RD Sharma Solutions for Class 8 Chapter 1 - Rational Numbers Exercise 1.5

RD Sharma Class 8 Solutions Chapter 1 Ex 1.5 PDF Free Download

In Exercise 1.5 of RD Sharma Class 8 Maths Chapter 1 Rational numbers, we shall discuss problems based on the multiplication of rational numbers. Students can refer and download RD Sharma Class 8 Maths from the links provided below. Solutions are solved by our experts in order to help students in learning the concepts with ease from the textbook.

Download PDF of RD Sharma Solutions for Class 8 Maths Exercise 1.5 Chapter 1 Rational Numbers

 

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rd sharma class 8 maths chapter 1
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rd sharma class 8 maths chapter 1
rd sharma class 8 maths chapter 1
rd sharma class 8 maths chapter 1
rd sharma class 8 maths chapter 1

 

Access Answers to RD Sharma Solutions for Class 8 Maths Exercise 1.5 Chapter 1 Rational Numbers

1. Multiply:

(i) 7/11 by 5/4

Solution:

7/11 by 5/4

(7/11) × (5/4) = (7×5)/(11×4)

= 35/44

(ii) 5/7 by -3/4

Solution:

5/7 by -3/4

(5/7) × (-3/4) = (5×-3)/(7×4)

= -15/28

(iii) -2/9 by 5/11

Solution:

-2/9 by 5/11

(-2/9) × (5/11) = (-2×5)/(9×11)

= -10/99

(iv) -3/17 by -5/-4

Solution:

-3/17 by -5/-4

(-3/17) × (-5/-4) = (-3×-5)/(17×-4)

= 15/-68

= -15/68

(v) 9/-7 by 36/-11

Solution:

9/-7 by 36/-11

(9/-7) × (36/-11) = (9×36)/(-7×-11)

= 324/77

(vi) -11/13 by -21/7

Solution:

-11/13 by -21/7

(-11/13) × (-21/7) = (-11×-21)/(13×7)

= 231/91 = 33/13

(vii) -3/5 by -4/7

Solution:

-3/5 by -4/7

(-3/5) × (-4/7) = (-3×-4)/(5×7)

= 12/35

(viii) -15/11 by 7

Solution:

-15/11 by 7

(-15/11) × 7 = (-15×7)/11

= -105/11

2. Multiply:

(i) -5/17 by 51/-60

Solution:

-5/17 by 51/-60

(-5/17) × (51/-60) = (-5×51)/(17×-60)

= -255/-1020

Further can divide by 255 we get,

-255/-1020 = 1/4

(ii) -6/11 by -55/36

Solution:

-6/11 by -55/36

(-6/11) × (-55/36) = (-6×-55)/(11×36)

= 330/396

Further can divide by 66 we get,

330/396 = 5/6

(iii) -8/25 by -5/16

Solution:

-8/25 by -5/16

(-8/25) × (-5/16) = (-8×-5)/(25×16)

= 40/400

Further can divide by 40 we get,

40/400 = 1/10

(iv) 6/7 by -49/36

Solution:

6/7 by -49/36

(6/7) × (-49/36) = (6×-49)/(7×36)

= 294/252

Further can divide by 42 we get,

294/252 = -7/6

(v) 8/-9 by -7/-16

Solution:

8/-9 by -7/-16

(8/-9) × (-7/-16) = (8×-7)/(-9×-16)

= -56/144

Further can divide by 8 we get,

-56/144 = -7/18

(vi) -8/9 by 3/64

Solution:

-8/9 by 3/64

(-8/9) × (3/64) = (-8×3)/(9×64)

= -24/576

Further can divide by 24 we get,

-24/576 = -1/24

3. Simplify each of the following and express the result as a rational number in standard form:

(i) (-16/21) × (14/5)

Solution:

(-16/21) × (14/5) = (-16/3) × (2/5) (divisible by 7)

= (-16×2)/(3×5)

= -32/15

(ii) (7/6) × (-3/28)

Solution:

(7/6) × (-3/28) = (1/2) × (-1/4) (divisible by 7 and 3)

= -1/8

(iii) (-19/36) × 16

Solution:

-19/36 × 16 = (-19/9) × 4 (divisible by 4)

= (-19×4)/9 = -76/9

(iv) (-13/9) × (27/-26)

Solution:

(-13/9) × (27/-26) = (-1/1) × (3/-2) (divisible by 13 and 9)

= -3/-2 = 3/2

(v) (-9/16) × (-64/-27)

Solution:

(-9/16) × (-64/-27) = (-1/1) × (-4/-3) (divisible by 9 and 16)

= 4/-3 = -4/3

(vi) (-50/7) × (14/3)

Solution:

(-50/7) × (14/3) = (-50/1) × (2/3) (divisible by 7)

= (-50×2)/(1×3)

= -100/3

(vii) (-11/9) × (-81/-88)

Solution:

(-11/9) × (-81/-88) = (-1/1) × (-9/-8) (divisible by 11 and 9)

= (-1×-9)/(1×-8)

= 9/-8 = -9/8

(viii) (-5/9) × (72/-25)

Solution:

(-5/9) × (72/-25) = (-1/1) × (8/-5) (divisible by 5 and 9)

= (-1×8)/(1×-5)

= -8/-5 = 8/5

4. Simplify:

(i) ((25/8) × (2/5)) – ((3/5) × (-10/9))

Solution:

((25/8) × (2/5)) – ((3/5) × (-10/9)) = (25×2)/(8×5) – (3×-10)/(5×9)

= 50/40 – -30/45

= 5/4 + 2/3 (divisible by 5 and 3)

By taking LCM for 4 and 3 which is 12

= ((5×3) + (2×4))/12

= (15+8)/12

= 23/12

(ii) ((1/2) × (1/4)) + ((1/2) × 6)

Solution:

((1/2) × (1/4)) + ((1/2) × 6) = (1×1)/(2×4) + (1×3) (divisible by 2)

= 1/8 +3

By taking LCM for 8 and 1 which is 8

= ((1×1) + (3×8))/8

= (1+24)/8

= 25/8

(iii) (-5 × (2/15)) – (-6 × (2/9))

Solution:

(-5 × (2/15)) – (-6 × (2/9)) = (-1 × (2/3)) – (-2 × (2/3)) (divisible by 5 and 3)

= (-2/3) + (4/3)

Since the denominators are same we can add directly

= (-2+4)/3

= 2/3

(iv) ((-9/4) × (5/3)) + ((13/2) × (5/6))

Solution:

((-9/4) × (5/3)) + ((13/2) × (5/6)) = (-9×5)/(4×3) + (13×5)/(2×6)

= -45/12 + 65/12

Since the denominators are same we can add directly

= (-45+65)/12

= 20/12 (divisible by 2)

= 10/6 (divisible by 2)

= 5/3

(v) ((-4/3) × (12/-5)) + ((3/7) × (21/15))

Solution:

((-4/3) × (12/-5)) + ((3/7) × (21/15)) = ((-4/1) × (4/-5)) + ((1/1) × (3/5)) (divisible by 3, 7)

= (-4×4)/(1×-5) + (1×3)/(1×5)

= -16/-5 + 3/5

Since the denominators are same we can add directly

= (16+3)/5

= 19/5

(vi) ((13/5) × (8/3)) – ((-5/2) × (11/3))

Solution:

((13/5) × (8/3)) – ((-5/2) × (11/3)) = (13×8)/(5×3) – (-5×11)/(2×3)

= 104/15 + 55/6

By taking LCM for 15 and 6 which is 30

= ((104×2) + (55×5))/30

= (208+275)/30

= 483/30

(vii) ((13/7) × (11/26)) – ((-4/3) × (5/6))

Solution:

((13/7) × (11/26)) – ((-4/3) × (5/6)) = ((1/7) × (11/2)) – ((-2/3) × (5/3)) (divisible by 13, 2)

= (1×11)/(7×2) – (-2×5)/(3×3)

= 11/14 + 10/9

By taking LCM for 14 and 9 which is 126

= ((11×9) + (10×14))/126

= (99+140)/126

= 239/126

(viii) ((8/5) × (-3/2)) + ((-3/10) × (11/16))

Solution:

((8/5) × (-3/2)) + ((-3/10) × (11/16)) = ((4/5) × (-3/1)) + ((-3/10) × (11/16)) (divisible by 2)

= (4×-3)/(5×1) + (-3×11)/(10×16)

= -12/5 – 33/160

By taking LCM for 5 and 160 which is 160

= ((-12×32) – (33×1))/160

= (-384 – 33)/160

= -417/160

5. Simplify:

(i) ((3/2) × (1/6)) + ((5/3) × (7/2) – (13/8) × (4/3))

Solution:

((3/2) × (1/6)) + ((5/3) × (7/2) – (13/8) × (4/3)) =

((1/2) × (1/2)) + ((5/3) × (7/2) – (13/2) × (1/3))

(1×1)/(2×2) + (5×7)/(3×2) – (13×1)/(2×3)

1/4 + 35/6 – 13/6

By taking LCM for 4 and 6 which is 24

((1×6) + (35×4) – (13×4))/24

(6 + 140 – 52)/24

94/24

Further divide by 2 we get, 94/24 = 47/12

(ii) ((1/4) × (2/7)) – ((5/14) × (-2/3) + (3/7) × (9/2))

Solution:

((1/4) × (2/7)) – ((5/14) × (-2/3) + (3/7) × (9/2)) =

((1/2) × (1/7)) – ((5/7) × (-1/3) + (3/7) × (9/2))

(1×1)/(2×7) – (5×-1)/(7×3) + (3×9)/(7×2)

1/14 + 5/21 + 27/14

By taking LCM for 14 and 21 which is 42

((1×3) + (5×2) + (27×3))/42

(3 + 10 + 81)/42

94/42

Further divide by 2 we get, 94/42 = 47/21

(iii) ((13/9) × (-15/2)) + ((7/3) × (8/5) + (3/5) × (1/2))

Solution:

((13/3) × (-5/2)) + ((7/3) × (8/5) + (3/5) × (1/2)) =

(13×-5)/(3×2) + (7×8)/(3×5) + (3×1)/(5×2)

-65/6 + 56/15 + 3/10

By taking LCM for 6, 15 and 10 which is 30

((-65×5) + (56×2) + (3×3))/30

(-325 + 112 + 9)/30

-204/30

Further divide by 2 we get, -204/30 = -102/15

(iv) ((3/11) × (5/6)) – ((9/12) × (4/3) + (5/13) × (6/15))

Solution:

((3/11) × (5/6)) – ((9/12) × (4/3) + (5/13) × (6/15)) =

((1/11) × (5/2)) – ((1/1) × (1/1) + (1/13) × (2/1))

(1×5)/(11×2) – 1/1 + (1×2)/(13×1)

5/22 – 1/1 + 2/13

By taking LCM for 22, 1 and 13 which is 286

((5×13) – (1×286) + (2×22))/286

(65 – 286 + 44)/286

-177/286


Access other Exercises of RD Sharma Solutions for Class 8 Maths Chapter 1 Rational Numbers

Exercise 1.1 Solutions 4 Questions

Exercise 1.2 Solutions 6 Questions

Exercise 1.3 Solutions 15 Questions

Exercise 1.4 Solutions 3 Questions

Exercise 1.6 Solutions 8 Questions

Exercise 1.7 Solutions 15 Questions

Exercise 1.8 Solutions 7 Questions

RD Sharma Solutions for Class 8 Maths Exercise 1.5 Chapter 1

Class 8 Maths Chapter 1 Rational Numbers Exercise 1.5 is based on the multiplication of rational numbers. These solutions are prepared by experienced faculty in accordance with CBSE syllabus for 8th standard. The exercise-wise solutions are explained in a simple and easily understandable language which helps students excel in their exams. Download free RD Sharma Class 8 Solutions Chapter 1 in PDF format which provides answers to all the questions.

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