashoka chakra in middle of white portion of the flag.

**(iii)How much of the flag will you colour green?**

**Solution:-**

(1/3)^{rd} portion of the flag will be coloured green.

**(iv) Is the white colour now less than 1/3 of the flag? Why?**

**Solution:-**

Yes, white colour is less than 1/3 of the flag. Because, Ashoka chakra is present in the white portion.

**2. Now look at this flag. How much of it is black?**

**Solution:-**

There are 3 portion, so (1/3)^{rd} portion of the flag contains black colour.

**(i) The green part of the flag can be written as .**

**Solution:-**

The green part of the flag can be written as one-third.

**(ii) Is red less than one-third of the flag? Why?**

**Solution:-**

Yes, red colour is less than 1/3 of the flag. Because, white emblem is present in the red portion.

**3. This is the flag of Myanmar, our neighbor.**

**(i) Is blue more than one-fourth of the flag or less?**

**Solution:-**

Blue colour is less than one-fourth of flag.

**(ii) Guess how much of the flag is red. Is it more than ½? Is it more than three-fourths?**

**Solution:-**

It is more than half and also it is more than three-fourths.

**4. Practice time**

**(A) Chocolate bar**

**Manju had a chocolate. She gave one-fourth of it to Raji, one-third to Sugatha and one-sixth to Sheela. She ate the remaining part. How many pieces of chocolate did each get? Write here.**

**Solution:-**

Manju had a chocolate.

Number of bites in the chocolate is 12.

She gave one-fourth of it to raji = ¼ × 12

= 3 bites

Sugatha got one-third of it = (1/3) × 12

= 4 bites

Sheela got one-sixth of it = (1/6) × 12

= 2 bites

**(i) What part of the chocolate did Manju eat?**

**Solution:-**

Part of the chocolate remains with manju = 12 – (3 + 4 + 2)

= 12 – 9

= 3 bites

Therefore, Manju eat 3 bites of chocolate.

**(B) Colour the hats**

**(i) Colour 1/3 of the hats red.**

**(ii) Colour three-fifth hats blue.**

**(iii) How many hats did you colour red?**

**(iv) How many hats did you colour blue?**

**(v) What part of the hats are not coloured?**

**Solution:-**

The total number of hats in the given figure = 15

**(i) **Out of 15 colour 1/3 of the hats red = 1/3 × 15

= 5 hats

**(ii) **Out of 15 colour three-fifth hats blue = 3/5 × 15

= 3 × 3

= 9 hats

**(iii)** 5 hats are coloured red.

**(iv) **9 hats are coloured blue.

**(v) **Number of hats coloured = 14

Total number of hats = 15

So, Number of hats not coloured = 15 – 14

= 1 hat

Therefore, (1/15)^{th} part of the hats are not coloured.

Patterns in parts Page: 57

**1) Make different patterns by colouring some squares in the grids B, C, D. What part of the grid did you colour? What part of the grid remained white? Write.**

**Solution:-**

**2) Look at grid A again. Is the grid coloured—**

**(a) ½ blue, ½ white? (b) 2/4 blue, 2/4 white?**

**(c) 3/8 blue, 5/8 white? (d) 4/8 blue, 4/8 white?**

**Mark (X) on the wrong answer.**

**Solution:-**

(a) ½ blue, ½ white (b) 2/4 blue, 2/4 white

(c) 3/8 blue, 5/8 white (X) (d) 4/8 blue, 4/8 white

Because,

(a) ½ blue, ½ white = 8/16 = ½ … [divide both denominator and numerator by 8]

(b) 2/4 blue, 2/4 white = 8/16 = 2/8 … [divide both denominator and numerator by 4]

(d) 4/8 blue, 4/8 white = 8/16 = 4/8 … [divide both denominator and numerator by 2]

**3) Draw grids of 16 squares and make patterns with**

**(a) 2/8 red, ½ yellow, ¼ green**

**(b) 3/16 blue, 5/16 red, ½ green**

**Solution:-**

(a) 2/8 red, ½ yellow, ¼ green

Out of 16 squares 2/8 red = 2/8 × 16

= 2 × 2

= 4 red squares

Out of 16 squares ½ yellow = ½ × 16

= 1 × 8

= 8 yellow squares

Out of 16 squares ¼ green = ¼ × 16

= 1 × 4

= 4 green squares

(b) 3/16 blue, 5/16 red, ½ green

Out of 16 squares 3/16 blue = 3/16 × 16

= 3 × 1

= 3 blue squares

Out of 16 squares 5/16 red = 5/16 × 16

= 5 × 1

= 5 red squares

Out of 16 squares ½ green = ½ × 16

= 1 × 8

= 8 green squares

Ramu’s vegetable field Page: 58

**Ramu’s vegetable field has 9 equal parts.**

**1. What vegetables does he grow?**

**Solution:-**

Ramu grows chillis, potatoes, brinjals, tomatoes and spinach in his vegetable field.

**i) Which vegetable grows in the biggest part of his field? What part?**

**Solution:-**

He grows tomato in the biggest part of the field.

Out of 9 equal parts 3 of them contains tomato i.e. (3/9)^{th} part of his field contains tomato.

**ii) On what part of the field does he grow potatoes?**

**Solution:-**

Out of 9 equal parts 2 of them contains potato.

So, (2/9)^{th} part of his field contains potato.

**iii) What part of the field is used to grow spinach? What part is used for brinjals?**

**Solution:-**

Out of 9 equal parts only one part contains spinach.

So, (1/9)^{th} part of his field contains spinach.

Out of 9 equal parts 2 parts contains brinjals.

So, (2/9)^{th} part of his field contains brinjals.

**2. Ramu wanted to give these vegetables to his friends. He gave Aboobacker one-fifth of these tomatoes and 1/3 of the potatoes. Srija got 2/5 of the tomatoes and 3/6 of the potatoes. Nancy got the rest of these vegetables. Circle Aboobacker’s share in blue. Circle Srija’s share in yellow.**

**Solution:-**

From the given figure,

Total number of potatoes = 18

Total number of tomatoes = 20

From the question,

Ramu wanted to give these vegetables to his friends.

Aboobacker got one-fifth of these tomatoes = (1/5) × 20

= 1 × 4

= 4

Aboobacker got 1/3 of the potatoes = (1/3) × 18

= 1 × 6

= 6

Srija got 2/5 of the tomatoes = (2/5) × 20

= 2 × 4

= 8

Srija got 3/6 of the potatoes = (3/6) × 18

= 3 × 3

= 9

Then,

Nancy got the rest of these vegetables.

Total number of vegetables including potatoes and tomatoes = 20 + 18

= 38

Number of vegetables got by Aboobacker and Srija = 4 + 6 + 8 + 9

= 27

So, Nancy got = 38 – 27

= 11 vegetables.

**(i) How many potatoes and tomatoes did Nancy get?**

**Solution:-**

From the above solution,

Total number of tomatoes = 20

Total number of potatoes = 18

Then,

Number of tomatoes got by Aboobacker and Srija = 4 + 8

= 12

Number of potatoes got by Aboobacker and Srija = 6 + 9

= 15

Now,

Number of tomatoes got by Nancy = 20 – 12

= 8 tomatoes

Number of potatoes got by Nancy = 18 – 15

= 3

Guess and Check Page: 61

**A) What part of each shape is coloured?**

**First guess the answer, then check.**

**Solution:-**

By looking at the figure we can say that, 1/8 of the shape is coloured.

**(2)**

**Solution:-**

By looking at the figure we can say that, 1/6 of the shape is coloured.

**(3)**

**Solution:-**

By looking at the figure we can say that, 2/9 of the shape is coloured.

**(4)**

**Solution:-**

By looking at the figure we can say that, 3/12 of the shape is coloured.

**2. Coloured Parts**

**Complete these**

**(i)**

**This circle is divided into two equal parts. Out of equal parts one part is coloured blue.**

**Solution:-**

This circle is divided into two equal parts. Out of equal 2 parts one part is coloured blue.

**(ii)**

**Here the circle is divided into ****equal parts. Out of equal parts, parts are coloured blue.**

**Solution:-**

Here the circle is divided into four equal parts. Out of four equal parts, parts two are coloured blue.

**(iii)**

**Here the circle is…………………………………………………………**

**Solution:-**

Here the circle is divided into six equal parts. Out of six equal parts, parts three are coloured blue.

**(iv)**

**Here the circle is…………………………………………………………**

**Solution:-**

Here the circle is divided into eight equal parts. Out of eight equal parts, parts four are coloured blue.

So we can say that ½ = (2/4) = (3/6) = (4/8)

**3. Cutting the Halwa**

**Ramesh bought a piece of halwa for his children Ammu and Anu.**

**He divided it equally for them.**

**(i) Each will get ________ part of halwa.**

**Solution:-**

Each will get ½ part of halwa.

**This piece is too big. We can’t eat it, they said.**

**(ii) So he divided the pieces into half again. Now how many pieces will Ammu get?**

**Solution:-**

Ammu get two pieces.

**(iii) What part of the halwa is it?**

**Solution:-**

2/4 part of halwa, or ½ part of halwa.

**“Make it even smaller, Dad” they asked.**

**So he again cut the halwa into smaller pieces.**

**“Ok, thank you, Dad”.**

**(i) Now how many pieces will each get?**

**Solution:-**

Now, Ammu and Anu get four piece each.

**(ii) What part of the halwa is each piece now?**

**Solution:-**

Each piece is now 1/8 part of halwa.

**(iii) If Ramesh had cut the halwa into 6 equal parts how many pieces each have got? Look at your answers for questions 1 to 4 and write — ½ = = =**

**Solution:-**

If Ramesh had cut the halwa into 6 equal parts each got 3 pieces of halwa.

Then,

½ = 2/4 = 3/6 = 4/8 = 5/10 = 6/12

**4. Parts of the Strip**

**(i) Look at the picture. Write what part of the strip is each green piece. Write the part for a piece of each colour.**

**Solution:-**

**(ii) How many one-fourths will make a half?**

**Solution:-**

Two one-fourth will make a half.

= ¼ + ¼

= 2/4 [divide both numerator and denominator by 2]

= ½ = half

**(iii) How many 1/8 will make ¼?**

**Solution:-**

Two 1/8 will make ¼.

= 1/8 + 1/8

= 2/8 [divide both numerator and denominator by 2]

= ¼

**(iv) How many 1/8 are in ½?**

**Solution:-**

Four 1/8 are in ½.

= 1/8 + 1/8 + 1/8 + 1/8

= 4/8

= ½ [divide both numerator and denominator by 4]

**5. Patterns**

**Look at the square.**

**(i) What part is coloured blue?**

**Solution:-**

From the above figure, we can say that, out of 16 squares 2 squares are coloured blue.

i.e. 2/16 or 1/8 part is coloured blue.

**(ii) What part is green?**

**Solution:-**

From the above figure, we can say that, out of 16 squares 1 square coloured green.

i.e. 1/16 part is coloured green.

**6. From a Part to the Whole**

**(i) This show 1/5 petals of a flower. Complete the flower by drawing the other petals.**

**Solution:-**

**(ii) The picture shows one-third of the blades of a fan. Complete the picture by drawing the other blades.**

**Solution:-**

**(iii)** **Half of the blades of another fan are shown here. Complete the picture by drawing the other half. How many blades have you drawn?**

**Solution:-**

**7. Rupees and Paise**

**(i) How many will make one rupee?**

**Solution:-**

Two 50 paise coin make one rupee coin.

**(ii) Is 50 paise half of one rupee?**

**Solution:-**

Yes, 50 paise is half of one rupee.

**(iii) How many will make one rupee?**

**Solution:-**

Four 25 paise coin make one rupee.

**(iv) 25 paise is _________ part of one rupee**

**Solution:-**

25 paise is ¼ part of one rupee.

**(v) 20 paise is _________ part of one rupee**

**Solution:-**

20 paise is 1/5 part of one rupee.

Five 20 paise coin make one rupee.

**(vi) How many 10 paise will make one rupee?**

**Solution:-**

Ten 10 paise coin make one rupee.

**(vii) So 10 paise is _____ part of one rupee.**

**Solution:-**

So 10 paise is 1/10 part of one rupee.

**8. Arun’s Time Table**

**Sleeping: One third of a day**

**Use different colours to show,**

**Playing: One eighth of a day**

**Studying: ¼ of a day**

**Solution:-**

We know that, 24 hours in a day and above figure contains 25 box.

So, Arun spent one eighth of a day for playing = (1/8) × 24

= 1 × 3

= 3 hours = 3 box

He spent ¼ of a day for studying = ¼ × 24

= 1 × 6

= 6 hours = 6 box

Sleeping Playing Studying Other activities

**(i). How many hours does Arun take for Sleeping, studying and Playing?**

**Solution:-**

8 hours for sleeping, 6 hours for studying and 3 hours for playing.

**(ii) What part of the day does he use for other activities?**

**Solution:-**

He use 7/24 part of the day for other activities.

**9. School Magazine**

**A school has decided to bring out a magazine every quarter of the year. How many magazines will they have in a year? If they want to print it at the end of each quarter of a year, which are the months for printing? Mark the number for those months.**

**Solution:-**

From the question it is given that, school has decided to bring out a magazine every quarter of the year.

We know that, there are 12 months in a year.

Quarter of the year = ¼ × 12

= 1 × 3

= 3 months

So, for every three months, school has to bring out a new magazine.

**10. Sleeping Beauty**

**Have you heard of Kumbhakarna, the brother of Ravana? He is famous for sleeping for half a year.**

**(i) Most people sleep about 8 hours a day. Then what part of a day is it?**

**Solution:-**

We know that, 24 hours in a day.

Given, most people sleep about 8 hours a day = 8/24

= 1/3 part of a day

**(ii) So what part of a year do they sleep? A person 60 years old must have slept _______ years!!!**

**Solution:-**

A person 60 years old must have slept for = 1/3 × 60

= 1 × 20

= 20 years

**11. Keerti’s shopping list**

**Look at the yellow price list.**

**a) How much does 2 kg of tomato cost?**

**Solution:-**

From the price list 1 kg of tomato = ₹ 12

Then, cost of 2 kg of tomato = 12 × 2

= ₹ 24

**b) How much does kg of tomato cost?**

**Solution:-**

From the price list 1 kg of tomato = ₹ 12

**c) Kiran wants 2½ kg of tomato. How much will it cost?**

**Solution:-**

From the price list 1 kg of tomato = ₹ 12

For ½ kg of tomato = ½ × 12

= ₹ 6

Then, cost of 2 kg of tomato = 12 × 2

= ₹ 24

So, cost of 2½ kg of tomato = 24 + 6

= ₹ 30

**d) How much does 3½ kg potato cost?**

**Solution:-**

From the price list 1 kg of potato = ₹ 10

For ½ kg of potato = ½ × 10

= ₹ 5

Then, 3 kg of potato = 3 × 10

= ₹ 30

So, cost of 3½ kg of potato = 30 + 5

= ₹ 35

**e) What is the price of 1¼ kg of carrot?**

**Solution:-**

From the price list 1 kg of Carrot = ₹ 18

For ¼ kg of carrot = ¼ × 18

= 9/2

= ₹ 4.5

Then, 1¼ kg of carrot = 18 + 4.5

= ₹ 22.5

**f)** **He bought a gourd of weight 4¾ kg and it costs?**

**Solution:-**

From the price list 1 kg of Gourd = ₹ 8

For 4 kg of Gourd = 8 × 4

= ₹ 32

For ¾ kg of Gourd = ¾ × 8

= 3 × 2

= ₹ 6

Then, cost of 4¾ kg of Gourd = 32 + 6

= ₹ 38

**g) Look at the shopping list in Keerti’s hand. How much will she have to pay to buy all of these?**

**Solution:-**

Item | Price per kg | Total price |

Potato 2¼ kg | 10 | 22.50 |

Carrot 3¼ kg | 18 | 67.50 |

Gourd 1 ½ kg | 8 | 12 |

Total | ₹ 102 |

**12. Raheem’s journey**

**Raheem has to travel 1¼ km to reach school. What distance does he travel to go to school and come back home?**

**Solution:-**

From the question it is given that,

To reach the school Raheem has to travel = 1 ¼ km = 5/4 km

From school to home = 1 ¼ km = 5/4 km

Total distance travelled by Raheem = 5/4 + 5/4

= 10/4

= 5/2

= 2 ½ km

Therefore, he travel to go to school and come back home = 2 ½ km

**13. What coins?**

**Latha bought a pencil and a pen for seven and a half rupees. She gave Rs 10/–. The shopkeeper gave back the money in half and quarter rupees. What are the coins she got?**

From the question it is given that,

Latha bought a pencil and a pen for = ₹ 7½

Money given by latha to the shopkeeper = ₹ 10

Shopkeeper gave back the money = 10 – 7.5

= ₹ 2.5

So, the shopkeeper can return as ₹ 2.5 in the following ways

a) 1 half rupee coin and 8 quarter rupee coins

b) 2 half rupee coins and 6 quarter rupee coins

c) 3 half rupee coins and 4 quarter rupee coins

d) 4 half rupee coins and 2 quarter rupee coins

**14. At the railway station**

**Your attention please. Mangalore Express coming from Mangalore and going to Thiruvananthapuram is now running late by half an hour.**

**Oh the train is late today. The right time is a quarter to 7.**

**a) What time is the train expected to come today?**

**Solution:-**

The right time is a quarter to 7 i.e. 6: 45

But, train is delayed by half an hour i.e. 30 minutes.

So, exact time train will arrive at 6: 45 + 0: 30 = 7: 15

**b) Nazia gets off at a station after 2½ hours from this station. What time will she get off?**

**Solution:-**

From the question,

Nazia gets off at a station after = 2: 30 hours

Then, total time taken by Nazia to reach = 2: 30 + 7: 15

= 9: 45

**c) Shaji will take 5 hours to reach Ernakulam by this train. At what time will he reach there?**

**Solution:-**

From the question, it is given that,

Shaji will take 5 hours to reach Ernakulam

Then, total time taken by Shaji to reach Ernakulam = 7: 15 + 5

= 12: 15