Q1): Simplify: 3/4 + 1/8
A) 1/2
B) 7/8
C) 5/8
D) 9/8
Answer: B) 7/8
Explanation:
- Step 1: LCM of 4 and 8 = 8
- Step 2: 3/4 = 6/8
- Step 3: 6/8 + 1/8 = 7/8
- Final: So option B is correct
Q2): Simplify: 5/6 – 1/3
A) 1/2
B) 2/3
C) 1/3
D) 5/9
Answer: A) 1/2
Explanation:
- Step 1: Convert 1/3 into sixths: 1/3 = 2/6
- Step 2: 5/6 – 2/6 = 3/6
- Step 3: 3/6 = 1/2
- Final: So option A is correct
Q3): Simplify: 7/9 × 3/14
A) 1/6
B) 1/4
C) 1/3
D) 1/2
Answer: A) 1/6
Explanation:
- Step 1: 7/9 × 3/14 = (7×3)/(9×14)
- Step 2: Cancel 7 with 14 → 7/14 = 1/2
- Step 3: Now = 3/(9×2) = 3/18
- Step 4: 3/18 = 1/6
- Final: So option A is correct
Q4): Simplify: 5/12 ÷ 10/9
A) 3/8
B) 5/8
C) 8/3
D) 9/24
Answer: A) 3/8
Explanation:
- Step 1: Division means multiply by reciprocal
- Step 2: 5/12 ÷ 10/9 = 5/12 × 9/10
- Step 3: 5/10 = 1/2, so = 9/(12×2) = 9/24
- Step 4: 9/24 = 3/8
- Final: So option A is correct
Q5): Which is greater? (5/8) or (3/5)
A) 5/8
B) 3/5
C) Both are equal
D) Cannot be compared
Answer: A) 5/8
Explanation:
- Step 1: Compare by cross-multiplication
- Step 2: 5/8 vs 3/5 → compare 5×5 and 3×8
- Step 3: 5×5 = 25, 3×8 = 24
- Final: Since 25 > 24, 5/8 is greater (option A)
Q6): Arrange in ascending order: 1/2, 2/3, 3/4
A) 3/4 < 2/3 < 1/2
B) 1/2 < 2/3 < 3/4
C) 2/3 < 1/2 < 3/4
D) 1/2 < 3/4 < 2/3
Answer: B) 1/2 < 2/3 < 3/4
Explanation:
- Step 1: Convert to decimals: 1/2=0.5, 2/3≈0.666, 3/4=0.75
- Step 2: 0.5 < 0.666 < 0.75
- Final: So option B is correct
Q7): Convert 3 2/5 into an improper fraction.
A) 15/5
B) 17/5
C) 13/5
D) 11/5
Answer: B) 17/5
Explanation:
- Step 1: Mixed to improper: (whole×denominator + numerator)/denominator
- Step 2: (3×5 + 2)/5 = (15 + 2)/5
- Step 3: = 17/5
- Final: So option B is correct
Q8): Convert 17/4 into a mixed fraction.
A) 4 1/4
B) 3 1/4
C) 4 1/3
D) 5 1/4
Answer: A) 4 1/4
Explanation:
- Step 1: 17 ÷ 4 = 4 remainder 1
- Step 2: Mixed form = 4 1/4
- Final: So option A is correct
Q9): Find 2/3 of 15.
A) 8
B) 9
C) 10
D) 12
Answer: C) 10
Explanation:
- Step 1: “Of” means multiply
- Step 2: 2/3 × 15
- Step 3: 15 ÷ 3 = 5
- Step 4: 5 × 2 = 10
- Final: So option C is correct
Q10): If 3/5 of a number is 18, then the number is:
A) 24
B) 30
C) 36
D) 40
Answer: B) 30
Explanation:
- Step 1: Let number be x
- Step 2: (3/5)x = 18
- Step 3: x = 18 × (5/3)
- Step 4: 18 ÷ 3 = 6, 6 × 5 = 30
- Final: So option B is correct
Q11): Reduce 84/126 to simplest form.
A) 2/3
B) 3/2
C) 4/7
D) 7/4
Answer: A) 2/3
Explanation:
- Step 1: HCF of 84 and 126 = 42
- Step 2: 84/126 = (84÷42)/(126÷42)
- Step 3: = 2/3
- Final: So option A is correct
Q12): Reciprocal of 9/11 is:
A) -9/11
B) 11/9
C) 9/11
D) 20/11
Answer: B) 11/9
Explanation:
- Step 1: Reciprocal means swap numerator and denominator
- Step 2: 9/11 → 11/9
- Final: So option B is correct
Q13): Decimal value of 3/8 is:
A) 0.25
B) 0.375
C) 0.625
D) 0.75
Answer: B) 0.375
Explanation:
- Step 1: Convert by division
- Step 2: 3 ÷ 8 = 0.375
- Final: So option B is correct
Q14): 7/20 as a percentage is:
A) 25%
B) 30%
C) 35%
D) 40%
Answer: C) 35%
Explanation:
- Step 1: Percentage = fraction × 100
- Step 2: (7/20) × 100 = 7 × 5
- Step 3: = 35
- Final: So option C is correct
Q15): Simplify: 1 1/4 + 2 2/3
A) 3 11/12
B) 3 7/12
C) 4 11/12
D) 4 7/12
Answer: A) 3 11/12
Explanation:
- Step 1: Convert to improper: 1 1/4 = 5/4, 2 2/3 = 8/3
- Step 2: LCM of 4 and 3 = 12
- Step 3: 5/4 = 15/12, 8/3 = 32/12
- Step 4: 15/12 + 32/12 = 47/12 = 3 11/12
- Final: So option A is correct
Q16): Simplify: 1/3 + 1/4 + 1/6
A) 3/4
B) 5/6
C) 1/2
D) 7/12
Answer: A) 3/4
Explanation:
- Step 1: LCM of 3, 4, 6 = 12
- Step 2: 1/3=4/12, 1/4=3/12, 1/6=2/12
- Step 3: Add = (4+3+2)/12 = 9/12
- Step 4: 9/12 = 3/4
- Final: So option A is correct
Q17): Simplify: (5/6) of (3/5)
A) 1/2
B) 5/18
C) 3/6
D) 2/3
Answer: A) 1/2
Explanation:
- Step 1: “Of” means multiply
- Step 2: 5/6 × 3/5
- Step 3: Cancel 5 with 5 → becomes 3/6
- Step 4: 3/6 = 1/2
- Final: So option A is correct
Q18): Which fraction is equivalent to 3/5?
A) 6/10
B) 9/20
C) 12/25
D) 15/40
Answer: A) 6/10
Explanation:
- Step 1: Multiply numerator and denominator by same number
- Step 2: 3/5 × 2/2 = 6/10
- Final: So option A is correct
Q19): Find x if x/18 = 5/6
A) 12
B) 15
C) 18
D) 20
Answer: B) 15
Explanation:
- Step 1: Cross-multiply: 6x = 5×18
- Step 2: 5×18 = 90
- Step 3: x = 90/6 = 15
- Final: So option B is correct
Q20): Simplify: (3/4) ÷ (6/5)
A) 5/8
B) 8/5
C) 15/24
D) 9/10
Answer: A) 5/8
Explanation:
- Step 1: Divide by fraction = multiply by reciprocal
- Step 2: 3/4 × 5/6
- Step 3: Cancel 3 with 6 → 1/2
- Step 4: Now = 5/(4×2) = 5/8
- Final: So option A is correct