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Page 1 Exercise 5.2 Page No: 5.7 1. Subtract the first rational number from the second in each of the following: (i) (3/8), (5/8) (ii) (-7/9), (4/9) (iii) (-2/11), (-9/11) (iv) (11/13), (-4/13) Solution: (i) Given (3/8), (5/8) (5/8) – (3/8) = (5 – 3)/8 = (2/8) = (1/4) (ii) Given (-7/9), (4/9) (4/9) – (-7/9) = (4/9) + (7/9) = (4 + 7)/9 = (11/9) (iii) Given (-2/11), (-9/11) (-9/11) – (-2/11) = (-9/11) + (2/11) = (-9 + 2)/ 11 = (-7/11) (iv) Given (11/13), (-4/13) (-4/13) – (11/13) = (-4 – 11)/13 = (-15/13) 2. Evaluate each of the following: (i) (2/3) – (3/5) (ii) (-4/7) – (2/-3) (iii) (4/7) – (-5/-7) (iv) -2 – (5/9) Solution: (i) Given (2/3) – (3/5) The LCM of 3 and 5 is 15 Page 2 Exercise 5.2 Page No: 5.7 1. Subtract the first rational number from the second in each of the following: (i) (3/8), (5/8) (ii) (-7/9), (4/9) (iii) (-2/11), (-9/11) (iv) (11/13), (-4/13) Solution: (i) Given (3/8), (5/8) (5/8) – (3/8) = (5 – 3)/8 = (2/8) = (1/4) (ii) Given (-7/9), (4/9) (4/9) – (-7/9) = (4/9) + (7/9) = (4 + 7)/9 = (11/9) (iii) Given (-2/11), (-9/11) (-9/11) – (-2/11) = (-9/11) + (2/11) = (-9 + 2)/ 11 = (-7/11) (iv) Given (11/13), (-4/13) (-4/13) – (11/13) = (-4 – 11)/13 = (-15/13) 2. Evaluate each of the following: (i) (2/3) – (3/5) (ii) (-4/7) – (2/-3) (iii) (4/7) – (-5/-7) (iv) -2 – (5/9) Solution: (i) Given (2/3) – (3/5) The LCM of 3 and 5 is 15 Consider (2/3) = (2/3) × (5/5) = (10/15) Now again (3/5) = (3/5) × (3/3) = (9/15) (2/3) – (3/5) = (10/15) – (9/15) = (1/15) (ii) Given (-4/7) – (2/-3) The LCM of 7 and 3 is 21 Consider (-4/7) = (-4/7) × (3/3) = (-12/21) Again (2/-3) = (-2/3) × (7/7) = (-14/21) (-4/7) – (2/-3) = (-12/21) – (-14/21) = (-12 + 14)/21 = (2/21) (iii) Given (4/7) – (-5/-7) (4/7) – (5/7) = (4 -5)/7 = (-1/7) (iv) Given -2 – (5/9) Consider (-2/1) = (-2/1) × (9/9) = (-18/9) -2 – (5/9) = (-18/9) – (5/9) = (-18 -5)/9 = (-23/9) 3. The sum of the two numbers is (5/9). If one of the numbers is (1/3), find the other. Solution: Given sum of two numbers is (5/9) And one them is (1/3) Let the unknown number be x x + (1/3) = (5/9) x = (5/9) – (1/3) LCM of 3 and 9 is 9 Consider (1/3) = (1/3) × (3/3) = (3/9) On substituting we get x = (5/9) – (3/9) x = (5 – 3)/9 x = (2/9) Page 3 Exercise 5.2 Page No: 5.7 1. Subtract the first rational number from the second in each of the following: (i) (3/8), (5/8) (ii) (-7/9), (4/9) (iii) (-2/11), (-9/11) (iv) (11/13), (-4/13) Solution: (i) Given (3/8), (5/8) (5/8) – (3/8) = (5 – 3)/8 = (2/8) = (1/4) (ii) Given (-7/9), (4/9) (4/9) – (-7/9) = (4/9) + (7/9) = (4 + 7)/9 = (11/9) (iii) Given (-2/11), (-9/11) (-9/11) – (-2/11) = (-9/11) + (2/11) = (-9 + 2)/ 11 = (-7/11) (iv) Given (11/13), (-4/13) (-4/13) – (11/13) = (-4 – 11)/13 = (-15/13) 2. Evaluate each of the following: (i) (2/3) – (3/5) (ii) (-4/7) – (2/-3) (iii) (4/7) – (-5/-7) (iv) -2 – (5/9) Solution: (i) Given (2/3) – (3/5) The LCM of 3 and 5 is 15 Consider (2/3) = (2/3) × (5/5) = (10/15) Now again (3/5) = (3/5) × (3/3) = (9/15) (2/3) – (3/5) = (10/15) – (9/15) = (1/15) (ii) Given (-4/7) – (2/-3) The LCM of 7 and 3 is 21 Consider (-4/7) = (-4/7) × (3/3) = (-12/21) Again (2/-3) = (-2/3) × (7/7) = (-14/21) (-4/7) – (2/-3) = (-12/21) – (-14/21) = (-12 + 14)/21 = (2/21) (iii) Given (4/7) – (-5/-7) (4/7) – (5/7) = (4 -5)/7 = (-1/7) (iv) Given -2 – (5/9) Consider (-2/1) = (-2/1) × (9/9) = (-18/9) -2 – (5/9) = (-18/9) – (5/9) = (-18 -5)/9 = (-23/9) 3. The sum of the two numbers is (5/9). If one of the numbers is (1/3), find the other. Solution: Given sum of two numbers is (5/9) And one them is (1/3) Let the unknown number be x x + (1/3) = (5/9) x = (5/9) – (1/3) LCM of 3 and 9 is 9 Consider (1/3) = (1/3) × (3/3) = (3/9) On substituting we get x = (5/9) – (3/9) x = (5 – 3)/9 x = (2/9) 4. The sum of two numbers is (-1/3). If one of the numbers is (-12/3), find the other. Solution: Given sum of two numbers = (-1/3) One of them is (-12/3) Let the required number be x x + (-12/3) = (-1/3) x = (-1/3) – (-12/3) x = (-1/3) + (12/3) x = (-1 + 12)/3 x = (11/3) 5. The sum of two numbers is (– 4/3). If one of the numbers is -5, find the other. Solution: Given sum of two numbers = (-4/3) One of them is -5 Let the required number be x x + (-5) = (-4/3) LCM of 1 and 3 is 3 (-5/1) = (-5/1) × (3/3) = (-15/3) On substituting x + (-15/3) = (-4/3) x = (-4/3) – (-15/3) x = (-4/3) + (15/3) x = (-4 + 15)/3 x = (11/3) 6. The sum of two rational numbers is - 8. If one of the numbers is (-15/7), find the other. Solution: Given sum of two numbers is -8 One of them is (-15/7) Let the required number be x x + (-15/7) = -8 The LCM of 7 and 1 is 7 Page 4 Exercise 5.2 Page No: 5.7 1. Subtract the first rational number from the second in each of the following: (i) (3/8), (5/8) (ii) (-7/9), (4/9) (iii) (-2/11), (-9/11) (iv) (11/13), (-4/13) Solution: (i) Given (3/8), (5/8) (5/8) – (3/8) = (5 – 3)/8 = (2/8) = (1/4) (ii) Given (-7/9), (4/9) (4/9) – (-7/9) = (4/9) + (7/9) = (4 + 7)/9 = (11/9) (iii) Given (-2/11), (-9/11) (-9/11) – (-2/11) = (-9/11) + (2/11) = (-9 + 2)/ 11 = (-7/11) (iv) Given (11/13), (-4/13) (-4/13) – (11/13) = (-4 – 11)/13 = (-15/13) 2. Evaluate each of the following: (i) (2/3) – (3/5) (ii) (-4/7) – (2/-3) (iii) (4/7) – (-5/-7) (iv) -2 – (5/9) Solution: (i) Given (2/3) – (3/5) The LCM of 3 and 5 is 15 Consider (2/3) = (2/3) × (5/5) = (10/15) Now again (3/5) = (3/5) × (3/3) = (9/15) (2/3) – (3/5) = (10/15) – (9/15) = (1/15) (ii) Given (-4/7) – (2/-3) The LCM of 7 and 3 is 21 Consider (-4/7) = (-4/7) × (3/3) = (-12/21) Again (2/-3) = (-2/3) × (7/7) = (-14/21) (-4/7) – (2/-3) = (-12/21) – (-14/21) = (-12 + 14)/21 = (2/21) (iii) Given (4/7) – (-5/-7) (4/7) – (5/7) = (4 -5)/7 = (-1/7) (iv) Given -2 – (5/9) Consider (-2/1) = (-2/1) × (9/9) = (-18/9) -2 – (5/9) = (-18/9) – (5/9) = (-18 -5)/9 = (-23/9) 3. The sum of the two numbers is (5/9). If one of the numbers is (1/3), find the other. Solution: Given sum of two numbers is (5/9) And one them is (1/3) Let the unknown number be x x + (1/3) = (5/9) x = (5/9) – (1/3) LCM of 3 and 9 is 9 Consider (1/3) = (1/3) × (3/3) = (3/9) On substituting we get x = (5/9) – (3/9) x = (5 – 3)/9 x = (2/9) 4. The sum of two numbers is (-1/3). If one of the numbers is (-12/3), find the other. Solution: Given sum of two numbers = (-1/3) One of them is (-12/3) Let the required number be x x + (-12/3) = (-1/3) x = (-1/3) – (-12/3) x = (-1/3) + (12/3) x = (-1 + 12)/3 x = (11/3) 5. The sum of two numbers is (– 4/3). If one of the numbers is -5, find the other. Solution: Given sum of two numbers = (-4/3) One of them is -5 Let the required number be x x + (-5) = (-4/3) LCM of 1 and 3 is 3 (-5/1) = (-5/1) × (3/3) = (-15/3) On substituting x + (-15/3) = (-4/3) x = (-4/3) – (-15/3) x = (-4/3) + (15/3) x = (-4 + 15)/3 x = (11/3) 6. The sum of two rational numbers is - 8. If one of the numbers is (-15/7), find the other. Solution: Given sum of two numbers is -8 One of them is (-15/7) Let the required number be x x + (-15/7) = -8 The LCM of 7 and 1 is 7 Consider (-8/1) = (-8/1) × (7/7) = (-56/7) On substituting x + (-15/7) = (-56/7) x = (-56/7) – (-15/7) x = (-56/7) + (15/7) x = (-56 + 15)/7 x = (-41/7) 7. What should be added to (-7/8) so as to get (5/9)? Solution: Given (-7/8) Let the required number be x x + (-7/8) = (5/9) The LCM of 8 and 9 is 72 x = (5/9) – (-7/8) x = (5/9) + (7/8) Consider (5/9) = (5/9) × (8/8) = (40/72) Again (7/8) = (7/8) × (9/8) = (63/72) On substituting x = (40/72) + (63/72) x = (40 + 63)/72 x = (103/72) 8. What number should be added to (-5/11) so as to get (26/33)? Solution: Given (-5/11) Let the required number be x x + (-5/11) = (26/33) x = (26/33) – (-5/11) x = (26/33) + (5/11) Consider (5/11) = (5/11) × (3/3) = (15/33) On substituting x = (26/33) + (15/33) x = (41/33) Page 5 Exercise 5.2 Page No: 5.7 1. Subtract the first rational number from the second in each of the following: (i) (3/8), (5/8) (ii) (-7/9), (4/9) (iii) (-2/11), (-9/11) (iv) (11/13), (-4/13) Solution: (i) Given (3/8), (5/8) (5/8) – (3/8) = (5 – 3)/8 = (2/8) = (1/4) (ii) Given (-7/9), (4/9) (4/9) – (-7/9) = (4/9) + (7/9) = (4 + 7)/9 = (11/9) (iii) Given (-2/11), (-9/11) (-9/11) – (-2/11) = (-9/11) + (2/11) = (-9 + 2)/ 11 = (-7/11) (iv) Given (11/13), (-4/13) (-4/13) – (11/13) = (-4 – 11)/13 = (-15/13) 2. Evaluate each of the following: (i) (2/3) – (3/5) (ii) (-4/7) – (2/-3) (iii) (4/7) – (-5/-7) (iv) -2 – (5/9) Solution: (i) Given (2/3) – (3/5) The LCM of 3 and 5 is 15 Consider (2/3) = (2/3) × (5/5) = (10/15) Now again (3/5) = (3/5) × (3/3) = (9/15) (2/3) – (3/5) = (10/15) – (9/15) = (1/15) (ii) Given (-4/7) – (2/-3) The LCM of 7 and 3 is 21 Consider (-4/7) = (-4/7) × (3/3) = (-12/21) Again (2/-3) = (-2/3) × (7/7) = (-14/21) (-4/7) – (2/-3) = (-12/21) – (-14/21) = (-12 + 14)/21 = (2/21) (iii) Given (4/7) – (-5/-7) (4/7) – (5/7) = (4 -5)/7 = (-1/7) (iv) Given -2 – (5/9) Consider (-2/1) = (-2/1) × (9/9) = (-18/9) -2 – (5/9) = (-18/9) – (5/9) = (-18 -5)/9 = (-23/9) 3. The sum of the two numbers is (5/9). If one of the numbers is (1/3), find the other. Solution: Given sum of two numbers is (5/9) And one them is (1/3) Let the unknown number be x x + (1/3) = (5/9) x = (5/9) – (1/3) LCM of 3 and 9 is 9 Consider (1/3) = (1/3) × (3/3) = (3/9) On substituting we get x = (5/9) – (3/9) x = (5 – 3)/9 x = (2/9) 4. The sum of two numbers is (-1/3). If one of the numbers is (-12/3), find the other. Solution: Given sum of two numbers = (-1/3) One of them is (-12/3) Let the required number be x x + (-12/3) = (-1/3) x = (-1/3) – (-12/3) x = (-1/3) + (12/3) x = (-1 + 12)/3 x = (11/3) 5. The sum of two numbers is (– 4/3). If one of the numbers is -5, find the other. Solution: Given sum of two numbers = (-4/3) One of them is -5 Let the required number be x x + (-5) = (-4/3) LCM of 1 and 3 is 3 (-5/1) = (-5/1) × (3/3) = (-15/3) On substituting x + (-15/3) = (-4/3) x = (-4/3) – (-15/3) x = (-4/3) + (15/3) x = (-4 + 15)/3 x = (11/3) 6. The sum of two rational numbers is - 8. If one of the numbers is (-15/7), find the other. Solution: Given sum of two numbers is -8 One of them is (-15/7) Let the required number be x x + (-15/7) = -8 The LCM of 7 and 1 is 7 Consider (-8/1) = (-8/1) × (7/7) = (-56/7) On substituting x + (-15/7) = (-56/7) x = (-56/7) – (-15/7) x = (-56/7) + (15/7) x = (-56 + 15)/7 x = (-41/7) 7. What should be added to (-7/8) so as to get (5/9)? Solution: Given (-7/8) Let the required number be x x + (-7/8) = (5/9) The LCM of 8 and 9 is 72 x = (5/9) – (-7/8) x = (5/9) + (7/8) Consider (5/9) = (5/9) × (8/8) = (40/72) Again (7/8) = (7/8) × (9/8) = (63/72) On substituting x = (40/72) + (63/72) x = (40 + 63)/72 x = (103/72) 8. What number should be added to (-5/11) so as to get (26/33)? Solution: Given (-5/11) Let the required number be x x + (-5/11) = (26/33) x = (26/33) – (-5/11) x = (26/33) + (5/11) Consider (5/11) = (5/11) × (3/3) = (15/33) On substituting x = (26/33) + (15/33) x = (41/33) 9. What number should be added to (-5/7) to get (-2/3)? Solution: Given (-5/7) Let the required number be x x + (-5/7) = (-2/3) x = (-2/3) – (-5/7) x = (-2/3) + (5/7) LCM of 3 and 7 is 21 Consider (-2/3) = (-2/3) × (7/7) = (-14/21) Again (5/7) = (5/7) × (3/3) = (15/21) On substituting x = (-14/21) + (15/21) x = (-14 + 15)/21 x = (1/21) 10. What number should be subtracted from (-5/3) to get (5/6)? Solution: Given (-5/3) Let the required number be x (-5/3) – x = (5/6) - x = (5/6) – (-5/3) - x = (5/6) + (5/3) Consider (5/3) = (5/3) × (2/2) = (10/6) On substituting - x = (5/6) + (10/6) - x = (15/6) x = (-15/6) 11. What number should be subtracted from (3/7) to get (5/4)? Solution: Given (3/7) Let the required number be x (3/7) – x = (5/4) - x = (5/4) – (3/7)Read More
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