RD SHARMA SOLUTION CHAPTER –2 Fractions | CLASS 7TH MATHEMATICS-EDUGROWN

Exercise 2.1

Question: 1

 Compare the following fractions by using the symbol > or < or =;

Solution:

(i) We have,

Taking the LCM of 9 and 13, we get,

9 x 13 = 117

Now, we convert the given fractions to equivalent fractions by making the denominators 117,

As we know, 91 > 72

Hence, 79 > 813

(ii)  We have,

The given fractions are equivalent fractions as the denominators are equal,

And we know that, 11 > 5

Therefore, 119 > 59

(iii)  We have,

Taking the LCM of 41 and 30, we get,

41 x 30 = 1230

Now, we convert the given fractions to equivalent fractions by making the denominators 1230,

Now, we clearly know 1110 > 779

Hence, 3741 > 1930

(iv) We have,

Taking the LCM of 15 and 105, we get,

5 x 3 x 7 = 105

Now, we convert the given fractions to equivalent fractions by making the denominators 105,

Question: 2

Arrange the following fractions in ascending order:

Solution:

(i)  We have,

Taking the LCM of 8, 6, 8, 4 and 3, we get,

2 x 4 x 3 = 24

Now, we convert the given fractions to equivalent fractions by making the denominators 24,

We know that, 8 < 9 < 12 < 18 < 20

Hence, 13 < 38 < 24 < 68 < 56

(ii) We have,

Taking the LCM of 6, 8, 12 and 16, we get,

2 x 2 x 2 x 2 x 3 = 48

Now, we convert the given fractions to equivalent fractions by making the denominators 48,

We know that, 12 < 15 < 18 < 32

Question: 3

Arrange the following fractions in descending order:

Solution:

(i)  We have,

Taking the LCM of 5, 10, 15 and 20, we get,

5 x 2 x 2 x 3 = 60

Now, we convert the given fractions to equivalent fractions by making the denominators 48

As we know 51 > 48 > 44 > 42

(ii) We have,

Taking the LCM of 7, 35, 14 and 28, we get,

7 x 5 x 2 x 2 = 140

Now, we convert the given fractions to equivalent fractions by making the denominators 140

As we know 40 > 44 > 65 > 90

Question: 4

Write the equivalent fractions of 3/5

Solution:

Multiplying or dividing both the numerator and denominator by the same number,

so that the fraction keeps its value.

So the equivalent fractions of 3/5 are

are the five equivalent fractions of 3/5

Question: 5

Find the sum:

Solution:

(i)  We have,

Taking the LCM of 8 and 10, we get,

2 x 4 x 5 = 40

Now, we convert the given fractions to equivalent fractions by making the denominators 40

(ii) We have,

Taking out the LCM of 4 and 5, we get,

4 x 5 = 20

Now, we convert the given fractions to equivalent fractions by making the denominators 20

(iii)  We have,

Taking out the LCM of 6 and 4, we get,

2 x 2 x 3 = 12

Now, we convert the given fractions to equivalent fractions by making the denominators 12

(iv) We have,

Taking out the LCM of 5, 10 and 15, we get,

5 x 2 x 3 = 30

Now, we convert the given fractions to equivalent fractions by making the denominators 30

Question: 6

Find the difference of

Solution:

(i)  We have,

Taking out the LCM of 24 and 16, we get,

2 x 2 x 2 x 2 x 3 = 48

Now, we convert the given fractions to equivalent fractions by making the denominators 48

(ii)  We have, 6 and 23/3

The difference between 6 and 23/3

(iii)  We have,

Taking out the LCM of 25 and 20, we get,

5 x 5 x 4 = 100

Now, we convert the given fractions to equivalent fractions by making the denominators 100

The difference between both the fractions are

(iv) We have,

Taking out the LCM of 10 and 15, we get,

2 x 3 x 5 = 30

Now, we convert the given fractions to equivalent fractions by making the denominators 30

The difference between both the fractions are

Question: 7

Find the difference:

Solution:

(i)  We have,

Taking out the LCM of 7 and 11, we get,

7 x 11 = 77

Now, we convert the given fractions to equivalent fractions by making the denominators 77

The difference between both the fractions are

(ii)  We have,

(iii) We have,

(iv) We have,

Taking out the LCM of 10 and 15, we get,

2 x 3 x 5 = 30

Now, we convert the given fractions to equivalent fractions by making the denominators 30

Question: 8

Simplify:

Solution:

(i) We have,

Taking out the LCM of 3, 6 and 9, we get,

3 x 3 x 2 = 18

Now, we convert the given fractions to equivalent fractions by making the denominators 18, we get,

(ii)  We have,

(iii) We have,

Taking out the LCM of 6, 8 and 12, we get,

2 x 2 x 2 x 3 = 48

Now, we convert the given fractions to equivalent fractions by making the denominators 48, we get,

Question: 9

What should be added to to get 12?

Solution:

We have,

Let x be the number added to 38/7 to get 12

Therefore,

x + 387 = 12

Question: 10

 What should be added to?

Solution:

Let x be the number added to 79/15 to get 63/5

Taking out the LCM of 5 and 15, we get,

3 x 5 = 15

Now, we convert the given fractions to equivalent fractions by making the denominators 15, we get,

Question: 11

Suman studies forhours daily. She devoteshours of her time for science and mathematics. How much time does she devote for other subjects?

Solution:

Given,

Suman studies forhours daily

She devoteshours of her time for science and mathematics. Let x be time she devotes for other subjects.

Taking out the LCM of 3 and 5, we get,

3 x 5 = 15

Now, we convert the given fractions to equivalent fractions by making the denominators 48, we get,

Question: 12

A piece of wire of lengthIf it is cut into two pieces in such a way that the length of one piece iswhat is the length of the other piece?

Solution:

A piece of wire of lengthone piece is

Let the length of other piece be x m.

Question: 13

A rectangular piece of paper islong andwide. Find its perimeter?

Solution:

Given,

A rectangular piece of paper islong andwide

Perimeter = 2(length + width)

Question: 14

In a “magic square”, the sum of numbers in each row, in each column and along the diagonal is 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:

Given,

4/11	9/11	2/11
3/11	5/11	7/11
8/11	1/11	6/11

Therefore, the sum of numbers in each row, in each column and along the diagonal is same and the sum is 15/11.

Question: 15

The cost of Mathematics book is Rsand that of science book isWhich costs more and by how much?

Solution:

Given,

The cost of Mathematics book is Rsand that of science book is

We need to compare the cost of mathematics and science book,

Taking out the LCM of 4 and 2, we get,

2 x 2 = 4

Now, we convert the given fractions to equivalent fractions by making the denominators 4, we get

= 103/4

As we know, 103 > 82

Hence, the cost of mathematics book is more than that of the cost of the science book.

Question: 16

 Provide the number in the box [] and also give its simplest form in each of the following:

Solution:

Exercise 2.2

Question: 1

Multiply

Solution:

(i)  We have,

(ii)  We have,

(iii)  We have,

(iv) We have,

Question: 2

Find the product:

Solution:

(i)  We have,

(ii) We have,

(iv) We have,

Question: 3

Simplify:

Solution:

(i)  We have,

(ii) We have,

(iii) We have,

Question: 4

Find:

Solution:

(i) We have,

(ii) We have,

(iii) We have,

Question: 5

Which is greater?

Solution:

While comparing two fractions, when the numerators of both the fractions are same, then the denominator having higher value shows the fraction has lower value.

So, 6/14 is greater.

Therefore, 1/2 of 6/7 is greater.

Question: 6

(i)  7/11 of 330

(ii) 5/9 of 108 meters

(iii) 3/7 of 42 litres

(iv) 1/12 of an hour

(v) 5/6 of an year

(vi) 3/20 of a Kg

(vii) 7/20 of a litres

(viii) 5/6 of a day

(ix)  2/7 of a week

Solution:

(i)  We have,

(ii)  We have,

5/9 of 108 meters

= 5/9 × 108 meters

= 5 × 12 meters

60 meters

(iii) We have,

3/7 of 42 litres

= 3/7× 42 litres

= 3 × 6 litres

=18 litres

(iv) We have,

1/12 of an hour

An hour = 60 minutes

Therefore, 1/12 × 60 minutes

= 5 minutes

(v) We have,

5/6 of an year

I Year = 12 months

Therefore,

5/6 × 12 months

= 5 × 2 months

= 10 months

(vi) We have,

3/20 of a kg

1 Kg = 1000 gms

Therefore,

3/20 × 1000 gms

= 3 × 50 gms

= 150 gms

(vii) We have, 

7/20 of a litre

1 litre = 1000 ml

Therefore,

7/20 × 1000 ml

= 7 × 50 ml

= 350 ml

(viii) We have,

5/6 of a day

I day = 24 hours

Therefore,

5/6 × 24 hours

= 5 × 4 hours

= 20 hours

(ix) We have,

2/7 of a week

I week = 7 days

Therefore,

2/7 × 7 days = 2 days

Question: 7

Shikha plans 5 saplings in a row in her garden. The distance between two adjacent saplings is 3/4 m. Find the distance between first and last sapling.

Solution:

There are 4 adjacent spacing for 5 saplings.

Given, the distance between two adjacent saplings is 3/4 m.

4 adjacent spacing for 5 saplings = 3/4 × 4 = 3 m

Therefore, the distance between first and last sapling is 3 m.

Question: 8

Ravish reads 1/3 part of a book in one hour. How much part of the book will be read in 2(1/5) hours?

Solution:

Let x be the full part of book.

Given, Ravish reads 1/3 part of a book in one hour

1 hour = (1/3) x

Part of the book will he read in 2(1/5) hours

Question: 9

Lipika reads a book for 1(3/4) hours every day. She reads the entire book in 6 days. How many hours in all were required by her to read the book?

Solution:

Given,

Time taken by Lipika to read a book per day = 1(3/4) = 7/4 hours

Time taken by Lipika to read a book for 6 days

Question: 10

Find the area of a rectangular park which is 41(2/3)m long and 18(3/5)m broad.

Solution:

Area of a rectangular park = (length x breadth)

Question: 11

If milk is available at Rs 17(3/4) per litre, find the cost of 7(2/5) litres of milk.

Solution:

Given,

Question: 12

Sharda can walk 8(1/3) km in one hour. How much distance will she cover in 2(2/5) hours.

Solution:

Given,

Distance covered by Sharda in one hour = 25/3 km

Question: 12

A sugar bag contains 30 kg of sugar. After consuming 2/3 of it, how much sugar is left in the bag

Solution:

Given, A sugar bag contains 30 kg of sugar

After consuming 23 of it, the amount of sugar left in the bag

Question: 14

Each side of a square is 6 (2/3)m long. Find its area.

Solution:

Given,

Question: 15

There are 45 students in a class and 3/5 of them are boys. How many girls are. there in the class?

Solution:

Given,

There are 45 students in a class,

And 3/5 of them are boys.

Therefore, no of girls in the class = 45 –3/5 × 45

= 45 – 27

= 18

Exercise 2.3

Question: 1

Find the reciprocal of each of the following fractions and classify them as proper, improper and whole numbers

(i) 3/7

(ii) 5/8

(iii) 9/7

(iv) 6/5

(v) 12/7

(vi) 1/8

Solution:

(i)  3/7

7/3 = improper number

(ii)  5/8

8/5 = improper number

(iii)  9/7 

7/9 = proper number

(iv) 6/5

5/6 = proper number

(v) 12/7

7/12 = proper number

(vi) 1/8

8 = whole number

Question: 2

Divide:

Solution:

Question: 3

Divide:

Solution:

Question: 4

Simplify:

Solution:

Question: 5

A wire of length 12(1/2)m is cut into 10 pieces of equal length. Find the length of each piece.

Solution:

Question: 6

The length of a rectangular plot of area 65(1/3) m² is 12(1/4) m. What is the width of the plot?

Solution:

Given,

The length of a rectangular plot of area 65(1/3) m² is 12(1/4) m. 

Question: 7

By what number 6(2/9) be multiplied to get 4(4/9)?

Solution:

Given,

Let x be the number which needs to be multiplied by 56/9,

Now,

Question: 8

The product of two numbers is 25(5/6). If one of the numbers is 6(2/3), find the other?

Solution:

Given,

The product of two numbers is 25(5/6). If one of the numbers is 6(2/3),

Let the other number be x.

Question: 9

The cost of 6(1/4) kg of apples is Rs 400. At what rate per kg are the apples being sold?

Solution:

Given,

Question: 10

By selling oranges at the rate of Rs 5(1/4) per orange, a fruit seller get Rs 630. How many dozens of oranges does he sell?

Solution:

Given,

By selling oranges at the rate of Rs 5(1/4) per orange, a fruit seller get Rs 630.

5(1/4) = 2(1/4)

12 apples =1 dozen

Therefore, 120 apples = 10 dozen

Question: 11

In mid-day meal scheme 3/10 litre of milk is given to each student of a primary school. If 30 litres of milk is distributed every-day in the school, how many students are there in the school?

Solution:

Given,

3/10  litre of milk is given to each student of a primary school.

30 litres of milk is distributed everyday in the school

Number of students given 3/10 litres of milk = 1

Number of students given 1 litre of milk = 10/3

Number of students given 30 litres of milk = 10/3 × 30 = 100 Students

Question: 12

In a charity show Rs 6496 were collected by selling some tickets. If the price of each ticket was Rs 50(3/4), how many tickets were sold?

Solution:

Given,

Rs 6496 were collected by selling some tickets. If the price of each ticket was Rs 50(3/4),