Page 1 Objective Type Questions page: 6.36 Mark the correct alternative in each of the following: 1. Which of the following is a proper fraction? (a) 4/3 (b) 3/4 (c) 13/4 (d) 21/5 Solution: The option (b) is correct answer. We know that in a proper fraction, the numerator is less than the denominator. 2. Which of the following is an improper fraction? (a) 1/2 (b) 3/7 (c) 7/3 (d) 3/15 Solution: The option (c) is correct answer. We know that in an improper fraction, the numerator is more than the denominator. 3. Which of the following is a fraction equivalent of 2/3? (a) 4/5 (b) 8/6 (c) 10/25 (d) 10/15 Solution: The option (d) is correct answer. Consider 10/15=2/3 By cross multiplication 10 × 3 = 2 × 15 We get 30 = 30 4. A fraction equivalent to 3/5is (a) 3+2/5+2 (b) 3-2/5-2 (c) 3×2/5×2 (d) None of these Solution: The option (c) is correct answer. We know that by dividing the numerator and denominator by 2, we obtain 3/5. 5. If 5/12 is equivalent of x/3, then x = Page 2 Objective Type Questions page: 6.36 Mark the correct alternative in each of the following: 1. Which of the following is a proper fraction? (a) 4/3 (b) 3/4 (c) 13/4 (d) 21/5 Solution: The option (b) is correct answer. We know that in a proper fraction, the numerator is less than the denominator. 2. Which of the following is an improper fraction? (a) 1/2 (b) 3/7 (c) 7/3 (d) 3/15 Solution: The option (c) is correct answer. We know that in an improper fraction, the numerator is more than the denominator. 3. Which of the following is a fraction equivalent of 2/3? (a) 4/5 (b) 8/6 (c) 10/25 (d) 10/15 Solution: The option (d) is correct answer. Consider 10/15=2/3 By cross multiplication 10 × 3 = 2 × 15 We get 30 = 30 4. A fraction equivalent to 3/5is (a) 3+2/5+2 (b) 3-2/5-2 (c) 3×2/5×2 (d) None of these Solution: The option (c) is correct answer. We know that by dividing the numerator and denominator by 2, we obtain 3/5. 5. If 5/12 is equivalent of x/3, then x = (a) 5/4 (b) 4/5 (c) 5/3 (d) 3/5 Solution: The option (a) is correct answer. Consider 5/12 = x/3 By cross multiplication 5 × 3 = 12 × x So we get x = (5 × 3)/12 = (5 × 3)/ (4 × 3) = 5/4 6. Which of the following are like fractions? (a) 3/5, 3/7, 3/11, 3/16 (b) 5/11, 7/11, 15/11, 2/11 (c) 2/3, 3/4,4/5, 6/7 (d) None of these Solution: The option (b) is correct answer. We know that like fractions are the fractions with the same denominator. 7. If 11/4 = 77/x, then x = (a) 28 (b) 77/28 (c) 44 (d) 308 Solution: The option (a) is correct answer. 11/4 = 77/x By cross multiplication 11 × x = 77 × 4 x = (77 × 4)/ 11 = (7 × 11 × 4)/ 11 Dividing both the numerator & denominator by 11, we obtain 28. 8. 1/ (2 1/3) +1/ (1 3/4) is equal to (a) 7/14 (b) 12/49 (c) 4 1/12 (d) None of these Solution: The option (d) is correct answer. Page 3 Objective Type Questions page: 6.36 Mark the correct alternative in each of the following: 1. Which of the following is a proper fraction? (a) 4/3 (b) 3/4 (c) 13/4 (d) 21/5 Solution: The option (b) is correct answer. We know that in a proper fraction, the numerator is less than the denominator. 2. Which of the following is an improper fraction? (a) 1/2 (b) 3/7 (c) 7/3 (d) 3/15 Solution: The option (c) is correct answer. We know that in an improper fraction, the numerator is more than the denominator. 3. Which of the following is a fraction equivalent of 2/3? (a) 4/5 (b) 8/6 (c) 10/25 (d) 10/15 Solution: The option (d) is correct answer. Consider 10/15=2/3 By cross multiplication 10 × 3 = 2 × 15 We get 30 = 30 4. A fraction equivalent to 3/5is (a) 3+2/5+2 (b) 3-2/5-2 (c) 3×2/5×2 (d) None of these Solution: The option (c) is correct answer. We know that by dividing the numerator and denominator by 2, we obtain 3/5. 5. If 5/12 is equivalent of x/3, then x = (a) 5/4 (b) 4/5 (c) 5/3 (d) 3/5 Solution: The option (a) is correct answer. Consider 5/12 = x/3 By cross multiplication 5 × 3 = 12 × x So we get x = (5 × 3)/12 = (5 × 3)/ (4 × 3) = 5/4 6. Which of the following are like fractions? (a) 3/5, 3/7, 3/11, 3/16 (b) 5/11, 7/11, 15/11, 2/11 (c) 2/3, 3/4,4/5, 6/7 (d) None of these Solution: The option (b) is correct answer. We know that like fractions are the fractions with the same denominator. 7. If 11/4 = 77/x, then x = (a) 28 (b) 77/28 (c) 44 (d) 308 Solution: The option (a) is correct answer. 11/4 = 77/x By cross multiplication 11 × x = 77 × 4 x = (77 × 4)/ 11 = (7 × 11 × 4)/ 11 Dividing both the numerator & denominator by 11, we obtain 28. 8. 1/ (2 1/3) +1/ (1 3/4) is equal to (a) 7/14 (b) 12/49 (c) 4 1/12 (d) None of these Solution: The option (d) is correct answer. 9. If 1/3 + 1/2 + 1/x = 4, then x = ? (a) 5/18 (b) 6/19 (c) 18/5 (d) 24/11 Solution: The option (b) is correct answer. It is given that 1/3 + ½ + 1/x = 4 On further calculation 1/x = 4 – 1/3 – 1/2 By taking LCM of 3 and 2 as 6 1/x = 24/6 – 2/6 – 3/6 So we get 1/x = (24 – 2 – 3)/ 6 = 19/6 Hence, x = 6/19 10. If 1/2 + 1/x = 2, then x = (a) 2/5 (b) 5/2 (c) 3/2 (d) 2/3 Solution: The option (d) is correct answer. It is given that ½ + 1/x = 2 On further calculation 1/x = 2 – 1/2 By taking LCM as 2 we get 1/x = 4/2 – 1/2 = (4 – 1)/2 = 3/2 Hence, x = 2/3 11. Which of the following fractions is the smallest? 1/2,3/7,3/5,4/9 (a) 4/9 (b) 3/5 (c) 3/7 Page 4 Objective Type Questions page: 6.36 Mark the correct alternative in each of the following: 1. Which of the following is a proper fraction? (a) 4/3 (b) 3/4 (c) 13/4 (d) 21/5 Solution: The option (b) is correct answer. We know that in a proper fraction, the numerator is less than the denominator. 2. Which of the following is an improper fraction? (a) 1/2 (b) 3/7 (c) 7/3 (d) 3/15 Solution: The option (c) is correct answer. We know that in an improper fraction, the numerator is more than the denominator. 3. Which of the following is a fraction equivalent of 2/3? (a) 4/5 (b) 8/6 (c) 10/25 (d) 10/15 Solution: The option (d) is correct answer. Consider 10/15=2/3 By cross multiplication 10 × 3 = 2 × 15 We get 30 = 30 4. A fraction equivalent to 3/5is (a) 3+2/5+2 (b) 3-2/5-2 (c) 3×2/5×2 (d) None of these Solution: The option (c) is correct answer. We know that by dividing the numerator and denominator by 2, we obtain 3/5. 5. If 5/12 is equivalent of x/3, then x = (a) 5/4 (b) 4/5 (c) 5/3 (d) 3/5 Solution: The option (a) is correct answer. Consider 5/12 = x/3 By cross multiplication 5 × 3 = 12 × x So we get x = (5 × 3)/12 = (5 × 3)/ (4 × 3) = 5/4 6. Which of the following are like fractions? (a) 3/5, 3/7, 3/11, 3/16 (b) 5/11, 7/11, 15/11, 2/11 (c) 2/3, 3/4,4/5, 6/7 (d) None of these Solution: The option (b) is correct answer. We know that like fractions are the fractions with the same denominator. 7. If 11/4 = 77/x, then x = (a) 28 (b) 77/28 (c) 44 (d) 308 Solution: The option (a) is correct answer. 11/4 = 77/x By cross multiplication 11 × x = 77 × 4 x = (77 × 4)/ 11 = (7 × 11 × 4)/ 11 Dividing both the numerator & denominator by 11, we obtain 28. 8. 1/ (2 1/3) +1/ (1 3/4) is equal to (a) 7/14 (b) 12/49 (c) 4 1/12 (d) None of these Solution: The option (d) is correct answer. 9. If 1/3 + 1/2 + 1/x = 4, then x = ? (a) 5/18 (b) 6/19 (c) 18/5 (d) 24/11 Solution: The option (b) is correct answer. It is given that 1/3 + ½ + 1/x = 4 On further calculation 1/x = 4 – 1/3 – 1/2 By taking LCM of 3 and 2 as 6 1/x = 24/6 – 2/6 – 3/6 So we get 1/x = (24 – 2 – 3)/ 6 = 19/6 Hence, x = 6/19 10. If 1/2 + 1/x = 2, then x = (a) 2/5 (b) 5/2 (c) 3/2 (d) 2/3 Solution: The option (d) is correct answer. It is given that ½ + 1/x = 2 On further calculation 1/x = 2 – 1/2 By taking LCM as 2 we get 1/x = 4/2 – 1/2 = (4 – 1)/2 = 3/2 Hence, x = 2/3 11. Which of the following fractions is the smallest? 1/2,3/7,3/5,4/9 (a) 4/9 (b) 3/5 (c) 3/7 (d) 1/2 Solution: The option (c) is correct answer. We know that the LCM of numerator is 12 By converting each fraction to an equivalent fraction having 12 as numerator 1/2 = 1/2 × 12/12 = 12/24 3/7 = 3/7 × 4/4 = 12/28 3/5 = 3/5 × 4/4 = 12/20 4/9 = 4/9 × 3/3 = 12/27 We know that if the numerator is same the fraction having larger denominator is the smallest. Hence, 3/7 is the smallest fraction. 12. Which of the following fractions is the greatest of all? 7/8, 6/7, 4/5, 5/6 (a) 6/7 (b) 4/5 (c) 5/6 (d) 7/8 Solution: The option (d) is correct answer. We know that the LCM of 8, 7, 6 and 5 is 840 By converting each fraction to an equivalent fraction having 840 as denominator 7/8 = 7/8 × 105/105 = 735/840 6/7 = 6/7 × 120/120 = 720/840 4/5 = 4/5 × 168/168 = 672/840 5/6 = 5/6 × 140/140 = 700/840 We know that if the denominator is same the fraction having larger numerator is the greatest. Hence, 7/8 is the greatest fraction. 13. What is the value of a+b/ a-b, If a/b=4? (a) 3/5 (b) 5/3 (c) 4/5 (d) 5/4 Solution: The option (b) is correct answer. It is given that a/b = 4 We can write it as a = 4b By substituting the value of a in a+b/a-b a+b/a-b = 4b+b/4b-b = 5b/3b Dividing numerator and denominator by b, the value is 5/3. 14. If a/b = 4/3, then the value of 6a+4b/ 6a-5b is (a) -1 (b) 3 (c) 4 (d) 5 Page 5 Objective Type Questions page: 6.36 Mark the correct alternative in each of the following: 1. Which of the following is a proper fraction? (a) 4/3 (b) 3/4 (c) 13/4 (d) 21/5 Solution: The option (b) is correct answer. We know that in a proper fraction, the numerator is less than the denominator. 2. Which of the following is an improper fraction? (a) 1/2 (b) 3/7 (c) 7/3 (d) 3/15 Solution: The option (c) is correct answer. We know that in an improper fraction, the numerator is more than the denominator. 3. Which of the following is a fraction equivalent of 2/3? (a) 4/5 (b) 8/6 (c) 10/25 (d) 10/15 Solution: The option (d) is correct answer. Consider 10/15=2/3 By cross multiplication 10 × 3 = 2 × 15 We get 30 = 30 4. A fraction equivalent to 3/5is (a) 3+2/5+2 (b) 3-2/5-2 (c) 3×2/5×2 (d) None of these Solution: The option (c) is correct answer. We know that by dividing the numerator and denominator by 2, we obtain 3/5. 5. If 5/12 is equivalent of x/3, then x = (a) 5/4 (b) 4/5 (c) 5/3 (d) 3/5 Solution: The option (a) is correct answer. Consider 5/12 = x/3 By cross multiplication 5 × 3 = 12 × x So we get x = (5 × 3)/12 = (5 × 3)/ (4 × 3) = 5/4 6. Which of the following are like fractions? (a) 3/5, 3/7, 3/11, 3/16 (b) 5/11, 7/11, 15/11, 2/11 (c) 2/3, 3/4,4/5, 6/7 (d) None of these Solution: The option (b) is correct answer. We know that like fractions are the fractions with the same denominator. 7. If 11/4 = 77/x, then x = (a) 28 (b) 77/28 (c) 44 (d) 308 Solution: The option (a) is correct answer. 11/4 = 77/x By cross multiplication 11 × x = 77 × 4 x = (77 × 4)/ 11 = (7 × 11 × 4)/ 11 Dividing both the numerator & denominator by 11, we obtain 28. 8. 1/ (2 1/3) +1/ (1 3/4) is equal to (a) 7/14 (b) 12/49 (c) 4 1/12 (d) None of these Solution: The option (d) is correct answer. 9. If 1/3 + 1/2 + 1/x = 4, then x = ? (a) 5/18 (b) 6/19 (c) 18/5 (d) 24/11 Solution: The option (b) is correct answer. It is given that 1/3 + ½ + 1/x = 4 On further calculation 1/x = 4 – 1/3 – 1/2 By taking LCM of 3 and 2 as 6 1/x = 24/6 – 2/6 – 3/6 So we get 1/x = (24 – 2 – 3)/ 6 = 19/6 Hence, x = 6/19 10. If 1/2 + 1/x = 2, then x = (a) 2/5 (b) 5/2 (c) 3/2 (d) 2/3 Solution: The option (d) is correct answer. It is given that ½ + 1/x = 2 On further calculation 1/x = 2 – 1/2 By taking LCM as 2 we get 1/x = 4/2 – 1/2 = (4 – 1)/2 = 3/2 Hence, x = 2/3 11. Which of the following fractions is the smallest? 1/2,3/7,3/5,4/9 (a) 4/9 (b) 3/5 (c) 3/7 (d) 1/2 Solution: The option (c) is correct answer. We know that the LCM of numerator is 12 By converting each fraction to an equivalent fraction having 12 as numerator 1/2 = 1/2 × 12/12 = 12/24 3/7 = 3/7 × 4/4 = 12/28 3/5 = 3/5 × 4/4 = 12/20 4/9 = 4/9 × 3/3 = 12/27 We know that if the numerator is same the fraction having larger denominator is the smallest. Hence, 3/7 is the smallest fraction. 12. Which of the following fractions is the greatest of all? 7/8, 6/7, 4/5, 5/6 (a) 6/7 (b) 4/5 (c) 5/6 (d) 7/8 Solution: The option (d) is correct answer. We know that the LCM of 8, 7, 6 and 5 is 840 By converting each fraction to an equivalent fraction having 840 as denominator 7/8 = 7/8 × 105/105 = 735/840 6/7 = 6/7 × 120/120 = 720/840 4/5 = 4/5 × 168/168 = 672/840 5/6 = 5/6 × 140/140 = 700/840 We know that if the denominator is same the fraction having larger numerator is the greatest. Hence, 7/8 is the greatest fraction. 13. What is the value of a+b/ a-b, If a/b=4? (a) 3/5 (b) 5/3 (c) 4/5 (d) 5/4 Solution: The option (b) is correct answer. It is given that a/b = 4 We can write it as a = 4b By substituting the value of a in a+b/a-b a+b/a-b = 4b+b/4b-b = 5b/3b Dividing numerator and denominator by b, the value is 5/3. 14. If a/b = 4/3, then the value of 6a+4b/ 6a-5b is (a) -1 (b) 3 (c) 4 (d) 5 Solution: The option (c) is correct answer. It is given that a/b = 4/3 We can write it as a = 4b/3 By substituting the value of a in 6a+4b/6a-5b 15. If 1/5 - 1/6 = 4/x, then x = (a) -120 (b) -100 (c) 100 (d) 120 Solution: The option (d) is correct answer. It is given that 1/5 – 1/6 = 4/x LCM of 5 and 6 is 30 4/x = 6/30 – 5/30 On further calculation 4/x = 1/30 So we get x = 4 (30) = 120 16. The fraction to be added to 6 7/15 to get 8 1/5 is equal to (a) 11/15 (b) 1 1/15 (c) 44/3 (d) 3/44 Solution:Read More

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