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NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals

Contents

NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals.

Board CBSE
Textbook NCERT
Class Class 7
Subject Maths
Chapter Chapter 2
Chapter Name Fractions and Decimals
Exercise Ex 2.1, Ex 2.2, Ex 2.3, Ex 2.4, Ex 2.5, Ex 2.6, Ex 2.7.
Number of Questions Solved 48
Category NCERT Solutions

NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals

Chapter 2 Fractions and Decimals Exercise 2.1

Ex 2.1 Class 7 Maths Question 1.
Solve :
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 1
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 2
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 3
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 4
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 5

Ex 2.1 Class 7 Maths Question 2.
Arrange the following in descending order :
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 6
Solution:
We observe that the given fractions neither have a common denominator nor a common numerator. So, first we convert them into like fractions, i.e., fractions having common denominator. For this, we first find the L.C.M. of the denominators of the given fractions.
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 7
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 8

Ex 2.1 Class 7 Maths Question 3.
In a “magic square”, the sum of the numbers in each row, in each column and along the diagonals is the same. Is this a magic square?
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 9
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 10

⇒ The sum of the numbers in each row, in each column and along the diagonals is the same.
So, the given square is a magic square.

Ex 2.1 Class 7 Maths Question 4.
A rectangular sheet of paper is 12 \(\frac { 1 }{ 2 } \) cm long and 10 \(\frac { 2 }{ 3 } \) cm wide.Find its perimeter.
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 11

Ex 2.1 Class 7 Maths Question 5.
Find the perimeters of (i) ∆ ABE (ii) the rectangle BCDE in this figure. Whose perimeter is greater?
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 12
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 13
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 14

Ex 2.1 Class 7 Maths Question 6.
Salil wants to put a picture in a frame. The picture is 7 \(\frac { 3 }{ 5 } \) cm wide. To fit in the frame, the picture cannot be more than 7 \(\frac { 3 }{ 10 } \) cm wide. How much should the picture be trimmed?
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 15

Ex 2.1 Class 7 Maths Question 7.
Ritu ate \(\frac { 3 }{ 5 } \) part of an apple and the remaining apple was eaten by her brother Somu. How much part of the apple did Somu eat? Who had the larger share? By how much?
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 16

Ex 2.1 Class 7 Maths Question 8.
Michael finished colouring a picture in \(\frac { 7 }{ 12 } \) hour. Vaibhav finished colouring the same picture in \(\frac { 3 }{ 4 } \) hour. Who worked longer? By what fraction was it longer?
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 17
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 18

Chapter 2 Fractions and Decimals Exercise 2.2

Ex 2.2 Class 7 Maths Question 1.
Which of the drawings (a) to (d) show :
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 19
Solution:
(i) → (d)
(ii) → (b)
(iii) → (a)
(iv) → (c)

Ex 2.2 Class 7 Maths Question 2.
Some pictures (a) to (c) are given below. Tell which of them show :
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 20
Solution:
(i)  → (c)
(ii) → (a)
(iii) → (b)

Ex 2.2 Class 7 Maths Question 3.
Multiply and reduce to lowest form and convert into a mixed fraction.
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 21
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 22
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 23

Ex 2.2 Class 7 Maths Question 4.
Shade :
(i) \(\frac { 1 }{ 2 } \) of the circles in box (a)
(ii) \(\frac { 2 }{ 3 } \) of the triangles in box (b)
(iii) \(\frac { 3 }{ 5 } \) of the squares in box (c).
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 24
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 25

Ex 2.2 Class 7 Maths Question 5.
Find :
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 26
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 27
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 28

Ex 2.2 Class 7 Maths Question 6.
Multiply and express as a mixed fraction :
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 29
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 30
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 31
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 32

Ex 2.2 Class 7 Maths Question 7.
Find :
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 33
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 34

Ex 2.2 Class 7 Maths Question 8.
Vidya and Pratap went for a picnic. Their mother gave them water bottle that contained 5 litres of water. Vidya consumed \(\frac { 2 }{ 5 } \) of the water. Pratap consumed the remaining water.
(i) How much water did Vidya drink?
(ii) What fraction of the total quantity of water did Pratap drink?
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 35
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 36

Chapter 2 Fractions and Decimals Exercise 2.3

Ex 2.3 Class 7 Maths Question 1.
Find :
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 37
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 38

Ex 2.3 Class 7 Maths Question 2.
Multiply and reduce to lowest form (if possible) :
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 39
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 40

 

Ex 2.3 Class 7 Maths Question 3.
Multiply the following fractions :
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 41
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 42
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 43

Ex 2.3 Class 7 Maths Question 4.
Which is greater?
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 44
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 45
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 46

Ex 2.3 Class 7 Maths Question 5.
Saili plants 4 saplings in a row, in her garden. The distance between two adjacent saplings is \(\frac { 3 }{ 4 } \) m. Find the distance between the first and the last sapling.
Solution:
Let four saplings be planted in a row at the points A, B, C and D such that AB = BC = CD = \(\frac { 3 }{ 4 } \) m
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 47

Ex 2.3 Class 7 Maths Question 6.
Lipika reads a book for 1 \(\frac { 3 }{ 4 } \) hours everyday. She reads the entire book in 6 days. How many hours in all were required by her to read the book?
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 48

Ex 2.3 Class 7 Maths Question 7.
A car runs 16 km using 1 litre of petrol. How much distance will it cover using 2 \(\frac { 3 }{ 4 } \) litres of petrol?
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 49

Ex 2.3 Class 7 Maths Question 8.
(a) (i) Provide the number in the box ( ), such that \(\frac { 2 }{ 3 } \) × ( ) = \(\frac { 10 }{ 30 } \)
(ii) The simplest form of the number obtained in ( ) is __________
(b) (i) Provide the number in the box ( ) such that \(\frac { 3 }{ 5 } \) × ( ) = \(\frac { 24 }{ 75 } \)
(ii) The simplets form of the number obtained in ( ) is __________
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 50

Chapter 2 Fractions and Decimals Exercise 2.4

Ex 2.4 Class 7 Maths Question 1.
Find :
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 51
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 52
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 53

Ex 2.4 Class 7 Maths Question 2.
Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers.
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 54
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 55

Ex 2.4 Class 7 Maths Question 3.
Find :
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 56
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 57
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 58

Ex 2.4 Class 7 Maths Question 4.
Find:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 59
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 60

Chapter 2 Fractions and Decimals Exercise 2.5

Ex 2.5 Class 7 Maths Question 1.
Which is greater?
(i) 0.5 or 0.05
(ii) 0.7 or 0.5
(iii) 7 or 0.7
(iv) 1.37 or 1.49
(v) 2.03 or 2.30
(vi) 0.8 or 0.88
Solution:
(i) To compare 0.5 and 0.05
Here, the whole number part in each decimal is equal to zero. So, whole number parts are equal. Therefore, we will compare the decimal parts. We observe that the extreme left digits in the decimal parts are 5 and 0, respectively such that 5 > 0.
∴ 0.5 > 0.05

(ii) To compare 0.7 and 0.5
Here, the whole number parts are equal, so we compare the decimal parts. In the decimal parts, the extreme left digits are 7 and 5, respectively such that 7 > 5.
∴ 0.7 > 0.5

(iii) To compare 7 and 0.7
The given decimals have distinct whole numbers, so we compare whole number parts only. These are 7 and 0, respectively such that 7 > 0.
∴ 7 > 0.7

(iv) To compare 1.37 and 1.49
Here, the whole number parts are equal, so we compare the decimal parts. In the decimal parts, the extreme left digits are 3 and 4, respectively such that 3 < 4; i.e., 4 > 3.
∴ 1.49 > 1.37

(v) To compare 2.03 and 2.30
Here, the whole number parts are equal, so we compare the decimal parts. In the decimal parts, the extreme left digits are 0 and 3, respectively such that 0 < 3, i.e., 3 > 0.
∴ 2.30 > 2.03

(vi) To compare 0.8 and 0.88
Here, the whole number parts are equal, so we compare the decimal parts. In decimal part also, digits up to tenths place are equal. So, compare the digits at hundredths place. The digits at hundredths place are 0 and 8 such that 8 > 0.
∴ 0.88 > 0.8

Ex 2.5 Class 7 Maths Question 2.
Express as rupees using decimals :
(i) 7 paise
(ii) 7 rupees 7 paise
(iii) 77 rupees 77 paise
(iv) 50 paise
(v) 235 paise
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 61

Ex 2.5 Class 7 Maths Question 3.
(i) Express 5 cm in metre and kilometre
(ii) Express 35 mm in cm, in and km
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 62
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 63

Ex 2.5 Class 7 Maths Question 4.
Express in kg :
(i) 200g
(ii) 3470 g
(iii) 4 kg 8 g
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 64

Ex 2.5 Class 7 Maths Question 5.
Write the following decimal numbers in the expanded form :
(i) 20.03
(ii) 2.03
(iii) 200.03
(iv) 2.034
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 65

Ex 2.5 Class 7 Maths Question 6.
Write the place value of 2 in the following decimal numbers :

  1. 2.56
  2. 21.37
  3. 10.25
  4. 9.42
  5. 63.352

Solution:

  1. Place value of 2 in 2.56 is ones.
  2. Place value of 2 in 21.37 is tens.
  3. Place value of 2 in 10.25 is tenths.
  4. Place value of 2 in 9.42 is hundredths.
  5. Place value of 2 in 63.352 is thousandths.

Ex 2.5 Class 7 Maths Question 7.
Dinesh went from place A to place B and from there to place C. A is 7.5 km from B and B is 12.7 km from C. Ayub went from place A to place D and from there to place C. D is 9.3 km from A and C is 11.8 km from D. Who travelled more and by how much?
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 66
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 67
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 68

Ex 2.5 Class 7 Maths Question 8.
Shyama bought 5 kg 300 g apples and 3 kg 250 g mangoes. Sarala bought 4 kg 800 g oranges and 4 kg 150 g bananas. Who bought more fruits?
Solution:
Shyama bought apples = 5 kg 300 g
Shyama bought mangoes = 3 kg 250 g
Toal fruits bought by Shyama
= 5 kg 300 g + 3 kg 250 g
= 5.300 kg + 3.250 kg
= 8.550 kg

Sarala bought oranges = 4 kg 800 g
Sarala bought banana = 4 kg 150 g
Total fruits bought by Sarala
= 4 kg 800 g + 4 kg 150 g
= 4.800 kg +4.150 kg
= 8.950 kg

Since, 8.950 > 8.550
∴ Sarala bought more fruits.

Ex 2.5 Class 7 Maths Question 9.
How much less is 28 km than 42.6 km?
Solution:
Required difference = 42.6 km – 28 km = 14.6 km
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 69

Chapter 2 Fractions and Decimals Exercise 2.6

Ex 2.6 Class 7 Maths Question 1.
Find :
(i) 0.2 × 6
(ii) 8 × 46
(iii) 2.71 × 5
(iv) 20.1 × 4
(v) 0.05 × 7
(vi) 211.02 × 4
(vii) 2 × 0.86
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 70

Ex 2.6 Class 7 Maths Question 2.
Find the area of rectangle whose length is 5.7 cm and breadth is 3 cm.
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 71

Ex 2.6 Class 7 Maths Question 3.
Find :

  1. 1.3 × 10
  2. 36.8 × 10
  3. 15a 7 × 10
  4. 168.07 × 10
  5. 31.1 × 100
  6. 156.1 × 100
  7. 3.62 × 100
  8. 43.07 × 100
  9. 0.5 × 10
  10. 0.08 × 10
  11. 0.9 × 100
  12. 0.03 × 1000

Solution:

  1. 1.3 × 10 = 13
  2. 36.8 × 10 = 368
  3. 153.7 × 10 = 1537
  4. 168.07 × 10 = 1680.7
  5. 31.1 × 100 = 3110
  6. 156.1 × 100 = 15610
  7. 3.62 × 100 = 362
  8. 43.07 × 100 = 4307
  9. 0.5 × 10 = 5
  10. 0.08 × 10 = 0.8
  11. 0.9 × 100 = 90
  12. 0.03 × 1000 = 30

Ex 2.6 Class 7 Maths Question 4.
A two wheeler covers a distance of 55.3 km in one litre of petrol. How much distance will it cover in 10 litres of petrol?
Solution:
Distance covered in one litre of petrol = 55.3 km
Distance covered in 10 litres of petrol = (55.3 × 10) km = 553 km

Ex 2.6 Class 7 Maths Question 5.
Find:
(i) 2.5 × 0.3
(ii) 0.1 × 51.7
(iii) 0.2 × 316.8
(iv) 1.3 × 3.1
(v) 0.5 × 0.05
(vi) 11.2 × 0.15
(vii) 1.07 × 0.02
(viii) 10.05 × 1.05
(ix) 101.01 × 0.01
(x) 100.01 × 1.1
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 72
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 73

Chapter 2 Fractions and Decimals Exercise 2.7

Ex 2.7 Class 7 Maths Question 1.
Find :
(i) 0.4 ÷ 2
(ii) 0.35 ÷ 5
(iii) 2.48 ÷ 4
(iv) 65.4 ÷ 6
(v) 651.2 ÷ 4
(vi) 14.49 ÷ 7
(vii) 3.96 ÷ 4
(viii) 0.80 ÷ 5
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 74
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 75

Ex 2.7 Class 7 Maths Question 2.
Find :

  1. 48 ÷ 10
  2. 52.5 ÷ 10
  3. 0.7 ÷ 10
  4. 361 ÷ 10
  5. 697 ÷ 10
  6. 272.23 ÷ 10
  7. 0.56 ÷ 10

Solution:

  1. 4.8 ÷ 10 = 0.48
  2. 52.5 ÷ 10 = 5.25
  3. 0.7 ÷ 10 = 0.07
  4. 33.1 ÷ 10 = 3.31
  5. 272.23 ÷ 10 = 27.223
  6. 0.56 ÷ 10 = 0.056
  7. 3.97 ÷ 10 = 0.397

Ex 2.7 Class 7 Maths Question 3.
Find :

  1. 2.7 ÷ 100
  2. 0.3 ÷ 100
  3. 0.78 ÷ 100
  4. 432.6 ÷ 100
  5. 23.6 ÷ 100
  6. 98.53 ÷ 100

Solution:

  1. 2.7 ÷ 100 = 0.027
  2. 0.3 ÷ 100 = 0.003
  3. 0.78 ÷ 100 = 0.0078
  4. 432.6 ÷ 100 = 4.326
  5. 23.6 ÷ 100 = 0.236
  6. 98.53 ÷ 100 = 0.9853

Ex 2.7 Class 7 Maths Question 4.
Find :

  1. 7.9 ÷ 1000
  2. 26.3 ÷ 1000
  3. 38.53 ÷ 1000
  4. 128.9 ÷ 1000
  5. 0.5 ÷ 1000

Solution:

  1. 7.9 ÷ 1000 = 0.0079
  2. 26.3 ÷ 1000 = 0.0263
  3. 38.53 ÷ 1000 0.03853
  4. 128.9 ÷ 1000 = 0.1289
  5. 0.5 ÷ 1000 = 0.0005

Ex 2.7 Class 7 Maths Question 5.
Find :
(i) 7 ÷ 3.5
(ii) 36 ÷ 0.2
(iii) 3.25 ÷ 0.5
(iv) 30.94 ÷ 0.7
(v) 0.5 ÷ 0.25
(vi) 7.75 ÷ 0.25
(vii) 76.5 ÷ 0.15
(viii) 37.8 ÷ 1.4
(ix) 2.73 ÷ 1.3
Solution:
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 76
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 77

Ex 2.7 Class 7 Maths Question 6.
A vehicle covers a distance of 43.2 km in 2.4 litres of petrol. How much distance will it cover in one litre of petrol?
Solution:
Distance covered in 2.4 litres of petrol = 43.2 km
Distance covered in 1 litre of petrol = (43.2 ÷ 2.4) km
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals 78

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