The PDF of RD Sharma Solutions for Class 7 Exercise 5.4 of Chapter 5 Operations on Rational Numbers is given below. Students can access and download the PDF for free. The solutions to this exercise come with detailed explanations collated by BYJU’S subject experts, that further make learning and understanding concepts an easy task. This exercise includes fifteen questions, all are based on the division of rational numbers. If x and y are two rational numbers, such that y is not equal to zero, then the result of dividing x by y is the rational number obtained by multiplying x by the reciprocal of y defines division. The division includes dividend, quotient and divisor. To learn more about these concepts, we suggest students go through the PDF of RD Sharma Solutions for Class 7 containing solutions.
RD Sharma Solutions for Class 7 Maths Chapter 5 – Operations on Rational Numbers Exercise 5.4
Access answers to Maths RD Sharma Solutions for Class 7 Chapter 5 – Operations on Rational Numbers Exercise 5.4
1. Divide:
(i) 1 by (1/2)
(ii) 5 by (-5/7)
(iii) (-3/4) by (9/-16)
(iv) (-7/8) by (-21/16)
(v) (7/-4) by (63/64)
(vi) 0 by (-7/5)
(vii) (-3/4) by -6
(viii) (2/3) by (-7/12)
Solution:
(i) Given 1 by (1/2)
1 ÷ (1/2) = 1 × 2 = 2
(ii) Given 5 by (-5/7)
5 ÷ (-5/7) = 5 × (-7/5)
= -7
(iii) Given (-3/4) by (9/-16)
(-3/4) ÷ (9/-16) = (-3/4) × (-16/9)
= (-4/-3)
= (4/3)
(iv) Given (-7/8) by (-21/16)
(-7/8) ÷ (-21/16) = (-7/8) × (16/-21)
= (-2/-3)
= (2/3)
(v) Given (7/-4) by (63/64)
(7/-4) ÷ (63/64) = (7/-4) × (64/63)
= (-16/9)
(vi) Given 0 by (-7/5)
0 ÷ (-7/5) = 0 × (5/7)
= 0
(vii) Given (-3/4) by -6
(-3/4) ÷ -6 = (-3/4) × (1/-6)
= (-1/-8)
= (1/8)
(viii) Given (2/3) by (-7/12)
(2/3) ÷ (-7/12) = (2/3) × (12/-7)
= (8/-7)
2. Find the value and express as a rational number in standard form:
(i) (2/5) ÷ (26/15)
(ii) (10/3) ÷ (-35/12)
(iii) -6 ÷ (-8/17)
(iv) (40/98) ÷ (-20)
Solution:
(i) Given (2/5) ÷ (26/15)
(2/5) ÷ (26/15) = (2/5) × (15/26)
= (3/13)
(ii) Given (10/3) ÷ (-35/12)
(10/3) ÷ (-35/12) = (10/3) × (12/-35)
= (-40/35)
= (- 8/7)
(iii) Given -6 ÷ (-8/17)
-6 ÷ (-8/17) = -6 × (17/-8)
= (102/8)
= (51/4)
(iv) Given (40/98) ÷ -20
(40/98) ÷ -20 = (40/98) × (1/-20)
= (-2/98)
= (-1/49)
3. The product of two rational numbers is 15. If one of the numbers is -10, find the other.
Solution:
Let required number be x
x × – 10 = 15
x = (15/-10)
x = (3/-2)
x = (-3/2)
Hence the number is (-3/2)
4. The product of two rational numbers is (- 8/9). If one of the numbers is (- 4/15), find the other.
Solution:
Given product of two numbers = (-8/9)
One of them is (-4/15)
Let the required number be x
x × (-4/15) = (-8/9)
x = (-8/9) ÷ (-4/15)
x = (-8/9) × (15/-4)
x = (-120/-36)
x = (10/3)
5. By what number should we multiply (-1/6) so that the product may be (-23/9)?
Solution:
Given product = (-23/9)
One number is (-1/6)
Let the required number be x
x × (-1/6) = (-23/9)
x = (-23/9) ÷ (-1/6)
x = (-23/9) × (-6/1)
x = (138/9)
x = (46/3)
6. By what number should we multiply (-15/28) so that the product may be (-5/7)?
Solution:
Given product = (-5/7)
One number is (-15/28)
Let the required number be x
x × (-15/28) = (-5/7)
x = (-5/7) ÷ (-15/28)
x = (-5/7) × (28/-15)
x = (-4/-3)
x = (4/3)
7. By what number should we multiply (-8/13) so that the product may be 24?
Solution:
Given product = 24
One of the number is = (-8/13)
Let the required number be x
x × (-8/13) = 24
x = 24 ÷ (-8/13)
x = 24 × (13/-8)
x = -39
8. By what number should (-3/4) be multiplied in order to produce (-2/3)?
Solution:
Given product = (-2/3)
One of the number is = (-3/4)
Let the required number be x
x × (-3/4) = (-2/3)
x = (-2/3) ÷ (-3/4)
x = (-2/3) × (4/-3)
x = (-8/-9)
x = (8/9)
9. Find (x + y) ÷ (x – y), if
(i) x = (2/3), y = (3/2)
(ii) x = (2/5), y = (1/2)
(iii) x = (5/4), y = (-1/3)
Solution:
(i) Given x = (2/3), y = (3/2)
(x + y) ÷ (x – y) = ((2/3) + (3/2)) ÷ ((2/3) – (3/2))
= (4 + 9)/6 ÷ (4 – 9)/6
= (4 + 9)/6 × (6/ (4 – 9)
= (4 + 9)/ (4 -9)
= (13/-5)
(ii) Given x = (2/5), y = (1/2)
(x + y) ÷ (x – y) = ((2/5) + (1/2)) ÷ ((2/5) – (1/2))
= (4 + 5)/10 ÷ (4 -5)/10
= (4 + 5)/10 × (10/ (4 – 5)
= (4 + 5)/ (4 -5)
= (9/-1)
(iii) Given x = (5/4), y = (-1/3)
(x + y) ÷ (x – y) = ((5/4) + (-1/3)) ÷ ((5/4) – (-1/3))
= (15 – 4)/12 ÷ (15 + 4)/12
= (15 – 4)/12 × (12/ (15 + 4)
= (15 – 4)/ (15 + 4)
= (11/19)
10. The cost of
Solution:
Given cost of
Cost per meter = (51/4) ÷ (23/3)
= (51/4) × (3/23)
= (153/92)
= Rs
11. The cost of
Solution:
Given cost of
Cost of cloth per meter =
= (301/4) ÷ (7/3)
= (301/4) × (3/7)
= (129/4)
= Rs
12. By what number should (-33/16) be divided to get (-11/4)?
Solution:
Let the required number be x
(-33/16) ÷ x = (-11/4)
x = (-33/16) ÷ (-11/4)
x = (-33/16) × (4/-11)
x = (3/4)
13. Divide the sum of (-13/5) and (12/7) by the product of (-31/7) and (-1/2)
Solution:
Given
((-13/5) + (12/7)) ÷ (-31/7) x (-1/2)
= ((-13/5) × (7/7) + (12/7) × (5/5)) ÷ (31/14)
= ((-91/35) + (60/35)) ÷ (31/14)
= (-31/35) ÷ (31/14)
= (-31/35) × (14/31)
= (-14/35)
= (-2/5)
14. Divide the sum of (65/12) and (8/3) by their difference.
Solution:
((65/12) + (8/3)) ÷ ((65/12) – (8/3))
= ((65/12) + (32/12)) ÷ ((65/12) – (32/12))
= (65 + 32)/12 ÷ (65 -32)/12
= (65 + 32)/12 × (12/ (65 – 32)
= (65 + 32)/ (65 – 32)
= (97/33)
15. If 24 trousers of equal size can be prepared in 54 metres of cloth, what length of cloth is required for each trouser?
Solution:
Given material required for 24 trousers = 54m
Cloth required for 1 trouser = (54/24)
= (9/4) metres
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