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:
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