Fractions – Medium Level Questions – UGC NET Paper 1

Q1): Simplify: 5/6 + 7/12 − 1/8
A) 29/24
B) 31/24
C) 25/24
D) 33/24

Answer: B) 31/24

Explanation:

  • Step 1: LCM of 6, 12, 8 = 24
  • Step 2: Convert: 5/6 = 20/24, 7/12 = 14/24, 1/8 = 3/24
  • Step 3: Compute: (20 + 14 − 3)/24 = 31/24
  • Final: So option B is correct

Q2): Simplify: (3/4) ÷ (9/16)
A) 3/4
B) 4/3
C) 2/3
D) 16/27

Answer: B) 4/3

Explanation:

  • Step 1: Division by a fraction = multiply by reciprocal
  • Step 2: (3/4) × (16/9)
  • Step 3: Cancel 16 with 4 → 16/4 = 4
  • Step 4: Result = (3×4)/9 = 12/9 = 4/3
  • Final: So option B is correct

Q3): If x/5 + 3/10 = 7/10, then x = ?
A) 1
B) 2
C) 3
D) 4

Answer: B) 2

Explanation:

  • Step 1: Move 3/10 to RHS: x/5 = 7/10 − 3/10
  • Step 2: x/5 = 4/10 = 2/5
  • Step 3: Multiply both sides by 5: x = 2
  • Final: So option B is correct

Q4): If 2/3 of a number is 14, then 5/7 of the same number is:
A) 12
B) 15
C) 18
D) 21

Answer: B) 15

Explanation:

  • Step 1: Let number be N, then (2/3)N = 14
  • Step 2: N = 14 × (3/2) = 21
  • Step 3: 5/7 of N = (5/7) × 21 = 15
  • Final: So option B is correct

Q5): Which fraction is the smallest?
A) 7/12
B) 5/8
C) 2/3
D) 9/16

Answer: D) 9/16

Explanation:

  • Step 1: Convert to comparable values (decimals)
  • Step 2: 7/12 ≈ 0.5833, 5/8 = 0.625, 2/3 ≈ 0.6667, 9/16 = 0.5625
  • Step 3: Smallest decimal is 0.5625
  • Final: So 9/16 (option D) is the smallest

Q6): Convert 0.375 into a fraction in simplest form.
A) 3/8
B) 5/8
C) 15/40
D) 375/800

Answer: A) 3/8

Explanation:

  • Step 1: 0.375 = 375/1000
  • Step 2: Divide numerator and denominator by 125
  • Step 3: 375/1000 = 3/8
  • Final: So option A is correct

Q7): Convert 2.4 into a fraction in simplest form.
A) 12/5
B) 24/5
C) 6/25
D) 5/12

Answer: A) 12/5

Explanation:

  • Step 1: 2.4 = 24/10
  • Step 2: Reduce 24/10 by 2
  • Step 3: 24/10 = 12/5
  • Final: So option A is correct

Q8): Simplify: 1 1/2 − 3/4 + 2/3
A) 17/12
B) 19/12
C) 13/12
D) 5/12

Answer: A) 17/12

Explanation:

  • Step 1: Convert 1 1/2 to improper fraction: 3/2
  • Step 2: 3/2 − 3/4 = 6/4 − 3/4 = 3/4
  • Step 3: 3/4 + 2/3 = 9/12 + 8/12 = 17/12
  • Final: So option A is correct

Q9): Simplify: (5/9) × (27/10)
A) 3/2
B) 5/6
C) 9/10
D) 2/3

Answer: A) 3/2

Explanation:

  • Step 1: Multiply: (5×27)/(9×10)
  • Step 2: Cancel 27 with 9 → 27/9 = 3
  • Step 3: Value = (5×3)/10 = 15/10 = 3/2
  • Final: So option A is correct

Q10): Find the simplest ratio of 3/5 : 9/10
A) 1 : 2
B) 2 : 3
C) 3 : 2
D) 5 : 6

Answer: B) 2 : 3

Explanation:

  • Step 1: Ratio (a:b) = a/b
  • Step 2: (3/5) ÷ (9/10) = (3/5) × (10/9)
  • Step 3: (3×10)/(5×9) = 30/45 = 2/3
  • Final: So the ratio is 2 : 3 (option B)

Q11): Find the missing number: 4/7 = x/28
A) 14
B) 16
C) 18
D) 20

Answer: B) 16

Explanation:

  • Step 1: Denominator 7 becomes 28 by ×4
  • Step 2: Multiply numerator also by 4
  • Step 3: x = 4×4 = 16
  • Final: So option B is correct

Q12): Find: reciprocal(4/5) + reciprocal(10/3)
A) 31/20
B) 29/20
C) 11/20
D) 21/20

Answer: A) 31/20

Explanation:

  • Step 1: Reciprocal of 4/5 is 5/4
  • Step 2: Reciprocal of 10/3 is 3/10
  • Step 3: 5/4 + 3/10 = 25/20 + 6/20 = 31/20
  • Final: So option A is correct

Q13): Simplify: (2/3 + 5/6) ÷ (7/4)
A) 6/7
B) 7/6
C) 3/7
D) 12/7

Answer: A) 6/7

Explanation:

  • Step 1: Add inside bracket: 2/3 = 4/6, so 4/6 + 5/6 = 9/6 = 3/2
  • Step 2: Divide by 7/4 → multiply by 4/7
  • Step 3: (3/2) × (4/7) = 12/14 = 6/7
  • Final: So option A is correct

Q14): If (5/12) of x = 25, then x = ?
A) 48
B) 60
C) 72
D) 75

Answer: B) 60

Explanation:

  • Step 1: (5/12)x = 25
  • Step 2: x = 25 × (12/5)
  • Step 3: 25/5 = 5, so x = 5×12 = 60
  • Final: So option B is correct

Q15): A tank is 3/5 full. After adding 18 L, it becomes 7/10 full. Capacity is:
A) 120 L
B) 150 L
C) 180 L
D) 200 L

Answer: C) 180 L

Explanation:

  • Step 1: Increase in fraction = 7/10 − 3/5
  • Step 2: 3/5 = 6/10, so increase = 7/10 − 6/10 = 1/10
  • Step 3: (1/10) of capacity = 18
  • Step 4: Capacity = 18×10 = 180 L
  • Final: So option C is correct

Q16): Simplify: 3/8 + 5/12 + 7/24
A) 11/12
B) 13/12
C) 1 1/12
D) 1 5/12

Answer: B) 13/12

Explanation:

  • Step 1: LCM of 8, 12, 24 = 24
  • Step 2: Convert: 3/8 = 9/24, 5/12 = 10/24, 7/24 = 7/24
  • Step 3: Add: (9 + 10 + 7)/24 = 26/24 = 13/12
  • Final: So option B is correct

Q17): If a/b = 3/4 and b/c = 5/6, then a/c = ?
A) 5/8
B) 3/5
C) 15/10
D) 2/3

Answer: A) 5/8

Explanation:

  • Step 1: a/c = (a/b) × (b/c)
  • Step 2: a/c = (3/4) × (5/6)
  • Step 3: (3×5)/(4×6) = 15/24 = 5/8
  • Final: So option A is correct

Q18): 60% of 30 is what fraction of 45?
A) 1/3
B) 2/5
C) 3/5
D) 4/9

Answer: B) 2/5

Explanation:

  • Step 1: 60% of 30 = (60/100)×30
  • Step 2: (3/5)×30 = 18
  • Step 3: Required fraction = 18/45
  • Step 4: Reduce 18/45 by 9 → 2/5
  • Final: So option B is correct

Q19): A fraction when increased by 1/6 becomes 3/4. The fraction is:
A) 5/12
B) 7/12
C) 2/3
D) 3/5

Answer: B) 7/12

Explanation:

  • Step 1: Let fraction be x, then x + 1/6 = 3/4
  • Step 2: x = 3/4 − 1/6
  • Step 3: LCM of 4 and 6 = 12 → 3/4 = 9/12, 1/6 = 2/12
  • Step 4: x = (9 − 2)/12 = 7/12
  • Final: So option B is correct

Q20): Simplify: [(4/5) − (1/2)] ÷ (3/10)
A) 1
B) 3/10
C) 10/3
D) 3/5

Answer: A) 1

Explanation:

  • Step 1: First bracket: 4/5 − 1/2
  • Step 2: Convert to tenths: 4/5 = 8/10, 1/2 = 5/10
  • Step 3: Difference = 8/10 − 5/10 = 3/10
  • Step 4: (3/10) ÷ (3/10) = 1
  • Final: So option A is correct

This Tutorial is Related to: Compare Fractions, Complex Fractions, Decimal To Fraction, Fraction Equations, Fraction Simplification, Fraction Word Problems, Fractions, Fractions Questions, Medium Level, Mixed Numbers, Reciprocals, Ugc Net Paper 1, Unit 5

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