Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

RD Sharma Class 8 – Chapter 1 Rational Numbers – Exercise 1.1

  • Last Updated : 31 Oct, 2020

Question 1. Add the following rational numbers:

(i) -5 / 7 and 3 / 7

Solution:

Hey! Looking for some great resources suitable for young ones? You've come to the right place. Check out our self-paced courses designed for students of grades I-XII

Start with topics like Python, HTML, ML, and learn to make some games and apps all with the help of our expertly designed content! So students worry no more, because GeeksforGeeks School is now here!

 



(-5 / 7) + 3 / 7

Since denominators are the same hence numerators will be directly added considering their sign.

Therefore, (-5 + 3) / 7 = (-2) / 7

(ii) -15 / 4 and 7 / 4

Solution:

Denominators are same so numerators are directly added.

= (-15) / 4 + 7 / 4

= (-15 + 7) / 4

= (-8) / 4

= (4 * (-2)) / 4

= (-2)

(iii) -8 / 11 and -4 / 11

Solution:

As denominators are the same numerators are added along with their sign.

= (-8) / 11 + (-4) / 11

= (-8 – 4) / 11  (integers with same sign are added)

= (-12) / 11

(iv) 6 / 13 and -9 / 13



Solution:

As, denominators are same numerators are added with their sign.

= 6 / 13 + (-9) / 13

= (6 – 9) / 13  (integers with opposite sign)

= (-3) / 13

Question 2. Add the following rational numbers:

(i) 3 / 4 and -5 / 8

Solution:

Denominators are different, so we need to take the LCM of denominators to make them into like fractions.

LCM of 4 and 8 = 8

= 3 / 4 + (-5) / 8

= (3 × 2 + (-5)) / 8

= (6 – 5) / 8

= 1 / 8

(ii) 5 / -9 and 7 / 3

Solution:

Denominators are different, so we need to take the LCM of denominators to make them into like fractions.

LCM of 9 and 3 = 9

= (-5 / 9) + 7 / 3

= (-5 + 7 × 3) / 9

= (-5 + 21) / 9



= 16 / 9

(iii) -3 and 3 / 5

Solution:

Denominators are different, so we need to take the LCM of denominators to make them into like fractions.

= (-3) / 1 + 3 / 5

LCM of 1 and 5 = 5

= ((-3) × 5 + 3) / 5

= (-15 + 3) / 5

= (-12) / 5

(iv) -7 / 27 and 11 / 18

Solution:

LCM of 27 and 18

27 = 3 × 3 × 3

18 = 2 × 3 × 3

LCM = 3 × 3 × 3 × 2 = 54

Therefore,

= (-7) / 27 + 11 / 18

= ((-7 × 2 + 11 × 3)) / 54

= (-14 + 33) / 54

= 19 / 54

(v) 31 / -4 and -5 / 8

Solution:

LCM of 4 and 8 = 8

= ((-31 × 2) + (-5)) / 8

= (-62 – 5) / 8

= (-67) / 8

(vi) 5 / 36 and -7 / 12

Solution:

LCM of 36 and 12 is 36

= 5 / 36 + (-7) / 12

= (5 + (-7 × 3)) / 36

= (5 + (-21)) / 36

= (-16) / 36

4 is the common factor theta can be canceled

= (-4) / 9

(vii) -5 / 16 and 7 / 24

Solution:

LCM of 16 and 24

16 = 2 × 2 × 2 × 2

24 = 2 × 2 × 2 × 3



LCM = 2 × 2 × 2 × 2 × 3 = 48

= (-5) / 16 + 7 / 24

= ((-5 × 3) + 7 × 2) / 48

= (-15 + 14) / 48

= (-1) / 48

(viii) 7 / -18 and 8 / 27

Solution:

LCM of 18 and 27

18 = 2 × 3 × 3

27 = 3 × 3 × 3

LCM = 3 × 3 × 3 × 2 = 54

= ((-7 × 3) + 8 × 2) / 54

= (-21 + 16) / 54

= (-5) / 54

Question 3. Simplify:

(i) 8 / 9 + -11 / 6

Solution:

LCM of 9 and 6

9 = 3 × 3

6 = 2 × 3

LCM = 2 × 3 × 3 = 18

= (8 × 2 + (-11 × 3)) / 18

= (16 – 33) / 18

= (-17) / 18

(ii) 3 + 5 / -7

LCM of 1 and 7 is 7

= (3 × 7 + (-5)) / 7

= (21 – 5) / 7

= 16 / 7

(iii) 1 / -12 + 2 / -15

Solution:

LCM of 12 and 15

12 = 2 × 2 × 3

15 = 3 × 5

LCM = 2 × 2 × 3 × 5 = 60

= ((-1 × 5) + (-2 × 4)) / 60

= (-5 – 8) / 60

= (-13) / 60

(iv) -8 / 19 + -4 / 57

Solution:

LCM of 19 and 57 is 57

= ((-8 × 3) + (-4)) / 57

= (-24 – 4) / 57

= (-28) / 57

(v) 7 / 9 + 3 / -4

Solution:

LCM of 9 and 4 is 36

= (7 × 4 + (-3 × 9)) / 36

= (28 – 27) / 36

= 1 / 36

(vi) 5 / 26 + 11 / -39

Solution:

LCM of 26 and 39

26 = 13×2

39 = 13×3

LCM = 13 × 2 × 3 = 78

= (5 × 3 + (-11 × 2)) / 78

= (15 – 22) / 78

= (-7) / 78

(vii) -16 / 9 + -5 / 12

Solution:



LCM of 16 and 12

9 = 3×3

12 = 2 × 2 × 3

LCM = 3 × 3 × 2 × 2 = 36

= ((-16 × 4) + (-5 × 3)) / 36

= (-64 – 15) / 36

= (-79) / 36

= (-79) / 36

(viii) -13 / 8 + 5 / 36

Solution:

LCM of 8 and 36

8 = 2 × 2 × 2

36 = 2 × 2 × 3 × 3

LCM = 2 × 2 × 2 × 3 × 3 = 72

= ((-13 × 9) + 5 × 2) / 72

= (-117 + 10) / 72

= (-107) / 72

(ix) 0 + -3 / 5

Solution:

0 is the additive identity, if added to any number gives the same number

= (-3) / 5

(x) 1 + -4 / 5

Solution:

LCM of 1 and 5 is 5

= (1 × 5 + (-4)) / 5

= (5 – 4) / 5

= 1 / 5

Question 4. Add and express the sum as mixed fraction:

(i) -12 / 5 and 43 / 10

Solution:

LCM is 10

= ((-12 × 2 + 43)) / 10

= (-24 + 43) / 10

= 19 / 10

Mixed\hspace{0.1cm}fraction\hspace{0.1cm}is: 1{\Large\frac{9}{10}}

(ii) 24 / 7 and -11 / 4

Solution:

LCM of 7 and 4 is 28

= (24 × 4 + (-11 × 7)) / 28

= (96 – 77) / 28

= 19 / 28

Proper fraction cannot be converted to mixed fraction

(iii) -31 / 6 and -27 / 8

Solution:

LCM of 8 and 6 is 24

= ((-31 × 4) + (-27 × 3)) / 16

= (-124 – 81) / 24

= (-205) / 24

Mixed\hspace{0.1cm}fraction\hspace{0.1cm}is: -8{\Large\frac{13}{24}}

(iv) 101 / 6 and 7 / 8

Solution:

LCM of 8 and 6 is 24

101 / 6 + 7 / 8

= (101 × 4 + 7 × 3) / 24

= (404 + 21) / 24

= 425 / 24

Mixed\hspace{0.1cm}fraction\hspace{0.1cm}is: 17{\Large\frac{17}{24}}




My Personal Notes arrow_drop_up
Recommended Articles
Page :

Start Your Coding Journey Now!