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 to and download RD Sharma Class 8 Solutions for Maths Exercise 1.5 from the links provided below. Problems discussed in the textbook are solved by our subject experts in order to help students in learning the concepts with ease.
RD Sharma Solutions for Class 8 Maths Exercise 1.5 Chapter 1 Rational Numbers
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 the same, we can add them 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 the same, we can add them 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 the same, we can add them 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
RD Sharma Solutions for Class 8 Maths Exercise 1.5 Chapter 1 Rational Numbers
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 the CBSE syllabus for Class 8. The exercise-wise solutions are explained in a simple and easily understandable language to help students excel in the annual exams. Download the free RD Sharma Solutions Chapter 1 in PDF format, which provide answers to all the questions.
Comments