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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)Read More
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