What Is a Fraction?
A fraction represents a part of a whole. It consists of two numbers:
- Numerator (top number) → Indicates how many parts we have.
- Denominator (bottom number) → Shows how many equal parts the whole is divided into.
Example: In 3/4,
- 3 = numerator (parts taken)
- 4 = denominator (total equal parts)
Types of Fractions with Examples
1. Proper Fraction
- Numerator < Denominator
- Value is less than 1
- Examples: 3/5, 7/10, 2/9
2. Improper Fraction
- Numerator ≥ Denominator
- Value is equal to or greater than 1
- Examples: 5/4, 9/9, 12/7
3. Mixed Fraction
- A whole number combined with a proper fraction
- Can be converted to an improper fraction (and vice versa)
- Examples: 2 ½, 5 ¾
4. Like Fractions
- Fractions with the same denominator
- Examples: 2/7, 5/7, 6/7
5. Unlike Fractions
- Fractions with different denominators
- Examples: 2/5, 3/8, 7/10
6. Equivalent Fractions
- Fractions that represent the same value despite different numerators & denominators
- Examples: 1/2 = 2/4 = 3/6
📝 Fraction Conversion Practice Questions
1️⃣ Convert 17/5 into a mixed fraction.
A) 3 1/2
B) 2 3/5
C) 3 2/5 ✅
D) 4 1/5
📌 Explanation: Divide 17 by 5 → 3 with a remainder of 2 → 3 2/5
2️⃣ Convert 3 ²⁄₇ into an improper fraction.
A) 23/7 ✅
B) 22/7
C) 17/7
D) 24/7
📌 Explanation: Multiply whole number (3) by denominator (7) → 21, then add numerator (2) → 23/7
3️⃣ Write 2/3 and 5/6 as like fractions.
A) 4/6 and 5/6
B) 8/12 and 10/12 ✅
C) 12/18 and 15/18
D) 6/9 and 9/9
📌 Explanation: LCM of 3 & 6 is 12 → 2/3 = 8/12, 5/6 = 10/12
4️⃣ Which fraction is equivalent to 4/5?
A) 12/15 ✅
B) 6/8
C) 8/12
D) 10/14
📌 Explanation: Multiply numerator & denominator by 3 → 12/15
5️⃣ Convert 6 ³⁄₈ into an improper fraction.
A) 51/8 ✅
B) 48/8
C) 49/8
D) 54/8
📌 Explanation: (6 × 8) + 3 = 48 + 3 = 51/8
6️⃣ Convert 45/7 into a mixed fraction.
A) 6 3/7 ✅
B) 6 4/7
C) 5 5/7
D) 7 2/7
📌 Explanation: 45 ÷ 7 = 6 remainder 3 → 6 3/7
7️⃣ Fill in the blank: 7/9 = ___ / 36
A) 26
B) 28 ✅
C) 27
D) 30
📌 Explanation: Multiply numerator & denominator by 4 → 28/36
8️⃣ Convert 3/8 + 5/12 into like fractions.
A) 9/24 + 10/24
B) 12/32 + 15/32
C) 18/48 + 20/48 ✅
D) 36/96 + 40/96
📌 Explanation: LCM of 8 & 12 is 48 → 3/8 = 18/48, 5/12 = 20/48
9️⃣ Convert 24/6 into a whole number.
A) 2
B) 3
C) 4 ✅
D) 6
📌 Explanation: 24 ÷ 6 = 4
🔟 Convert 1 1/4 and 2 2/3 into like fractions.
A) 5/4 and 8/3
B) 20/12 and 32/12
C) 15/12 and 32/12 ✅
D) 24/16 and 48/16
📌 Explanation: LCM of 4 & 3 is 12 → 1 1/4 = 15/12, 2 2/3 = 32/12
✅ Answer Key & Explanations
| Q# | Correct Answer | Explanation |
|---|---|---|
| 1 | C | 17 ÷ 5 = 3 R2 → 3 2/5 |
| 2 | A | (3 × 7) + 2 = 23/7 |
| 3 | B | LCM of 3 & 6 = 12 → 8/12 & 10/12 |
| 4 | A | 4/5 × 3/3 = 12/15 |
| 5 | A | (6 × 8) + 3 = 51/8 |
| 6 | A | 45 ÷ 7 = 6 R3 → 6 3/7 |
| 7 | B | 7/9 × 4/4 = 28/36 |
| 8 | C | LCM of 8 & 12 = 48 → 18/48 + 20/48 |
| 9 | C | 24 ÷ 6 = 4 |
| 10 | C | LCM of 4 & 3 = 12 → 15/12 & 32/12 |
Fraction Practice Test: 10+ MCQs with Detailed Solutions & Explanations”
📚 Basic Level Fraction Questions
1. Identifying Proper Fractions
Q: Which of the following is a proper fraction?
A) 5/3
B) 7/7
C) 3/8 ✅
D) 12/5
📝 Explanation:
A proper fraction has a numerator smaller than its denominator (value < 1). Here, only 3/8 meets this condition.
2. Mixed to Improper Fraction Conversion
Q: Convert 4 ²⁄₅ into an improper fraction.
A) 18/5
B) 22/5 ✅
C) 21/5
D) 20/5
📝 Explanation:
Use the formula: (Whole × Denominator) + Numerator
(4 × 5) + 2 = 20 + 2 = 22/5
3. Simplifying Fractions
Q: Simplify 12/16.
A) 3/4 ✅
B) 4/3
C) 6/8
D) 8/12
📝 Explanation:
Find the GCD of 12 and 16 (which is 4) and divide both numerator and denominator by it → 3/4
4. Improper to Mixed Fraction Conversion
Q: Convert 13/4 into a mixed fraction.
A) 3 1/4 ✅
B) 4 1/3
C) 3 2/4
D) 2 3/4
📝 Explanation:
Divide 13 by 4 → 3 with remainder 1 → 3 1/4
5. Equivalent Fractions
Q: Which fraction is equivalent to 2/3?
A) 4/9
B) 8/12 ✅
C) 5/8
D) 10/20
📝 Explanation:
Multiply numerator and denominator by the same number (4) → 8/12
🚀 Advanced Level Fraction Challenges
6. Finding Like Fractions (LCM Method)
Q: Find like fractions for 5/6 and 7/8.
A) 20/24 and 21/24
B) 40/48 and 42/48 ✅
C) 45/54 and 48/54
D) 35/48 and 42/48
📝 Explanation:
LCM of denominators (6,8) is 48 →
5/6 = 40/48, 7/8 = 42/48
7. Comparing Fractions
Q: Which fraction is the largest?
A) 7/10 = 0.7
B) 3/4 = 0.75
C) 4/5 = 0.8
D) 5/6 ≈ 0.833 ✅
📝 Explanation:
Convert all to decimals for easy comparison → 5/6 is largest
8. Equivalent Fractions with Higher Terms
Q: Fill in the blank: 15/20 = __ / 100.
A) 80
B) 70
C) 75 ✅
D) 85
📝 Explanation:
Multiply numerator and denominator by 5 → 75/100
9. Converting Mixed Numbers to Like Fractions
Q: Convert 2 3/5 and 1 4/5 into like fractions.
A) 13/5 and 9/5
B) 26/10 and 18/10 ✅
C) 16/5 and 14/5
D) 28/10 and 19/10
📝 Explanation:
Convert to improper fractions first →
Find LCM (5,5) = 10 →
13/5 = 26/10, 9/5 = 18/10
10. Dividing Fractions
Q: Simplify: (4/9) ÷ (2/3).
A) 6/9
B) 2/3 ✅
C) 4/6
D) 2/9
📝 Explanation:
Division rule: multiply by reciprocal →
(4/9) × (3/2) = 12/18 = 2/3
🧩 Word Problems with Fractions
11. Adding Fractions
Q: Ali ate 3/8 of a cake and his sister ate 2/8 of it. What fraction was eaten together?
A) 5/8 ✅
B) 6/8
C) 1/8
D) 3/8
📝 Explanation:
Same denominators → simply add numerators: 3 + 2 = 5/8
12. Fraction of a Quantity
Q: A 12m rope has 3/4 used. How many meters remain?
A) 3 m
B) 4 m ✅
C) 5 m
D) 6 m
📝 Explanation:
3/4 of 12m = 9m used → 12 – 9 = 4m remaining
✅ Answer Key Summary
| Question | Correct Answer | Key Concept |
|---|---|---|
| 1 | C | Proper fractions |
| 2 | B | Mixed→Improper conversion |
| 3 | A | Simplifying fractions |
| 4 | A | Improper→Mixed conversion |
| 5 | B | Equivalent fractions |
| 6 | B | Finding like fractions |
| 7 | D | Comparing fractions |
| 8 | C | Higher-term equivalents |
| 9 | B | Mixed→Like fractions |
| 10 | B | Dividing fractions |
| 11 | A | Adding fractions |
| 12 | B | Fraction of quantity |
