RD Sharma Solutions: Fractions (Exercise 2.1)

Q.1. Compare the following fractions by using the symbol > or < or =:

(i) 

(ii)

(iii)

(iv)

Ans: First, we need to find the LCM of denominators in each case. After that, we will equate the denominators in order to compare the two fractions. 

(i) LCM of 9 and 13 is 117.

Now make both fraction equivalent with denominator as 117

⇒

we know 91 > 72

⇒

⇒

(ii) both fraction have same denominator as 9

we know 11 > 5

⇒

(iii) LCM of 41 and 30 is 1230 

Now convert both fraction to their equivalent fractions with denominator as 1230

we know 

1110 > 779

(iv) LCM of 15 and 105 is 105.

Now convert fraction to its equivalent fractions with denominator as 105

⇒

Q.2. Arrange the following fractions in ascending order:

(i)

(ii)

Ans: 

(i)

LCM of the denominators 8, 6, 4 and 3 is 24.

Now, convert all fractions into their equivalent fractions with denominator 24.

We know:

8 < 9 < 12 < 18 < 20

(ii)

LCM of the denominators 8, 12, 16 and 3 is 48.

Now, convert all fractions into their equivalent fractions with denominator 48.

we know

15 < 18 < 24 < 64

Q.3. Arrange the following fractions in descending order:

(i)

(ii)

Ans: 

(i)

LCM of the denominators 5, 10, 15 and 20 is 60.

Now, convert all fractions to their equivalent fractions with denominator 60.

We know:

51 > 48 > 44 > 42

(ii)

LCM of the denominators 7, 35, 14 and 28 is 140.

Now, convert all fractions to their equivalent fractions with denominator 140.

We know:

90 > 65 > 44  > 40

Q.4. Write five equivalent fractions of.

Ans: Five equivalent fractions of  are:

(i)

(ii)

(iii)

(iv)

(v)

Q.5. Find the sum:

(i)

(ii)

(iii)

(iv)

Ans: 

(i)

LCM of 8,10  is 40.

⇒

(ii)

LCM of 5,4 is 20.

(iii)

LCM of 6,4 is 24.

(iv)

or

LCM of 15,10 and 5 is 30.

Q.6. Find the difference of

(i)

(ii)

(iii)

(iv)

Ans: 

(i)

LCM of 24 and 16 is 48.

(ii)

LCM of 3 and 1 is 3.

(iii)

LCM of 20,25 is 100.

(iv)

LCM of 10 and 15 is 30.

Q.7. Find the difference:

(i)

(ii)

(iii)

(iv)

Ans: 

(i)

LCM of 7 and 11 is 77.

(ii)

LCM of 1 and 9 is 9.

(iii)

LCM of 1 and 3 is 3.

(iv)

LCM of 10 and 15 is 30.

Q.8. Simplify:

(i)

(ii)

(iii)

Ans: 

(i)

LCM of 3.6 and 9 is 18.

(ii)

LCM of 2 and 1 is 2.

(iii)

LCM of 6,8 and 12 is 24.

Q.9. What should be added toto get 12?

Ans: 

Let x be the required fraction.

According to the question:

⇒ 

⇒ 

⇒ 

Q.10. What should be added toto get?

Ans: 

Let x be the required fraction.

According to the question:

⇒

⇒

LCM of 5 and 15 is 15.

⇒

⇒

Q.11. Suman studies forhours daily. She devoteshours of her time for Science and Mathematics. How much time does she devote for other subjects?

Ans: Suman studies for hours daily. Therefore, we have

hours =

She studies science and mathematics forhours. Therefore, we have

hours =

Time devoted to other subjects = Total study time - Time devoted to science and mathematics 

==

=

Q.12. A piece of wire is of lengthm. If it is cut into two pieces in such a way that the length of one piece ism, what is the length of the other piece?

Ans: Let the length of second piece be x.

Total length of wire = Length of one piece + Length of second piece

⇒ 

⇒

⇒

⇒

Q.13. A rectangular sheet of paper iscm long andcm wide. Find its perimeter.

Ans: 

Perimeter of rectangle = 2(length + width)

=

=

=

=cm

Q.14. In a "magic square", the sum of the numbers in each row, in each column and along the diagonal is the same. Is this a magic  square?

Ans: Sum along columns and rows:

Sum along diagonals :

Since, all the sums in the square   are equal along rows,columns and diagonals,it is a magic square.

Q.15. The cost of Mathematics book is Rs and that of Science book is Rs. Which costs more and by how much? 

Ans: Cost of mathematics book =

Cost of Science book =

We know        

82 < 103

Thus, Mathematics book costs more.Difference in the cost of Mathematics and Science book = cost of Mathematics book-Cost of Science book

=

= = = Rs

So, Mathematics book costs more by Rs

Q.16. (i) Provide the number in boxand also give its simplest from in each of the following:

(i)

(ii)

Ans: 

(i)

(ii)