R. D. Sharma | EXERCISE 1.7 PAGE NO: 1.35

 

EXERCISE 1.7 PAGE NO: 1.35

1. Divide:

(i) 1 by 1/2

Solution:

1/1/2 = 1 × 2/1 = 2

(ii) 5 by -5/7

Solution:

5/-5/7 = 5 × 7/-5 = -7

(iii) -3/4 by 9/-16

Solution:

(-3/4) / (9/-16)

(-3/4) × -16/9 = 4/3

(iv) -7/8 by -21/16

Solution:

(-7/8) / (-21/16)

(-7/8) × 16/-21 = 2/3

(v) 7/-4 by 63/64

Solution:

(7/-4) / (63/64)

(7/-4) × 64/63 = -16/9

(vi) 0 by -7/5

Solution:

0 / (7/5) = 0

(vii) -3/4 by -6

Solution:

(-3/4) / -6

(-3/4) × 1/-6 = 1/8

(viii) 2/3 by -7/12

Solution:

(2/3) / (-7/12)

(2/3) × 12/-7 = -8/7

(ix) -4 by -3/5

Solution:

-4 / (-3/5)

-4 × 5/-3 = 20/3

(x) -3/13 by -4/65

Solution:

(-3/13) / (-4/65)

(-3/13) × (65/-4) = 15/4

2. Find the value and express as a rational number in standard form:

(i) 2/5 ÷ 26/15

Solution:

(2/5) / (26/15)

(2/5) × (15/26)

(2/1) × (3/26) = (2×3)/ (1×26) = 6/26 = 3/13

(ii) 10/3 ÷ -35/12

Solution:

(10/3) / (-35/12)

(10/3) × (12/-35)

(10/1) × (4/-35) = (10×4)/ (1×-35) = -40/35 = -8/7

(iii) -6 ÷ -8/17

Solution:

-6 / (-8/17)

-6 × (17/-8)

-3 × (17/-4) = (-3×17)/ (1×-4) = 51/4

(iv) -40/99 ÷ -20

Solution:

(-40/99) / -20

(-40/99) × (1/-20)

(-2/99) × (1/-1) = (-2×1)/ (99×-1) = 2/99

(v) -22/27 ÷ -110/18

Solution:

(-22/27) / (-110/18)

(-22/27) × (18/-110)

(-1/9) × (6/-5)

(-1/3) × (2/-5) = (-1×2) / (3×-5) = 2/15

(vi) -36/125 ÷ -3/75

Solution:

(-36/125) / (-3/75)

(-36/125) × (75/-3)

(-12/25) × (15/-1)

(-12/5) × (3/-1) = (-12×3) / (5×-1) = 36/5

3. The product of two rational numbers is 15. If one of the numbers is -10, find the other.

Solution:

We know that the product of two rational numbers = 15

One of the number = -10

∴ other number can be obtained by dividing the product by the given number.

Other number = 15/-10

= -3/2

4. The product of two rational numbers is -8/9. If one of the numbers is -4/15, find the other.

Solution:

We know that the product of two rational numbers = -8/9

One of the number = -4/15

∴ other number is obtained by dividing the product by the given number.

Other number = (-8/9)/(-4/15)

= (-8/9) × (15/-4)

= (-2/3) × (5/-1)

= (-2×5) /(3×-1)

= -10/-3

= 10/3

5. By what number should we multiply -1/6 so that the product may be -23/9?

Solution:

Let us consider a number = x

So, x × -1/6 = -23/9

x = (-23/9)/(-1/6)

x = (-23/9) × (6/-1)

= (-23/3) × (2×-1)

= (-23×-2)/(3×1)

= 46/3

6. By what number should we multiply -15/28 so that the product may be -5/7?

Solution:

Let us consider a number = x

So, x × -15/28 = -5/7

x = (-5/7)/(-15/28)

x = (-5/7) × (28/-15)

= (-1/1) × (4×-3)

= 4/3

7. By what number should we multiply -8/13 so that the product may be 24?

Solution:

Let us consider a number = x

So, x × -8/13 = 24

x = (24)/(-8/13)

x = (24) × (13/-8)

= (3) × (13×-1)

= -39

8. By what number should -3/4 be multiplied in order to produce 2/3?

Solution:

Let us consider a number = x

So, x × -3/4 = 2/3

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

x = (2/3) × (4/-3)

= -8/9

9. Find (x+y) ÷ (x-y), if

(i) x= 2/3, y= 3/2

Solution:

(x+y) ÷ (x-y)

(2/3 + 3/2) / (2/3 – 3/2)

((2×2 + 3×3)/6) / ((2×2 – 3×3)/6)

((4+9)/6) / ((4-9)/6)

(13/6) / (-5/6)

(13/6) × (6/-5)

-13/5

(ii) x= 2/5, y= 1/2

Solution:

(x+y) ÷ (x-y)

(2/5 + 1/2) / (2/5 – 1/2)

((2×2 + 1×5)/10) / ((2×2 – 1×5)/10)

((4+5)/10) / ((4-5)/10)

(9/10) / (-1/10)

(9/10) × (10/-1)

-9

(iii) x= 5/4, y= -1/3

Solution:

(x+y) ÷ (x-y)

(5/4 – 1/3) / (5/4 + 1/3)

((5×3 – 1×4)/12) / ((5×3 + 1×4)/12)

((15-4)/12) / ((15+4)/12)

(11/12) / (19/12)

(11/12) × (12/19)

11/19

(iv) x= 2/7, y= 4/3

Solution:

(x+y) ÷ (x-y)

(2/7 + 4/3) / (2/7 – 4/3)

((2×3 + 4×7)/21) / ((2×3 – 4×7)/21)

((6+28)/21) / ((6-28)/21)

(34/21) / (-22/21)

(34/21) × (21/-22)

-34/22

-17/11

(v) x= 1/4, y= 3/2

Solution:

(x+y) ÷ (x-y)

(1/4 + 3/2) / (1/4 – 3/2)

((1×1 + 3×2)/4) / ((1×1 – 3×2)/4)

((1+6)/4) / ((1-6)/4)

(7/4) / (-5/4)

(7/4) × (4/-5) = -7/5

10. The cost of

$\begin{array}{l}7\frac{2}{3}\end{array}$

meters of rope is Rs 12 ¾. Find the cost per meter.

Solution:

We know that 23/3 meters of rope = Rs 51/4

Let us consider a number = x

So, x × 23/3 = 51/4

x = (51/4)/(23/3)

x = (51/4) × (3/23)

= (51×3) / (4×23)

= 153/92

=

$\begin{array}{l}1\frac{61}{92}\end{array}$

∴ cost per meter is Rs

$\begin{array}{l}1\frac{61}{92}\end{array}$

11. The cost of

$\begin{array}{l}2\frac{1}{3}\end{array}$

meters of cloth is Rs 75 ¼. Find the cost of cloth per meter.

Solution:

We know that 7/3 meters of cloth = Rs 301/4

Let us consider a number = x

So, x × 7/3 = 301/4

x = (301/4)/(7/3)

x = (301/4) × (3/7)

= (301×3) / (4×7)

= (43×3) / (4×1)

= 129/4

= 32.25

∴ cost of cloth per meter is Rs 32.25

12. By what number should -33/16 be divided to get -11/4?

Solution:

Let us consider a number = x

So, (-33/16)/x = -11/4

-33/16 = x × -11/4

x = (-33/16) / (-11/4)

= (-33/16) × (4/-11)

= (-33×4)/(16×-11)

= (-3×1)/(4×-1)

= ¾

13. Divide the sum of -13/5 and 12/7 by the product of -31/7 and -1/2.

Solution:

sum of -13/5 and 12/7

-13/5 + 12/7

((-13×7) + (12×5))/35

(-91+60)/35

-31/35

Product of -31/7 and -1/2

-31/7 × -1/2

(-31×-1)/(7×2)

31/14

∴ by dividing the sum and the product we get,

(-31/35) / (31/14)

(-31/35) × (14/31)

(-31×14)/(35×31)

-14/35

-2/5

14. Divide the sum of 65/12 and 12/7 by their difference.

Solution:

The sum is 65/12 + 12/7

The difference is 65/12 – 12/7

When we divide, (65/12 + 12/7) / (65/12 – 12/7)

((65×7 + 12×12)/84) / ((65×7 – 12×12)/84)

((455+144)/84) / ((455 – 144)/84)

(599/84) / (311/84)

599/84 × 84/311

599/311

15. If 24 trousers of equal size can be prepared in 54 meters of cloth, what length of cloth is required for each trouser?

Solution:

We know that total number trousers = 24

Total length of the cloth = 54

Length of the cloth required for each trouser = total length of the cloth/number of trousers

= 54/24

= 9/4

∴ 9/4 meters is required for each trouser.

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