NCERT Solutions for Class 7 Maths Exercise 2.1 Chapter 2 Fractions and Decimals

NCERT Solutions For Class 7 Maths Ex 2.1 PDF Free Download

NCERT Solutions for Class 7 Maths Exercise 2.1 Chapter 2 Fractions and Decimals in simple PDF are given here. This exercise of NCERT Solutions for Class 7 Chapter 2 contains topics related to the introduction of Fractions. From this exercise, students can recall the study of fractions including proper, improper and mixed fractions as well as their addition and subtraction. To cover the entire syllabus in Maths, the NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals is a necessary material as it gives a wide range of questions that test the students understanding of concepts.

Download the PDF of NCERT Solutions For Class 7 Maths Chapter 2 Fractions and Decimals – Exercise 2.1

 

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ncert solution class 7 maths chapter 2 exercise 2.1
ncert solution class 7 maths chapter 2 exercise 2.1
ncert solution class 7 maths chapter 2 exercise 2.1
ncert solution class 7 maths chapter 2 exercise 2.1
ncert solution class 7 maths chapter 2 exercise 2.1
ncert solution class 7 maths chapter 2 exercise 2.1
ncert solution class 7 maths chapter 2 exercise 2.1

 

Access answers to Maths NCERT Solutions for Class 7 Chapter 2 – Fractions and Decimals Exercise 2.1

1. Solve:

(i) 2 – (3/5)

Solution:-

For subtraction of two unlike fractions, first change them to the like fractions.

LCM of 1, 5 = 5

Now, let us change each of the given fraction into an equivalent fraction having 5 as the denominator.

= [(2/1) × (5/5)] = (10/5)

= [(3/5) × (1/1)] = (3/5)

Now,

= (10/5) – (3/5)

= [(10 – 3)/5]

= (7/5)

(ii) 4 + (7/8)

Solution:-

For addition of two unlike fractions, first change them to the like fractions.

LCM of 1, 8 = 8

Now, let us change each of the given fraction into an equivalent fraction having 8 as the denominator.

= [(4/1) × (8/8)] = (32/8)

= [(7/8) × (1/1)] = (7/8)

Now,

= (32/8) + (7/8)

= [(32 + 7)/8]

= (39/8)

=NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 1

(iii) (3/5) + (2/7)

Solution:-

For addition of two unlike fractions, first change them to the like fractions.

LCM of 5, 7 = 35

Now, let us change each of the given fraction into an equivalent fraction having 35 as the denominator.

= [(3/5) × (7/7)] = (21/35)

= [(2/7) × (5/5)] = (10/35)

Now,

= (21/35) + (10/35)

= [(21 + 10)/35]

= (31/35)

(iv) (9/11) – (4/15)

Solution:-

For subtraction of two unlike fractions, first change them to the like fractions.

LCM of 11, 15 = 165

Now, let us change each of the given fraction into an equivalent fraction having 165 as the denominator.

= [(9/11) × (15/15)] = (135/165)

= [(4/15) × (11/11)] = (44/165)

Now,

= (135/165) – (44/165)

= [(135 – 44)/165]

= (91/165)

(v) (7/10) + (2/5) + (3/2)

Solution:-

For addition of two unlike fractions, first change them to the like fractions.

LCM of 10, 5, 2 = 10

Now, let us change each of the given fraction into an equivalent fraction having 35 as the denominator.

= [(7/10) × (1/1)] = (7/10)

= [(2/5) × (2/2)] = (4/10)

= [(3/2) × (5/5)] = (15/10)

Now,

= (7/10) + (4/10) + (15/10)

= [(7 + 4 + 15)/10]

= (26/10)

= (13/5)

=NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 2

(vi) NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 3

Solution:-

First convert mixed fraction into improper fraction,

=NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 4= 8/3

= 3 ½ = 7/2

For addition of two unlike fractions, first change them to the like fractions.

LCM of 3, 2 = 6

Now, let us change each of the given fraction into an equivalent fraction having 6 as the denominator.

= [(8/3) × (2/2)] = (16/6)

= [(7/2) × (3/3)] = (21/6)

Now,

= (16/6) + (21/6)

= [(16 + 21)/6]

= (37/6)

=NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 5

(vii) NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 6

Solution:-

First convert mixed fraction into improper fraction,

= 8 ½ = 17/2

=NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 7= 29/8

For Subtraction of two unlike fractions, first change them to the like fractions.

LCM of 2, 8 = 8

Now, let us change each of the given fraction into an equivalent fraction having 35 as the denominator.

= [(17/2) × (4/4)] = (68/8)

= [(29/8) × (1/1)] = (29/8)

Now,

= (68/8) – (29/8)

= [(68 – 29)/8]

= (39/8)

=NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 8

2. Arrange the following in descending order:

(i) 2/9, 2/3, 8/21

Solution:-

LCM of 9, 3, 21 = 63

Now, let us change each of the given fraction into an equivalent fraction having 63 as the denominator.

[(2/9) × (7/7)] = (14/63)

[(2/3) × (21/21)] = (42/63)

[(8/21) × (3/3)] = (24/63)

Clearly,

(42/63) > (24/63) > (14/63)

Hence,

(2/3) > (8/21) > (2/9)

Hence, the given fractions in descending order are (2/3), (8/21), (2/9)

(ii) 1/5, 3/7, 7/10

Solution:-

LCM of 5, 7, 10 = 70

Now, let us change each of the given fraction into an equivalent fraction having 70 as the denominator.

[(1/5) × (14/14)] = (14/70)

[(3/7) × (10/10)] = (30/70)

[(7/10) × (7/7)] = (49/70)

Clearly,

(49/70) > (30/70) > (14/70)

Hence,

(7/10) > (3/7) > (1/5)

Hence, the given fractions in descending order are (7/10), (3/7), (1/5)

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?

4/11

9/11

2/11

3/11

5/11

7/11

8/11

1/11

6/11

Solution:-

Sum along the first row = (4/11) + (9/11) + (2/11) = (15/11)

Sum along the second row = (3/11) + (5/11) + (7/11) = (15/11)

Sum along the third row = (8/11) + (1/11) + (6/11) = (15/11)

Sum along the first column = (4/11) + (3/11) + (8/11) = (15/11)

Sum along the second column = (9/11) + (5/11) + (1/11) = (15/11)

Sum along the third column = (2/11) + (7/11) + (6/11) = (15/11)

Sum along the first diagonal = (4/11) + (5/11) + (6/11) = (15/11)

Sum along the second diagonal = (2/11) + (5/11) + (8/11) = (15/11)

Yes. The sum of the numbers in each row, in each column and along the diagonals is the same, so it is a magic square.

4. A rectangular sheet of paper is 12 ½ cm long and NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 9 cm wide. Find its perimeter.

Solution:-

From the question, it is given that,

Length = 12 ½ cm = 25/2 cm

Breadth =
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 10cm = 32/3 cm

We know that,

Perimeter of the rectangle = 2 × (length + breadth)

= 2 × [(25/2) + (32/3)]

= 2 × {[(25 × 3) + (32 × 2)]/6}

= 2 × [(75 + 64)/6]

= 2 × [139/6]

= 139/3 cm

Hence, the perimeter of the sheet of paper is
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 11cm

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

NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 12

Solution:-

From the fig,

AB = (5/2) cm

AE =
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 13= 18/5 cm

BE =
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 14= 11/4 cm

ED = 7/6 cm

(i) We know that,

Perimeter of the triangle = Sum of all sides

Then,

Perimeter of triangle ABE = AB + BE + EA

= (5/2) + (11/4) + (18/5)

The LCM of 2, 4, 5 = 20

Now, let us change each of the given fraction into an equivalent fraction having 20 as the denominator.

= {[(5/2) × (10/10)] + [(11/4) × (5/5)] + [(18/5) × (4/4)]}

= (50/20) + (55/20) + (72/20)

= (50 + 55 + 72)/20

= 177/20

=NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 15cm

(ii) Now, we have to find the perimeter of the rectangle,

We know that,

Perimeter of the rectangle = 2 × (length + breadth)

Then,

Perimeter of rectangle BCDE = 2 × (BE + ED)

= 2 × [(11/4) + (7/6)]

The LCM of 4, 6 = 12

Now, let us change each of the given fraction into an equivalent fraction having 20 as the denominator

= 2 × {[(11/4) × (3/3)] + [(7/6) × (2/2)]}

= 2 × [(33/12) + (14/12)]

= 2 × [(33 + 14)/12]

= 2 × (47/12)

= 47/6

= NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 16

Finally, we have find which one is having greater perimeter.

Perimeter of triangle ABE = (177/20)

Perimeter of rectangle BCDE = (47/6)

The two perimeters are in the form of unlike fraction.

Changing perimeters into like fractions we have,

(177/20) = (177/20) × (3/3) = 531/60

(43/6) = (43/6) × (10/10) = 430/60

Clearly, (531/60) > (430/60)

Hence, (177/20) > (43/6)

∴ Perimeter of Triangle ABE > Perimeter of Rectangle (BCDE)

6. Salil wants to put a picture in a frame. The picture is NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 17 cm wide. To fit in the frame the picture cannot be more than NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 18 cm wide. How much should the picture be trimmed?

Solution:-

From the question, it is given that,

Picture having a width of =
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 19= 38/5 cm

Frame having a width of =
NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals image 20= 73/10 cm

∴The picture should be trimmed by = [(38/5) – (73/10)]

The LCM of 5, 10 = 10

Now, let us change each of the given fraction into an equivalent fraction having 10 as the denominator.

= [(38/5) × (2/2)] – [(73/10) × (1/1)]

= (76/10) – (73/10)

= (76 – 73)/10

= 3/10 cm

Thus, the picture should be trimmed by (3/10) cm

7. Ritu ate (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:-

From the question, it is given that,

Part of apple eaten by Ritu is = (3/5)

Part of apple eaten by Somu is = 1 – Part of apple eaten by Ritu

= 1 – (3/5)

The LCM of 1, 5 = 5

Now, let us change each of the given fraction into an equivalent fraction having 10 as the denominator.

= [(1/1) × (5/5)] – [(3/5) × (1/1)]

= (5/5) – (3/5)

= (5 – 3)/5

= 2/5

∴ Part of apple eaten by Somu is (2/5)

So, (3/5) > (2/5) hence, Ritu ate larger size of apple.

Now, the difference between the 32 shares = (3/5) – (2/5)

= (3 – 2)/5

= 1/5

Thus, Ritu’s share is larger than share of Somu by (1/5)

8. Michael finished colouring a picture in (7/12) hour. Vaibhav finished colouring the same picture in (3/4) hour. Who worked longer? By what fraction was it longer?

Solution:-

From the question, it is given that,

Time taken by the Michael to colour the picture is = (7/12)

Time taken by the Vaibhav to colour the picture is = (3/4)

The LCM of 12, 4 = 12

Now, let us change each of the given fraction into an equivalent fraction having 12 as the denominator.

(7/12) = (7/12) × (1/1) = 7/12

(3/4) = (3/4) × (3/3) = 9/12

Clearly, (7/12) < (9/12)

Hence, (7/12) < (3/4)

Thus, Vaibhav worked for longer time.

So, Vaibhav worked longer time by = (3/4) – (7/12)

= (9/12) – (7/12)

= (9 – 7)/12

= (2/12)

= (1/6) of an hour.


Access other exercises of NCERT Solutions For Class 7 Chapter 2 – Fractions and Decimals

Exercise 2.2 Solutions

Exercise 2.3 Solutions

Exercise 2.4 Solutions

Exercise 2.5 Solutions

Exercise 2.6 Solutions

Exercise 2.7 Solutions

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