The PDF of RD Sharma Solutions for Class 7 Exercise 5.4 of Chapter 5 Operations on Rational numbers are given below. Students can access and download the PDF for free. The solutions to this exercise come with detailed explanations structured by BYJUâ€™S expert teachers that further makes learning and understanding of 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 on multiplying x by reciprocal of y defines division. The division includes dividend, quotient and divisor. To know more about these concepts, we suggest you to go through the PDF of RD Sharma Solutions for Class 7 containing solutions.

## Download the PDF of 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 Ã· (1/2) = 1 Ã— 2 = 2

(ii) Given 5 by (-5/7)

5 Ã· (-5/7) = 5 Ã— (-7/5)

= -7

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

(-3/4) Ã· (9/-16) = (-3/4) Ã— (-16/9)

= (-4/-3)

= (4/3)

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

(-7/8) Ã· (-21/16) = (-7/8) Ã— (16/-21)

= (-2/-3)

= (2/3)

(v) Given (7/-4) by (63/64)

(7/-4) Ã· (63/64) = (7/-4) Ã— (64/63)

= (-16/9)

(vi) Given 0 by (-7/5)

0 Ã· (-7/5) = 0 Ã— (5/7)

= 0

(vii) Given (-3/4) by -6

(-3/4) Ã· -6 = (-3/4) Ã— (1/-6)

= (-1/-8)

= (1/8)

(viii) Given (2/3) by (-7/12)

(2/3) Ã· (-7/12) = (2/3) Ã— (12/-7)

= (8/-7)

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

**(i) (2/5) Ã· (26/15)**

**(ii) (10/3) Ã· (-35/12)**

**(iii) -6 Ã· (-8/17)**

**(iv) (40/98) Ã· (-20)**

**Solution:**

(i) Given (2/5) Ã· (26/15)

(2/5) Ã· (26/15) = (2/5) Ã— (15/26)

= (3/13)

(ii) Given (10/3) Ã· (-35/12)

(10/3) Ã· (-35/12) = (10/3) Ã— (12/-35)

= (-40/35)

= (- 8/7)

(iii) Given -6 Ã· (-8/17)

-6 Ã· (-8/17) = -6 Ã— (17/-8)

= (102/8)

= (51/4)

(iv) Given (40/98) Ã· -20

(40/98) Ã· -20 = (40/98) Ã— (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 Ã— – 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 Ã— (-4/15) = (-8/9)

x = (-8/9) Ã· (-4/15)

x = (-8/9) Ã— (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 Ã— (-1/6) = (-23/9)

x = (-23/9) Ã· (-1/6)

x = (-23/9) Ã— (-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 Ã— (-15/28) = (-5/7)

x = (-5/7) Ã· (-15/28)

x = (-5/7) Ã— (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 Ã— (-8/13) = 24

x = 24 Ã· (-8/13)

x = 24 Ã— (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 Ã— (-3/4) = (-2/3)

x = (-2/3) Ã· (-3/4)

x = (-2/3) Ã— (4/-3)

x = (-8/-9)

x = (8/9)

**9. Find (x + y) Ã· (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) Ã· (x – y) = ((2/3) + (3/2)) Ã· ((2/3) â€“ (3/2))

= (4 + 9)/6 Ã· (4 â€“ 9)/6

= (4 + 9)/6 Ã— (6/ (4 â€“ 9)

= (4 + 9)/ (4 -9)

= (13/-5)

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

(x + y) Ã· (x – y) = ((2/5) + (1/2)) Ã· ((2/5) â€“ (1/2))

= (4 + 5)/10 Ã· (4 -5)/10

= (4 + 5)/10 Ã— (10/ (4 â€“ 5)

= (4 + 5)/ (4 -5)

= (9/-1)

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

(x + y) Ã· (x – y) = ((5/4) + (-1/3)) Ã· ((5/4) â€“ (-1/3))

= (15 – 4)/12 Ã· (15 + 4)/12

= (15 – 4)/12 Ã— (12/ (15 + 4)

= (15 – 4)/ (15 + 4)

= (11/19)

**10. The cost of \(7\frac{2}{3}\) meters of rope is Rs. \(12\frac{3}{4}\). Find its cost per meter. **

**Solution:**

Given cost of \(7\frac{2}{3}\) = (23/3) meters of rope is Rs. \(12\frac{3}{4}\) = (51/4)

Cost per meter = (51/4) Ã· (23/3)

= (51/4) Ã— (3/23)

= (153/92)

= Rs \(1\frac{61}{92}\)

**11. The cost of \(2\frac{1}{3}\) meters of cloth is Rs.\(75\frac{1}{4}\). Find the cost of cloth per meter. **

**Solution:**

Given cost of \(2\frac{1}{3}\) metres of rope = Rs. \(75\frac{1}{4}\)

Cost of cloth per meter = \(75\frac{1}{4}\) Ã· \(2\frac{1}{3}\)

= (301/4) Ã· (7/3)

= (301/4) Ã— (3/7)

= (129/4)

= Rs \(32\frac{1}{4}\)

**12. By what number should (-33/16) be divided to getÂ (-11/4)?**

**Solution:**

Let the required number be x

(-33/16) Ã· x = (-11/4)

x = (-33/16) Ã· (-11/4)

x = (-33/16) Ã— (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)) Ã· (-31/7) x (-1/2)

= ((-13/5) Ã— (7/7) + (12/7) Ã— (5/5)) Ã· (31/14)

= ((-91/35) + (60/35)) Ã· (31/14)

= (-31/35) Ã· (31/14)

= (-31/35) Ã— (14/31)

= (-14/35)

= (-2/5)

**14. Divide the sum of (65/12) and (8/3) by their difference.**

**Solution:**

((65/12) + (8/3)) Ã· ((65/12) â€“ (8/3))

= ((65/12) + (32/12)) Ã· ((65/12) â€“ (32/12))

= (65 + 32)/12 Ã· (65 -32)/12

= (65 + 32)/12 Ã— (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) meters