Objective Type Question Fractions - Class 6 Mathematics | Fully Solved Notes For Students

 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 
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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: