**“Parts and Wholes” **is **Chapter 4** from **Merry Math V **for students of** Class 5th **of **JKBOSE**. This post is about **Parts and Wholes Chapter 4 Class 5 JKBOSE Solutions**. In a previous post, you read about **How Many Squares Chapter 3 Class 5 Math JKBOSE**. Let’s get started:

**Parts and Wholes Chapter 4 Class 5 JKBOSE Solutions**

**Page No. 51 Solutions**

**Do you know how to draw the flag?**

Ans. Yes, I know.

Draw a rectangle of length 8 cm and width 6 cm. Divide it into three equal parts.

**Now Answer these questions:**

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

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

**Where will you draw the Ashoka Chakra? **

Ans. The Ashoka chakra is drawn in the white part of the flag.

**How much of the flag will you colour green?**

Ans. I will colour one-third ⅓ of the flag green.

**Is the white colour now less than ⅓ of the flag? Why?**

Ans. Yes, the white colour is a little less than ⅓ of the flag. Because of the blue Ashoka chakra in the white part of the flag.

**Now look at this flag:**

**How much of it is black? ________**

Ans. One-third ⅓ of the flag is black.

**The green part of the flag can be written as________**

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

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

Ans. Yes, the red colour is a little less than one-third of the flag because of the white emblem in the red part of the flag.

**This is the Flag of Myanmar, our neighbours.**

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

Ans. The blue colour is a little less than one-fourth of the flag.

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

Ans. It is more than three-fourths of the flag. Yes, it is more than ½.

**Page No. 53 Solutions**

**Magic Top**

**What do you see? Can you see all the colours? Write what you see in your notebook.**

Ans. We see that different colours will disappear and the top will look like of white colour.

**Practice Time**

**(A) Chocolate bar**

Ulfat had a chocolate. She gave one-fourth of it to Nighat, one-third to Sumaira and one-sixth to Ishrat. She ate the remaining part.

**How many pieces of chocolate did each get?**

Sol. Total number of pieces = 12

The number of pieces she gave to Nighat = ¼ of 12 = 12/4 = 3

The number of pieces she gave to Nighat = ⅓ of 12 = 12/3 = 4

The number of pieces she gave to Nighat = ⅙ of 12 = 12/6 = 2

The number of pieces Ulfat got = 12 – (3 + 4 + 2) = 3.

**What part of Chocolate did Ulfat eat?**

Ans. Ulfat ate 3 chocolate pieces out of 12.

So, she ate 3/12 = ¼ (one-fourth) of the chocolate.

**Page No. 54 Solutions**

**(B) Colour the hats**

Colour ⅓ of the hats red.

Colour three-fifths of the hats blue.

**How many hats did you colour red?**

Sol. The total number of hats = 15

⅓ **of** the hats = ⅓ × 15 = 15/3 = 5

So, 5 hats were coloured in red.

**How many hats did you colour blue? **

Ans. The total number of hats = 15

⅗ of the hats = ⅗ × 15 = 45/5 = 9

So, 9 hats were coloured in blue.

**What part of the hats are not coloured?**

Sol. Total number of hats = 15

Sum of coloured hats = 5 + 9 = 14

Number of hats left uncoloured = 15 – 14 = 1

Thus = 1/15 of the hats are not coloured.

**(C) Equal parts of a triangle.**

Now try to make three equal parts of this triangle differently. Colour each one-third with a different colour.

Sol.

**Page No. 55 Solutions**

**(D) Six parts of a rectangle**

Bisma has divided a green rectangle into six equal parts like this.

Divide each of these rectangles into six equal parts.

Sol.

**Greedy Gate Keepers**

Remember Birbal, The clever minister of King Akbar? Do you know how he became a minister?

Birbal was then a young boy living in a village. He was very clever and could write poetry.

He thought he would try his luck in the King’s court. So he took some of his poems and set off for the city.

When he reached the outer gate of the palace, he was stopped by the gatekeeper.

“Hey! Stop there! Where are you going?”, shouted the gatekeeper.

“I am a poet. I want to see King Akbar and show my poems to him”, replied the poet.

“Oh, you are a poet! The king is kind, he will surely give you a prize. I will let you in if you give me 1/10 of your prize.”

Young Birbal agreed since he had no other way.

When he went in, the gatekeeper calculated “If he gets 100 gold coins I will get** 10 **gold coins”.

The poet came to a second gatekeeper. This gatekeeper also said, “I will let you in Our if you give me two-fifths of your prize”. The poet agreed.

The gatekeeper happily calculated, “The poet will get at least 100 gold coins so I will get** 40 **gold coins!”

The poet reached the last gate. The gatekeeper said, “I will allow you to see the king only If you give me half of the prize that you get”. The poet had no other way. He agreed and went inside.

The gatekeeper thought, “Today is a great day. If he gets 100 gold coins.

I will get 50 gold coins. But if he gets 1000 coins – wow! I will get ** 500**.”

The king was very happy with the poems and said, “Your work is very good. You can ask anything as your prize”.

“My Lord, I want 100 slaps”. “What! 100 slaps?

“The king was shocked.

**What happened after that? Complete the story. What part of the prize did the poet get?**

Ans. The first gatekeeper got 10 slaps, the second gatekeeper got 40 slaps and the last gatekeeper got 50 slaps. The poet got zero slaps.

**Page No. 58 Solutions**

**Pattern in Parts**

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

Sol.

**Look at grid A again. Is the grid coloured:**

Ans. (c) is the wrong answer.

**Page No. 59 Solutions**

**3. Draw grids of 16 squares and make patterns, with:**

Ans.

**Farooq’s Vegetable Field**

Farooq’s vegetable field has 9 equal parts.

**What vegetables does he grow?**

Ans. Farooq grows potatoes, brinjals, chillies, tomatoes and spinach.

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

Ans. Tomatoes grow in the biggest part of his field. It grows in one-third part of the field.

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

Ans. He grows potatoes on 2/9 (two-ninth) part of the field.

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

Ans. 1/9 part of the field is used to grow spinach and 2/9 part of the field is used for brinjals.

**Page No. 60 Solutions**

Farooq wanted to give these vegetables to his friends. He gave Rafiq one-fifth of these tomatoes and ⅓ of the potatoes.

Sumaiya got ⅖ of the tomatoes and 3/6 of the potatoes. Yasmeen got the rest of these vegetables. Circle Rafiq’s share in blue. Circle Sumaiya’s share in yellow.

Ans.

**How many potatoes and tomatoes did Yasmeen get?**

Sol. Total Number of tomatoes = 20

Rafiq got 4 tomatoes and Sumaiya got 8 tomatoes.

Sum of both = 4 + 8 = 12

Remaining tomatoes =20 – 12 = 8

(Yasmeen got 8 tomatoes)

Total number of potatoes = 18

Rafiq got 6 potatoes and Sumaiya got 9 potatoes.

Sum of both = 6 + 9 = 15

Remaining potatoes = 18 15 = 3

(Yasmeen got 3 potatoes)

**Page No. 62 Solutions**

**Guess and Check**

**(A) What of each shape is coloured? part First guess the answer, then check.**

1)

Ans. By guess = 1/8

2)

Ans. By guess = 1/6

3)

Ans. By guess = 2/9

4)

Ans. By guess = 4/15

**Page No. 63 Solutions**

**(B) Do you remember this picture? Look at the small triangle. What part of the square is it? How will you find this out?**

**Divide the big triangles and other shapes into small triangles (like the red one). How many small triangles are there altogether?**

Sol. By dividing the square into entire small triangles as shown in the following fig. We find that there are 16 such triangles.

The coloured small triangle is 1/16 of the square.

**Coloured Parts**

**Complete these:**

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

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

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

Ans. Here the circle is divided into ** four** equal parts. Out of

**equal parts,**

__four__**parts are coloured blue.**

__two__**Here the circle is…………….**

Ans. 3. Here the circle is __divided into six equal three parts. Out of six equal parts, parts are coloured blue.__

**Here the circle is…………….**- Here the circle is
__divided into eight equal parts. Out of eight equal parts, four parts are coloured blue.__

**So, we can say that ½ = 2/…. = …. /6 = …. /8**

Ans. ½ = 2/4 = 3/6 = 4/8

Since, in each circle, the coloured parts are equal.

**Page No. 64 Solutions**

**Cutting the Halwa**

Javaid bought a piece of halwa for his children Nafisa and Ulfat.

He divided it equally for them.

**Each will get………….. part of halwa.**

Ans. Each will get ** ½** part of the halwa.

**“This piece is too big. We can’t eat it,” they said. So he divided the pieces into half again. Now how many pieces will Nafisa get?**

Ans. Nafisa will get 2 pieces of halwa.

**What part of the halwa is it?**

Ans. It is 2/4 part of the halwa.

**“Make it even smaller. Dad” they asked. So he again cut the halwa into smaller pieces. “Ok, thank you, Dad.”**

**Page No. 65 Solutions**

**Now how many pieces will each get?**

Ans. Now each of them will get four pieces.

**What part of the halwa is each piece now?**

Ans. Each piece is now ⅛ part of the halwa.

**If Javaid had cut the halwa into 6 equal parts how many pieces would each have got? Look at your answers for questions 1 to 4 and write —**

Ans. If Javaid had cut the halwa into 6 equal parts then each would get 3 pieces.

½ = 2/4 = 3/6 = 4/8 = 5/10 = 6/12

**Parts of the Strip**

**Look at the picture:**

**Write what part of the strip is each green piece.**

Ans. Each green part represents ¼ (one-fourth) of the green piece.

**Write the part for a piece of each colour.**

**How many one-fourths will make a half?**

Sol. Two-one-fourth will make a half.

For Example, ¼ + ¼ = 2/4 = ½

**How many will ⅛ make ¼?**

Sol. Two ⅛ will make ¼

For Example, ⅛ + ⅛ = 2/8 = ¼

**How many ⅛ are in ½?**

Sol. Four one-eighths (⅛) will make ½.

⅛ + ⅛ + ⅛ + ⅛ = 4/8 = ½

**Patterns**

**Look at this square**

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

Sol. One-eighth (⅛) part of the square is coloured blue.

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

Sol. One-sixteenth (1/16) part of the square is green.

**Puzzle: Is it Equal?**

**Aminah says half of half and one-third of three quarters are equal. Do you agree? How will you show this?**

Ans. Look at these figures carefully:

Half of half = One-third of three-quarter

= ½ × ½ = 1/3 × ¾

= ¼ = ¼

Thus, it is equal.

**Page No. 66 Solutions**

**From a Part to the Whole**

**This shows ⅕ petals of a flower. Complete the flower by drawing the other petals.**

Ans. Completing the flower with 5 petals.

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

Ans.

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

Ans. We have drawn two blades.

**Rupees and Paise**

**How many 50 paise will make a rupee?**

Ans. Two 50 paise will make one rupee.

**Is 50 paise half of one rupee? **

Ans. Yes, 50-paise is half of one rupee.

**How many 25 paise will make one rupee?**

Ans. Four 25 paise will make one rupee.

**25 paise is _________ part of one rupee?**

Ans. 25 paise is one-fourth part of one rupee.

**20 paise is _________ part of one rupee?**

Ans. 20 paise is one-fifth part of one rupee.

**How many 10 paise will make one rupee? **

Ans. Ten 10-paise will make one rupee.

So 10 paise is ________ part of one rupee?

Ans. So 10 paise is1/10 part of one rupee.

**Page No. 67 Solutions**

**An Old Woman’s Will**

Once there lived an old woman. She lived with her three daughters. She was quite rich and had 19 camels. One day she fell ill. The daughters called the doctor. The doctor tried his best but could not save the woman. After her death, the daughters read what she had written in her will.

The daughters were really puzzled. “How can I get ½ of the 19 camels? asked the eldest daughter.

“Half of 19 is nine and a half. But we can’t cut the camel!” The second daughter said.

“That is right, but what will we do now?” asked the third daughter.

Just then they saw their aunt coming, and the daughters told her their problem.

“Show me the will. I have an idea. You take my camel. So, you have 20 camels. Now can you divide them as your mother wanted?” the aunt said.

“You want half of the camels, don’t you? Take 10 camels,” she said to the eldest daughter.

“Take your share”, the aunt told the second daughter. She took one-fourth of the camels and got** 5** camels.

⅕ × 20 = 5

“You can take one-fifth of the camels,” the aunt told the third daughter. She got** 4 **camels. The daughters were very happy and counted their camels 10+

**+**

__4__**= 19.**

__5__**Page No. 68 Solutions**

“The one remaining is mine.” said the aunt and took her camel away!

**How did this happen? Discuss.**

Sol. The eldest daughter got ½ of the total camels.

The second daughter got ¼ of the total camels.

The third daughter got ⅕ of the total camels.

So, each got = ½ + ¼ + ⅕

= 10 + 5 + 4/20 = 19/20

LCM = 2 × 2 × 5 = 4 x 5 = 20

Eldest daughter’s share = 10 camels

The second daughter’s share = 5 camels

The third daughter’s share = 4 camels.

We know that their mother had 19 camels.

But it is difficult to give ½ part of the total camels to her eldest daughter. So their aunt gave them one camel for division. After division, one camel is left, which belongs to Aunt. Therefore, in the end, she took her camel away.

**Asif’s Timetable**

Asif sleeps at 10 pm and wakes up at 6 am.

He plays from 7 to 8 am and again from 4 to 6 pm

**His Time – Table**

Sleeping: One-third of a day.

Playing: One-eighth of a day.

Studying: One-fourth (¼) of a day.

(We know that there are 24 hours in a day)

**How many hours does Asif take to sleep?**

Ans. Asif sleeps at 10 pm and wakes up at 6 am. So he takes 8 hours to sleep. This is the one-third of the day

**How many hours does Asif take for studying?**

Sol. Asif studies for ¼ of a day

Total hours in a day = 24 hours

¼ of 24 = ¼ × 24 = 6 hours

He studies 6 hours a day.

**How many hours does Asif take to play?**

Sol. He plays one-eighth of a day. So, he takes 3 hours to play

⅛ × 24 = 3 hours

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

Sol. Asif takes 8 hours to sleep, 6 hours for studying and 3 hours for playing.

Total hours which he spends = 8 + 6 + 3 = 17 hours

Number of hours used for other activities = (24 – 17) = 7

Therefore 7/24 part of the day he uses for other activities.

**Page No. 69 Solutions**

**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?**

Sol. They will have four (4) magazines in a year.

(Every quarter of the year means ¼ of the year)

1 year = 12 months

¼ × 12 = 3 months

**If they want to print it at the end of each quarter of a year, which are the months for printing?**

Sol. If they want to print it at the end of each quarter of a year. The months for printing are March, June, September and December.

**Mark the number for those months.**

Ans.

**Sleeping Beauty**

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

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

Ans. Yes, I have heard of Kumbhakarna, the brother of Ravana.

Most people sleep about 8 hours a day. It is** one-third **part of the day.

**So what part of the year do they sleep? **

Ans. They sleep for one-third of a year.** **

A **person 60 years old must have slept _________ years!!!**

Ans. A person 60 years old must have slept** for 20 **years.

Because one-third of 60 years

⅓ × 60 years = 20 years

**Page No. 70 Solutions**

**Gazala’s Shopping Lists**

**Look at the yellow price list**

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

Sol. Cost of 1 kg tomato = ₹ 12

Cost of 2 kg tomato = ₹ 12 × 2 = ₹ 24

**(b) How much does ½ kg of tomato cost?**

Sol. Cost of 1 kg tomato = ₹ 12

Cost of ½ kg tomato = ₹ 12 × ½ = ₹ 6

**(c) Aslam wants 2 ½ kg of tomato. How much will it cost?**

Sol. Cost of 1 kg tomato = ₹ 12

Cost of 2 ½ **=** 5/2 kg tomato

₹ 12 × 5/2 = ₹ 30

**(d) How much does 3 ½ kg potato cost?**

Sol. Cost of 1 kg potato = 10

Cost of 3 ½** **kg potato = 7/2 kg potato

= 7/2 × 10 = ₹ 35

**(e) What is the price of 1 ¼ kg of carrot?**

Sol. Cost of 1 kg carrot = 18

Cost of 1 ¼ kg carrot = 5/4 kg carrot

5/4 × 18 = ₹ 22.50.

**(f) He bought a gourd of weight 4 ¾ kg and it costs……**

Sol. Cost of 1 kg gourd = ₹ 8

Cost of 4 ¾ kg gourd = 19/4 kg gourd

= ₹ 8 × 19/4 = ₹ 38.

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

Sol.

She will have to pay ₹ 102 to buy all of these.

**(b) Make a bill of your own for the vegetables you want to buy. Find the total money you will have to pay.**

Ans. Try it yourself

**Page No. 71 Solutions**

**Practice Time**

**1. Raheem’s journey**

**Raheem has to travel 1**¼ **km to reach school. What distance does he travel to go to school and come back home?**

Sol. The distance that Raheem travels to go to school and come back home:

= 1¼ km + 1¼ km = 5/4 km + 5/4 km

= 5+5 / 4 km

= 10/4 km = 5/2 km = 2½ km

**2. What coins?**

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

Sol. The amount she got = ₹ 10 – ₹ 7. 5 = ₹ 2.5

The coins she got 50 Paise coins = 4

25 Paisa Coins = 2

**3. At the railway station**

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

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

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

Sol. The right time = a quarter to 7 = 6:45

The train is late by = 30 mins

So, the train is expected to come today = 6:45 +: 30 mins = 7:15

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

Sol. Nazia will get off after = 2½ hours = 2:30 hours

The time at which she gets off = 6:45 + 2:30 = 8:75

= 9: 15 hour

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

Sol. The train is expected to come = 7:15

He will reach Ernakulam in time = 5 hours

The time at which he will reach there = 7:15 + 5:00 = 12:15

That’s it about **Parts and Wholes Chapter 4 Class 5 JKBOSE Solutions**. Hope it has helped. Do share your views about this post in the comment section below.

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