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NCERT Solutions for class 7 Maths chapter 2 – Fractions and Decimals

Back Exercise

Exercise 2.1

Question 1.
Solve :

Solution:

Question 2.
Arrange the following in descending order

Solution:
(i) Converting the given fractions into like fractions, we have


(ii) Converting the given fractions into like fractions, we have

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:
Yes ! this is a magic square.

Question 4.
A rectangular sheet of paper is 12 $\frac { 1 }{ 2 }$ cm long 10 $\frac { 2 }{ 3 }$ cm wide. find its perimeter
Solution:
Perimeter of the rectangular sheet of paper

Question 5.
Find the perimeters of (i) A ABE (ii) the rectangle BCDE in this figure. Whose perimeter is greater?
Solution:
(i) Perimeter of ∆ ABE = AB + BE + EA

(ii) Perimeter of the rectangle BCDE = BC + CD + DE + EB

So, the perimeter of A ABE is greater than the perimeter of the rectangle BCDE.

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:
The picture should be trimmed by

Question 7.
Ritu are $\frac { 3 }{ 5 }$ 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:
Part of the apple ate by Somu

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:

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:

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

Solution:

Question 4.
Shade

1. $\frac { 1 }{ 2 }$ of the circles in box (a)
2. $\frac { 2 }{ 3 }$ of the triangles in box (b)
3. $\frac { 3 }{ 5 }$ 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 a water bottle that contained 5 liters 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:
(i) Quantity of water drank by Vidya

(ii) Quantity of water drank by Pratap
= 5 litres – 2 litres = 3 litres
∴ The fraction of the total quantity of water drank by Pratap

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 $\frac { 3 }{ 4 }$ m. Find the distance between the first and the last sapling.
Solution:

Let A, B, C and D be the four saplings planted in a row.
Distance between two adjacent saplings = $\frac { 3 }{ 4 }$ m
∴ Distance between the first and the last sapling = AD = 3 × AB

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:
Hours in all required by Lipika to read the book

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:
Distance covered by the car using 2 $\frac { 3 }{ 4 }$ litres of petrol

Question 8.

Solution:

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:

Exercise 2.5

Question 1.
Which is greater?

1. 0.5 or 0.05
2. 0.7 or 0.5
3. 7 or 0.7
4. 1.37 or 1.49
5. 2.03 or 2.30
6. 0.8 or 0.88

Solution:

Question 2.
Express as rupees using decimals:

1. 7 paise
2. 7 rupees 7 paise
3. 77 rupees 77 paise
4. 50 paise
5. 235 paise.

Solution:

1. 7 paise = ₹ 0.07
2. 7 rupees 7 paise = ₹ 7.07
3. 77 rupees 77 paise = ₹ 77.77
4. 50 paise – ₹ 0.50
5. 235 paise = ₹ 2.35

Question 3.

1. Express 5 cm in metre and kilometre
2. Express 35 mm in cm, m and km?

Solution:

1. 5 cm = 0.05 m = 0.00005 km
2. 35 mm = 3.5 cm = 0.035 m = 0.000035 km

Question 4.
Express in kg:

1. 200 g
2. 3470 g
3. 4 kg 8 g

Solution:

1. 200 g = 0.200 kg = 0.2 kg
2. 3470 g = 3.470 kg
3. 4 kg 8 g = 4.008 kg.

Question 5.
Write the following decimal numbers in the expanded form:

1. 20.03
2. 2.03
3. 200.03
4. 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:
(i) Place value of 2 in the decimal number 2.56 = 2 × 1 = 2
(ii) Place value of 2 in decimal number 21.37 = 2 × 10 = 20
(iii) Place value of 2 in the decimal number

Question 7.
Dinesh went from place A to place t 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. f 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:
For Shyama
Apples bought = 5 kg 300 g = 5.300 kg
Mangoes bought = 3 kg 250 g = 3.250 kg
∴ Fruits bought = Apples bought
+ Mangoes bought = 5.300 kg + 3.250 kg

For Sarala
Oranges bought = 4 kg 800 g = 4.800 kg
Bananas bought = 4 kg 150 g = 4.150 kg
∴ Fruits bought = Oranges bought
+ Bananas bought

Question 9.
How much less is 28 km than 42.6 km?
Solution:

So, 28 km is less than 42.6 km by 14.6 km.

Exercise 2.6

Question 1.
Find:

1. 0.2 × 6
2. 8 × 4.6
3. 2.71 × 5
4. 20.1 × 4
5. 0.05 × 7
6. 211.02 × 4
7. 2 × 0.86

Solution:

1. 0.2 × 6 = 1.2
2. 8 × 4.6 = : 36.8
3. 2.71 × 5 = 13.55
4. 20.1 × 4 = 80.4
5. 0.05 × 7 = 0.35
6. 211.02 × 4 = 844.08
7. 2 × 0.86 = 1.72

Question 2.
Find the area of rectangle whose length is 5.7 cm and breadth is 3 cm.
Solution:
Length of the rectangle = 5.7 cm
Breadth of the rectangle = 3 cm
∴ Area of the rectangle
= Length × Breadth
= 5.7 × 3 = 17.1 cm²

Question 3.
Find:

1. 1.3 × 10
2. 36.8 × 10
3. 153.7 × 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 = 13.0
2. 36.8 × 10 = 368.0
3. 153.7 × 10 = 1537.0
4. 168.07 × 10 = 1680.70
5. 31.1 × 100 = = 3110.0
6. 156.1 × 100 = 15610.0
7. 3.62 × 100 = = 362.00
8. 43.07 × 100 = 4307.00
9. 0.5 × 10 = 5 .0
10. 0.08 × 10 = 0.80
11. 0.9 × 100 = 90.0
12. 0.03 × 1000 = 30.0.

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 liter of petrol = 55.3 km
Distance covered in 10 litres of petrol = (55.3 × 10) km = 553 km

Question 5.
Find:

1. 2.5 × 0.3
2. 0.1 × 51.7
3. 0.2 × 316.8
4. 1.3 × 3.1
5. 0.5 × 0.05
6. 11.2 × 0.15
7. 1.07 × 0.02
8. 10.05 × 1.05
9. 101.01 × 0.01
10. 100.01 × 1.1

Solution:

1. 2.5 × 0.3 = 0.75
2. 0.1 × 51.7 = 5 .17
3. 0.2 × 316.8 = 63.36
4. 1.3 × 3.1 = 4.03
5. 0.5 × 0.05 = 0 .025
6. 11.2 × 0.15 = 1.680
7. 1.07 × 0.02 = 0.0214
8. 10.05 × 1.05 = 10.5525
9. 101.01 × 0.01 = 1.0101
10. 100.01 × 1.1 = 110.011

Exercise 2.7

Question 1.
Find:

1. 0.4 ÷ 2
2. 0.35 ÷ 5
3. 2.48 ÷ 4
4. 65.4 ÷ 6
5. 651.2 ÷ 4
6. 114.49 ÷ 7
7. 3.96 ÷ 4
8. 0.80 ÷ 5

Solution:

Question 2.
Find:

1. 4.8 ÷ 10
2. 52.5 ÷ 10
3. 0.7 ÷ 10
4. 33.1 ÷ 10
5. 272.23 ÷ 1o
6. 0.56 ÷ 10
7. 3.97 ÷ 10

Solution:

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 ÷ 2000
3. 38.53 ÷ 1000
4. 128.9 ÷ 2000
5. 0.5 ÷ 2000

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:

1. 7 ÷ 3.5
2. 36 ÷ 0.2
3. 3.25 ÷ 0.5
4. 30.94 ÷ 0.7
5. 0.5 ÷ 0.25
6. 7.75 ÷ 0.25
7. 76.5 ÷ 0.15
8. 37.8 ÷ 1.4
9. 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 travelled in 1 litre of petrol = 43.2 ÷ 2.4