NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals

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

Question 1.
Solve :

Solution:

Question 2.
Arrange the following in descending order :

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.

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?

Solution:

⇒ 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.

Question 4.
A rectangular sheet of paper is 12 cm long and 10 cm wide.Find its perimeter.
Solution:

Question 5.
Find the perimeters of (i) ∆ ABE (ii) the rectangle BCDE in this figure. Whose perimeter is greater?

Solution:

Question 6.
Salil wants to put a picture in a frame. The picture is 7 cm wide. To fit in the frame, the picture cannot be more than 7 cm wide. How much should the picture be trimmed?
Solution:

Question 7.
Ritu ate 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:

Question 8.
Michael finished colouring a picture in hour. Vaibhav finished colouring the same picture in hour. Who worked longer? By what fraction was it longer?
Solution:

Chapter 2 Fractions and Decimals Exercise 2.2

Question 1.
Which of the drawings (a) to (d) show :

Solution:
(i) → (d)
(ii) → (b)
(iii) → (a)
(iv) → (c)

Question 2.
Some pictures (a) to (c) are given below. Tell which of them show :

Solution:
(i)  → (c)
(ii) → (a)
(iii) → (b)

Question 3.
Multiply and reduce to lowest form and convert into a mixed fraction.

Solution:

Question 4.
Shade :
(i) of the circles in box (a)
(ii) of the triangles in box (b)
(iii) of the squares in box (c).

Solution:

Question 5.
Find :

Solution:

Question 6.
Multiply and express as a mixed fraction :

Solution:

Question 7.
Find :

Solution:

Question 8.
Vidya and Pratap went for a picnic. Their mother gave them water bottle that contained 5 litres of water. Vidya consumed 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:

Chapter 2 Fractions and Decimals Exercise 2.3

Question 1.
Find :

Solution:

Question 2.
Multiply and reduce to lowest form (if possible) :

Solution:

Question 3.
Multiply the following fractions :

Solution:

Question 4.
Which is greater?

Solution:

Question 5.
Saili plants 4 saplings in a row, in her garden. The distance between two adjacent saplings is 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 = m

Question 6.
Lipika reads a book for 1 hours everyday. She reads the entire book in 6 days. How many hours in all were required by her to read the book?
Solution:

Question 7.
A car runs 16 km using 1 litre of petrol. How much distance will it cover using 2 litres of petrol?
Solution:

Question 8.
(a) (i) Provide the number in the box ( ), such that × ( ) =
(ii) The simplest form of the number obtained in ( ) is __________
(b) (i) Provide the number in the box ( ) such that × ( ) =
(ii) The simplets form of the number obtained in ( ) is __________
Solution:

Chapter 2 Fractions and Decimals Exercise 2.4

Question 1.
Find :

Solution:

Question 2.
Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers.

Solution:

Question 3.
Find :

Solution:

Question 4.
Find:

Solution:

Chapter 2 Fractions and Decimals Exercise 2.5

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

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:

Question 3.
(i) Express 5 cm in metre and kilometre
(ii) Express 35 mm in cm, in and km
Solution:

Question 4.
Express in kg :
(i) 200g
(ii) 3470 g
(iii) 4 kg 8 g
Solution:

Question 5.
Write the following decimal numbers in the expanded form :
(i) 20.03
(ii) 2.03
(iii) 200.03
(iv) 2.034
Solution:

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.

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?

Solution:

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.

Question 9.
How much less is 28 km than 42.6 km?
Solution:
Required difference = 42.6 km – 28 km = 14.6 km

Chapter 2 Fractions and Decimals Exercise 2.6

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:

Question 2.
Find the area of rectangle whose length is 5.7 cm and breadth is 3 cm.
Solution:

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

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

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:

Chapter 2 Fractions and Decimals Exercise 2.7

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:

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

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

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

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:

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

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