# Class 8 RD Sharma – Chapter 1 Rational Numbers – Exercise 1.4

• Last Updated : 05 Nov, 2020

### Problem 1. Simplify each of the following and write as a rational number in the form of p/q:

(i) 3/4 + 5/6 + -7/8

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!

2 = 2 × 2

6 = 2 × 3

8 = 2 × 2 × 2

LCM is 2 × 2 × 2 × 3 = 24

= (3 × 6 + 5 × 4 + (-7 × 3)) / 24

= (18 + 20 – 21) / 24

= (38 – 21) / 24

= 17 / 24

(ii) 2/3 + -5/6 + -7/9

Solution:

LCM of 3, 6 and 9 is 18

= (2 × 6 + (-5 × 3) + (-7 × 2)) / 18

= (12 – 15 – 14) / 18

= (12 – 29) / 18

= -17 / 18

(iii) -11/2 + 7/6 + -5/8

Solution:

2 = 2 × 1

6 = 2 × 3

8 = 2 × 2 × 2

LCM is 2 × 2 × 2 × 3 = 24

= (-11 × 12 + 7 × 4 + (-5 × 3)) / 24

= (-132 + 28 – 15) / 24

= (-147 + 28) / 24

= -119 / 24

(iv) -4/5 + -7/10 + -8/15

Solution:

10 = 5 × 2

15 = 3 × 5

LCM is 5 × 2 × 3 = 30

= (-4 × 6 + (-7 × 3) + (-8 × 2)) / 30

= (-24 – 21 – 16) / 30

= -61 / 30

(v) -9/10 + 22/15 + 13/-20

Solution:

This can be written as

-9/10 + 22/15 + -13/20

10 = 2 × 5

15 = 3 × 5

20 = 2 × 2 × 5

LCM is 2 × 2 × 3 × 5 = 60

= (-9 × 6 + 22 × 4 + (-13 × 3)) / 60

= (-54 + 88 – 39) / 60

= (-93 + 88) / 60

= -5 / 60

= -1 / 12

(vi) 5/3 + 3/-2 + -7/3 + 3

Solution:

This can be written as

5 / 3 + -3 / 2 + -7 / 3 + 3 / 1

LCM is 6

= (5 × 2 + (-3 × 3) + (-7 × 2) + 3 × 6) / 6

= (10 – 9 -14 + 18) / 6

= (28 – 23) / 6

= 5 / 6

### Problem 2. Express each of the following as a rational number of the form p/q:

(i) -8/3 + -1/4 + -11/6 + 3/8 + -3

Solution:

4 = 2 × 2

6 = 2 × 3

8 = 2 × 2 × 2

LCM is 2 × 2 × 2 × 3 = 24

= (-8 × 8 + (-1 × 6) + (-11 × 4) + 3 × 3 + (-3 × 24)) / 24

= (-64 – 6 – 44 + 9 – 72) / 24

= (-186 + 9) / 24

= -177 / 24

= -59 / 8

(ii) 6/7 + 1 + -7/9 + 19/21 + -12/7

Solution:

(6 / 7 + -12 / 7) + (-7 / 9) + 19 / 21 + 1(Taking numbers with same denominators together)

= (6 – 12) / 7 + (-7 / 9) + 19 / 21+1

= -6 / 7 + -7 / 9 + 19 / 21 + 1 / 1

9 = 3 × 3

21 = 3 × 7

LCM of 7, 1, 9 and 21 is 63

= (-6 × 9 + (-7 × 7) + 19 × 3 + 1 × 63) / 63

= (-54 – 49 + 57 + 63) / 63

= (-103 + 120) / 63

= 17 / 63

(iii) 15/2 + 9/8 + -11/3 + 6 + -7/6

Solution:

15 / 2 + 9/8 + (-11 / 3) + 6 / 1 + (-7 / 6)

LCM of 2, 8, 3, 1 and 6 is 24

= (15 × 12 + 9 × 3 + (-11 × 8) + 6 × 24 + (-7 × 4)) / 24

= (180 + 27 – 88 + 144 – 28) / 24

= (351 – 116) / 24

= (235) / 24

(iv) -7/4 + 0 + -9/5 + 19/10 + 11/14

Solution:

4 = 2 × 2

5 = 5 × 1

10 = 2 × 5

14 = 2 × 7

LCM is 2 × 2 × 5 × 7 is 140

= (-7 × 35 + (-9 × 28) + 19 × 14 + 11 × 10) / 140

= (-245 – 252 + 266 + 110) / 140

= (-497 + 376) / 140

= (-121) / 140

(v) -7/4 + 5/3 + -1/2 + -5/6 + 2

Solution:

LCM of 4, 3, 2 and 6 is 12

= (-7 × 3 + 5 × 4 + (-1 × 6) + (-5 × 2) + 2 × 12) / 12

= (-21 + 20 – 6 – 10 + 24) / 12

= (-37 + 44) / 12

= 7 / 12

### Problem 3. Simplify:

(i) -3/2 + 5/4 + -7/4

Solution:

Taking numbers with the same denominators together

= -3 / 2 + (5 – 7) / 4

= -3 / 2 – 2 / 4

LCM of 2 and 4 is 4

= (-3 × 2 – 2 × 1) / 4

= (-6 – 2) / 4

= (-8) / 4

= -2

(ii) 5/3 + -7/6 + -2/3

Solution:

Taking numbers with same denominators together

(5 / 3 + -2 / 3) + -7 / 6

= (5 – 2) / 3 + -7 / 6

= 3 / 3 + (-7 / 6)

LCM of 3 and 6 is 6

= (3 × 2 + (-7 × 1)) / 6

= (6 – 7) / 6

= -1 / 6

(iii) 5/4 – 7/6 – (-2/3)

Solution:

This can be written as

5 / 4 – 7 / 6 + 2 / 3

LCM of 4,6 and 3 is 12

= (5 × 3 – 7 × 2 + 2 × 4) / 12

= (15 – 14 + 8) / 12

= (23 – 14) / 12

= 9 / 12

= 3 / 4

(iv) -2/5 – (-3/10) – (-4/7)

Solution:

This can be written as:

-2 / 5 + 3 / 10 + 4 / 7

LCM of 5,10 and 7 is 70

= (-2 × 14 + 3 × 7 + 4 × 10) / 70

= (-28 + 21 + 40) / 70

= (-28 + 61) / 70

= 33 / 70

(v) 5/6 + -2/5 – (-2/15)

Solution:

This can be written as

5 / 6 + -2 / 5 + 2 / 15

6 = 2 × 3

5 = 5 × 1

15 = 3 × 5

LCM is 2 × 3 × 5 = 30

= (5 × 5 + (-2 × 6) + 2 × 2) / 30

= (25 – 12 + 4) / 30

= (29 – 12) / 30

= 17 / 30

(vi) 3/8 – (-2/9) + (-5/36)

Solution:

This can be written as

3 / 8 + 2 / 9  – 5 / 36

8 = 2 × 2 × 2

9 = 3 × 3

36 = 2 × 2 × 3 × 3

LCM is 2 × 2 × 2 × 3 × 3 = 72

= (3 × 9 + 2 × 8 – 5 × 2) / 72

= (27 + 16 – 10) / 72

= (43 – 10) / 72

= 33 / 72

= 11 / 24

My Personal Notes arrow_drop_up