Exercise 5.4
1. Divide:
Solution:
2. Find the value and express as rational number is standard form:
(i) (2/5) ÷(26/15)
Solution:
Given (2/5) ÷(26/15)
(2/5) ÷(26/15) = (2/5)×(15/26)
= (3/13)
(ii) (10/3) ÷(-35/12)
Solution:
Given (10/3) ÷(-35/12)
(10/3) ÷(-35/12) = (2/5)×(12/-35)
= (-40/35)
= (-8/7)
(iii) – 6÷(-8/17)
Solution:
Given – 6 ÷(- 8/17)
– 6 ÷(- 8/17) = – 6 ×(17/-8)
= (102/8)
= (51/4)
(iv) (40/98) ÷(-20)
Solution:
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 the number to be found be x
x ×- 10 = 15
x = 15/(-10)
x = 3/(-2)
x = (-3)/2
Then, the number is x = (-3)/2
4. The product of two rational numbers is – 8/9. If one of the numbers is – 4/15, find the other.
Solution:
5. By what number should we multiply -1/6 so that the product may be -23/9?
Solution:
6. By what number should we multiply -15/28 so that the product may be -5/7?
Solution:
Given product 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 we multiply (-8/13) so that the product may be 24?
Solution:
24 ÷ -8/13
=> 24 x -13/8
=> -39
8. By what number should -3/4 be multiplied in order to produce -2/3?
Solution:
Hence the number is x = 8/9
9. Find (x+y) (x-y), if
(i) x = (2/3), (3/2)
Sol:
(i) Given x = (2/3), (3/2)
(x+y) ÷(x-y) = ((2/3)+ (3/2))÷((2/3) – (3/2))
=(4+9)/6÷(4-9)/6)
= (4+9)/ (4-9)
= (13/-5)
(ii) x= (2/5), y = (1/2)
Sol:
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) x = (5/4), y = (-1/3)
Sol:
Given x = (5/4), y = (-1/3)
(x+y) ÷(x-y) = ((5/4) + (1/3)) ÷((5/4) – (-1/3))
= (15-4)/ 12 ×(12/ (15+4)
= (15-4)/(15+4)
= (11/19)
10. The cost of 7(2/3) metres of rope is Rs. 12(3/4). Find its cost per metre. 7(2/3) metres of rope cost = Rs. 12(3/4).
Solution:
Given cost of 7 (2/3) = 23/3) metres of rope is Rs. 12 (3/4)= (51/4)
Cost per meter = (51/4) ÷(23/3)
= (51/4)×(3/23)
= (153/92)
=Rs 1 (61/92)
11. The cost of 2(1/3) metres of cloth is Rs.75 1/4. Find the cost of cloth per metre. 2(1/3) metres of rope cost = Rs. 75(1/4)
Solution:
Given cost of 2 (1/3) = (23/3) meters of rope = Rs. 75 (1/4)
Cost of cloth per meter = 75 (1/4) ÷2 (1/3)
= (301/4) ÷(7/3)
= (301/4) ×(3/7)
= (129/4)
= Rs 32 (1/4)
12. By what number should (-33)/16 be divided to get (-11)/4?
Solution:
The number is x = 3/4
13. Divide the sum of (-13)/5 and 12/7 by the product of (-31)/7 and (-1)/2
Solution:
14. Divide the sum of 65/12 and 8/3 by their difference.
Solution:
((65/12 + (8/7)) ÷((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:
9/4 metres of cloth is required to make each trouser