Class : V Subject: Maths Chapter: Parts and wholes

Fraction:

A part of a whole is called a fraction.

It has two parts. ½ is a fraction i.e, N/D

Here, 1 – Numerator 2 – Denominator.

Write the fraction for the following shaded shapes.

a) b) c) d)

1 5 4 4

3 12 9 6

Shade the given shapes using given fraction:

a)5 4 10 8

8 5 14 10

NCERT Textbook pg. no :50

Our National Flag

Our national flag is in tricolour.

The top- one third of our flag is saffron. i.e, ⅓

The bottom one-third of our flag is green. i.e,⅓

The middle portion of our flag is little less than ⅓. Because of Ashoka Chakra.

The flag of Afganistan

a)How much of it is black?One-third (⅓) of the flag is black.

b)The green part of the flag can be written asOne-third (⅓)

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

Ans: Yes, the red part is a little less than one third (⅓) of the flag. This is

because of the white emblem in the red portion.

The flag of Myanmar

a)blue –little less than One – fourth (¼) of the flag because of emblem.

b) red – Three- fourth of the flag.

NCERT Textbook pg. no: 51

Red –Two – fifth (⅖), Green – One – fifth ( ⅕) , Blue –One – fifth (⅕),

Yellow – Little less than one – fifth (⅕)of the flag because of emblem.

NCERT Textbook pg. no: 52

Draw a circle and divide it into 8 equal parts. Colour2/8 red, 1/8 orange and 1/8

yellow.

Answer these:

Write the fraction:

a)Numerator 8, Denominator = 15 Fraction = 8

15

b) N – 25 , D – 79 Fraction = 25

9

Types of fraction:

1.Proper fraction: Numerator is smaller than Denominator.

Eg: 4, 6 , 3

9 15 4

2. Improper fraction: Numerator is greater than denominator.

Eg: 9 , 12 , 4

4 7 2

3. Unit fraction: If the numerator of the fraction is one, it is called unit fraction.

Eg: 1 , 1 , 1

5 7 15

4. Mixed fraction: A mixed fraction contains a whole number with a proper

fraction. Eg:

Here, 4, 2, 3 are the whole numbers.

⅔, ⅕, ¼ are the proper fractions.

5. Like fraction:If the denominator of a given set of fraction is same, they are

called like fraction.

Eg: 2 , 7 , 1 , 8

9 9 9 9

Unlike fraction: If the denominator of a given set of fraction is not same, they

are called unlike fraction.

Eg: 7 , 12 , 3

4 19 10

Write the mixed fraction:

a) -

b) -

Compare and write ˂ , ˃ or =.

a)⅚ ⅙ b) ⅖ ⅘ c)⅞ ⅜

Write the following fractions in ascending order.

a)9, 4, 7, 1, 3

10 10 10 10 10

Ans: 1 ˂ 3 ˂ 4 ˂ 7 ˂ 9 10 10 10 10 10

b) 13, 21, 15, 8, 25

27 27 27 27 27

Ans: 8 ˂ 13 ˂ 15 ˂ 21 ˂ 25

27 27 27 27 27

Write the following fractions in descending order.

a)10, 3, 9, 1, 7

11 11 11 11 11

Ans: 10 ˃ 9 ˃ 7 ˃ 3 ˃ 1

11 11 11 11 11

b) 4, 45, 29, 12, 30

33 33 33 33 33

Ans: 45 ˃ 30 ˃ 29 ˃ 12 ˃ 4

33 33 33 33 33

˃ ˃ ˂

Add:

a)7 + 4 = 11 b) 1 + 3 = 4 c) 6 + 2 = 8

20 20 20 5 5 5 11 11 11

Subtract:

a)6 - 1 = 5 b) 20 - 12 = 8 c) 8 - 7 = 1

7 7 7 22 22 22 9 9 9

Writethe division fact for the following fractions.

a)4 = 4 ÷ 5 b) 7 = 7 ÷ 12 c) 5 = 5 ÷19

5 12 19

Write the fraction as its division fact:

a)9 ÷ 17 = 9 b) 1 ÷ 20 = 1 c) 17 ÷ 52 = 17

17 20 52

Solve

a)1 of 45

5

1 x 45 = 45 = 45 ÷ 5 = 9

5 5

Ans: 9

b) 3 of 20

10

3 x 20 = 60 = 60 ÷ 10 = 6

10 10

Ans: 6

NCERT Textbook pg. no: 52

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?

Total number of pieces = 12

Raji ( ¼ part of 12)

= ¼ x 12 = 12/4 = 12÷ 4 = 3pieces.

Sugatha ( ⅓ part of 12 pieces

= ⅓ x 12 = 12/3 = 12 ÷ 3 = 4 pieces.

Sheela (1/6 part of 12 )

= 1/ 6 x 12= 12 ÷ 6 = 2 pieces.

What part of the chocolate did Manju eat?

Total no of pieces = 12 -

Shared pieces = 9

3

Ans: Manju ate 3 pieces.

B) Colour the hats colour of the hats red.

Colour ⅓ of the hats red. Colour three-fifth hats blue.

How many hats did you colour red?

How many hats did you colour blue?

What part of the hats are not coloured?

Ans. Total number of hats=15

of the hats= of 15 = = 15/ 3 = 15 ÷ 3 =5

of the hats = of 15 = 45/5 = 9

Five hats were coloured red. Nine hats were coloured blue.

Number of hats left uncoloured=15 – 5 – 9 = 1

Thus, of the hats are not coloured.

C) Equal parts of a triangle

Try to make three equal parts of this triangle in different way.

D) Six parts of a rectangle

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

Now you divide each of these rectangles into six equal parts. Use a different

way for each of the three rectangles.

NCERT Textbook pg. no: 55

Greedy gatekeepers

If a poet will get 100 gold coins

I gatekeeper (1/10th part of 100 gold coins)

No of gold coins = 1/10th of 100

= 1 x 100 = 100 = 100 ÷ 10 = 10gold coins.

10 10

Ans : 10 gold coins.

II Gatekeeper (Two – fifth (2/5) of 100 gold coins)

No. of gold coins = 2/5th of 100

= 2 x 100 = 200 = 200 ÷ 5 = 40 gold coins.

5 5

Ans: 40 gold coins

III Gatekeeper (half of 100 gold coins)

No. of gold coins = ½ of 100

= 1 x 100 = 100 = 100 ÷ 2 = 50 gold coins.

2 2

Ans: 50 gold coins

If a poet will get 1000 gold coins

I gatekeeper (1/10th part of 1000 gold coins)

No of gold coins = 1/10th of 1000

= 1 x 1000 = 1000 = 1000 ÷ 10 = 100gold coins.

10 10

Ans : 100 gold coins

II Gatekeeper (Two – fifth (2/5) of 1000gold coins)

No. of gold coins = 2/5th of 1000

= 2 x 1000 = 2000 = 2000 ÷ 5 = 400 gold coins.

5 5

Ans: 400 gold coins

III Gatekeeper (half of 1000 gold coins)

No. of gold coins = ½ of 1000

= 1 x 1000 = 1000 = 1000 ÷ 2 = 500 gold coins.

2 2

Ans: 500 gold coins

Fill in the blanks

a)3 x 4 = b) 2 = 16 c) = 1

8 x4 32 5 6 3

NCERT Textbook pg. no: 57

Patterns in parts

1) Make different patterns by colouring some squares in the grids A, B, C, D.

What part of the grid did you colour?

What part of the grid remained white? Write.

(Students are adviced to find out their own answer)

A

Ans.(a) blue, white.

12

40

2

2) Mark (X) on the wrong answer.

Look at grid A again. Is the grid coloured:

(a) blue, white? (b) blue, white?

(c) blue, white? (d) blue, white?

Ans. (c) is the wrong answer.

Draw grids of 16 squares and make patterns with

(a)2/8 red, 1/2 yellow, 1/4 green

Red = 2 x 2 = 4 Yellow = 1x 8 = 8 Green = 1x 4 = 4

8 x 2 16 2 x 8 16 4 x 4 16

(b)3/16 blue, 5/16 red, 1/2 yellow

Blue = 3 Red = 5 Yellow = 1 x 8 = 8

16 16 2 x 8 16

NCERT Textbook pg. no: 58

Ramu’s Vegetable field

Ramu’s vegetable field has 9 equal parts. What vegetables does he grow?

Ans: Ramu grows chillies, potatoes, brinjals, tomatoes and spinach.

Q.1: Which vegetable grows in the biggest part of the field? What part?

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

( ⅓ )part of the field.

Q.2: On what part of the field does he grow potatoes?

Ans: e grows potatoes on part of the field.

Q.3: What parts of the field is used to grow spinach? What part is used for

brinjals?

Ans: part of field is used to grow spinach. part of the field is used

for brinjals.

Q.4:Ramu wanted to give below vegetables to his friends. He gave

Aboobacker one-fifth of these tomatoes and 1/3of 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.

Soln:

Total number of tomatoes = 20 Total number of potatoes = 18

Aboobacker’s share

Tomatoes = 1 of 20 Potatoes = 1 of 18

5 3

= 1 x 20 = 20 = 1 x 18 = 18

5 5 3 3

= 20 ÷ 5 = 4 tomatoes = 18 ÷ 3 = 6 potatoes

Srija’s share

Tomatoes = 2 of 20 Potatoes = 3 of 18

5 6

= 2 x 20 = 40 = 3 x 18 = 54

5 5 6 6

= 40 ÷ 5 = 8 tomatoes = 54 ÷ 6 = 9 potatoes

How many potatoes and tomatoes did Nancy get?

Nancy’s ahare

Ramu gave 4 tomatoes to Aboobacker and 8 tomatoes to Srija. So, he gave

a total of 12 tomatoes to Aboobacker and Srija.

Now, Ramu gave 6 potatoes to Aboobacker and 9 potatoes to Srija. So, he

gave a total of 15 potatoes to Aboobacker and Srija.

Number of tomatoes left = 20 − 12 = 8 tomatoes

Number of potatoes left = 18 − 15 = 3 potatoes

Ans: Nancy got 8 tomatoes and 3 potatoes.

NCERT Textbook pg. no: 61

A)What part of each shape is coloured?

First guess the answer, then check.

1) One-eighth(1/8) of the shape is coloured

2) One-sixth (1/6) of the shape is coloured.

3) Two-ninth (1/9)of the shape is coloured

4) Four-fifteenth ( 1/15 ) of the shape is coloured

B) Look at the small triangle. What part of the square is it? How will you

find this out?

We will divide the whole square into small triangles as shown in the

figure.

We will get 16 such triangles.

Total number of triangles = 16 Number of coloured triangles

Ans: coloured small triangle is one-sixteenth ( 1/ 16 ) of the square.

Equivalent fractions

Find four equivalent fractions for

a)4/5

4 x 2 = 8 4 x 3 = 12

5 x 2 10 5 x 3 15

4 x 4 = 16 4 x 5 = 20

5 x 4 20 5 x 5 25

Ans: 8 = 12 = 16 = 20

10 15 20 25

b) 2/9

2 x 2 = 4 2 x 3 = 6

9 x 2 18 9 x 3 27

2 x 4 = 8 2 x 5 = 10

9 x 4 36 9 x 5 45

Ans: 4 = 6 = 8 = 10

18 27 36 45

NCERT Textbook pg. no: 61

Coloured Parts

Complete these

1) Blue - ½, Pink - ½ 2) Blue – 2/4, Pink – 2/4

3) Blue – 3/6, Pink – 3/6 4) Blue – 4/8, Pink – 4/8

Ans: Equivalent fractions 1 = 2 = 3 = 4

2 4 6 8

NCERT Textbook pg. no: 61

NCERT Textbook pg. no: 63

Cutting the Halwa

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

divided it equally for them.

a)Each will get part of halwa.

He divided the piece into half again. How, many pieces will Ammu get? 2

pieces.

b) What part of the halwa is it?

he again cut the halwa into smaller pieces.

c)Now how many pieces will each get? 4 pieces.

d)What part of the halwa is each piece now?

Ans. Each piece now is of the halwa.

(e) If Ramesh 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 Ramesh had cut the halwa into 6 equal parts, then each would get 3

pieces.

Ans: (equivalent fractions)

NCERT Textbook pg. no: 64

Parts of the Strip

Look at the picture. Write what part of the strip is each green piece. Write the

part for a piemce of each colour.

1.How many one-fourths will make a half? Two one-fourths will make a half.

2.How many 1/8 will make 1/4? Two 1/8 will make 1/4.

3. How many 1/8 are in ½? Four 1/8 are there in ½.

Patterns

Look at this square.

What part is coloured blue? 2/16

What part is green? 1/16

NCERT Textbook pg. no: 65

From the part to the whole

1.This show 15petals of a flower. Complete the flower by drawing the

other petals.

Answer

2. The picture shows one-third of the blades of a fan. Complete the picture by

drawing the other blades.

Answer

3. Half of the blades of another fan are shown here. Complete the picture by

drawing the other half. How many blades have you drawn?

Answer:

Rupees and Paise

a)How many will make one rupee? Two 50-paise

b) Is 50 paise half of one rupee? Yes

c) How many will make one rupee? Four 25-paise

d) 25 paise is part of one rupee.

e) 20 paise is part of one rupee.

d) How many 10-paise will make one rupee? Ten 10-paise

e) 10 paise is 1/10 part of 1 rupee.

NCERT Textbook pg. no: 66

An Old Woman’s Will

The old woman had 19 camels.

By adding the aunt’s camel, the number of camel became 20.

First daughter’s share = 1/2 of 20

= 1 x 20 = 20 = 20 ÷ 2 = 10

2 2

Second daughter’s share = 1/4 of 20

= 1 × 20 = 20 = 20 ÷ 4 = 5

4 4

Third daughter’s share = 1/5 of 20

= 1 x 20 = 20 = 20 ÷ 5 = 4

5 5

Finally, 10 + 5 + 4 = 19 which is equal to the original number of camels.

NCERT Textbook pg. no: 67

Arun’s Time Table

Use different colours to show

Sleeping: One third of a day Playing: One eight of a day

Studying: ¼ of a day

1.How many hours does Arun take for

Sleeping? hours

Studying? hours

Playing? hours

Soln:

One day is 24 hours.

Sleeping = ⅓ of 24 hours = ⅓ x 24 = 24 ÷ 3 = 8 hours

Playing = 1/8th of 24 hours = 1/8 x 24 = 24 ÷ 8 = 3 hours

Studying = ¼ of 24 hours = ¼ x 24 = 24 ÷ 4 = 6 hours.

Other activities = 24 – 8 – 3 – 6 = 7 hours.

NCERT Textbook pg. no: 68

School Magazine

1.A school has decided to bring out a magazine every quarter of a 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.

Ans. They will have 4 magazines in a year.

The magazines will be printed in the months of March, June, September and

December.

Sleeping Beauty!

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

Ans: It is 8/24 = 1/3 part of a day.

NCERT Textbook pg. no: 69

Keerti’s Shopping List

Look at the yellow price list.

a)How much does 2kg of tomato cost?

Cost of 1 kg tomato = Rs.12

Cost of 2kg of tomato = Rs. 12 2 = Rs. 24

b) How much does kg of tomato cost?

Cost of 1 kg tomato = Rs. 12

kg of tomato costs = Rs. 12 = Rs. 6

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

Cost of kg of tomato= Cost of 2kg of tomatoes +Cost of kg of

tomato

= Rs. 12 2+Rs. 12

= Rs. 24 +Rs.6 = Rs. 30

d) How much does kg of potato cost?

Cost of kg of potato = Cost of 3 kg of potato + Cost of kg of potato

= 10 3+Rs. 10

=Rs. 30+ Rs. 5= Rs. 35

e) What is the price of kg of carrot?

Cost of kg of carrot = Cost of 1kg of carrot + Cost of kg of carrot

= Rs. 18+ Rs. 18

= Rs. 18 + Rs. 4.50= Rs. 22.50

f) He bought a gourd of weight kg and it costs……

Cost of kg of gourd = Cost of 4 kg of gourd + Cost of of gourd kg

= Rs. 8 4 + Rs. 8

= Rs. 32 + Rs. 6 = Rs. 38

g) Look at the shopping list in Keerti’s hand. How much will she have to pay to

buy all the these?

NCERT Textbook pg. no: 70

1)Raheem’s Journey

Raheem has to travel km to reach school. What distance does he travel to

go to school and come back home?

The distance travelled by Raheem to go to school and come back

= km 2 =1 km 2 + ¼ x 2

=2 + ½ km = km

2) What coins?

Lata 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

coin she get?

Ans. She might have got either of

(1) One 50-paise coin and eight 25-paise coins.

(2) Two 50-paise coins and six 25-paise coins.

(3) Three 50-paise coins and four 25-paise coins.

(4) Four 50-paise coins and two 25-paise coins.

17. 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?

Ans. The expected time of the train to come today is quarter past 7.

(b) Nazia gets off at a station after hours from this station. What time will

she get off?

Ans. Nazia will get off at quarter to 10.

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

reach there?

Ans. Shaji will reach Ernakulam by this train at a quarter past 12.