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Operations On Rational Numbers (Exercise 5.4) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

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 Page 1


 
 
 
 
 
 
 
Exercise 5.4         Page No: 5.13 
 
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 
Page 2


 
 
 
 
 
 
 
Exercise 5.4         Page No: 5.13 
 
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. 
Page 3


 
 
 
 
 
 
 
Exercise 5.4         Page No: 5.13 
 
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) 
Page 4


 
 
 
 
 
 
 
Exercise 5.4         Page No: 5.13 
 
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: 
Page 5


 
 
 
 
 
 
 
Exercise 5.4         Page No: 5.13 
 
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 7 2/3 meters of rope is Rs. 12 3/4. Find its cost per meter.
Solution: 
Given cost of 7 2/3 = (23/3) meters 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 meters of cloth is Rs. 75 1/4. Find the cost of cloth per meter.
Solution: 
Given cost of 2 1/3 metres 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) 
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