Algebraic_Fractions_Entry_Test_Class8_Expanded.docx

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1. Entry Test Preparation – Class 8
Topic: Algebraic Fractions and Operations Between Them
Prepared for Cadet College Entry Test Students
By: Mathematics Teacher
1. Introduction and Definition of Fractions
A fraction is a number that represents a part of a whole. It is written in the form: Numerator /
Denominator.
Example: 3/5 (Here, 3 is numerator, 5 is denominator).
2. Types of Fractions
a) Proper Fraction: Numerator smaller than denominator. Example: 3/5, 7/9
b) Improper Fraction: Numerator greater than or equal to denominator. Example: 7/4, 9/3
c) Mixed Fraction: Combination of whole number and proper fraction. Example: 2 1/3 = 7/3
3. Algebraic Fraction
An algebraic fraction contains algebraic expressions (letters/variables) in numerator,
denominator, or both.
Examples: x/y, (3a + 2b)/4c, 2x²/3y
4. Parts of an Algebraic Fraction
1. Numerator – Expression above the line. Example: (3x + 2)/y → numerator = 3x + 2
2. Denominator – Expression below the line. Example: (3x + 2)/y → denominator = y
Note: Denominator can never be zero.
5. Operations Between Algebraic Fractions
A. Addition of Algebraic Fractions
(i) (3x/y) + (2x/y) = (5x/y)
(ii) (2/x) + (3/y) = (2y + 3x)/xy
(iii) (a/3b) + (b/3b) = (a + b)/3b
(iv) (4/p) + (5/q) = (4q + 5p)/pq
(v) (x/2y) + (3x/4y) = (5x/4y)
B. Subtraction of Algebraic Fractions
(i) (5x/3y) - (2x/3y) = (3x/3y) = x/y

2. (ii) (a/x) - (b/x) = (a - b)/x
(iii) (2/p) - (1/q) = (2q - p)/pq
(iv) (3a/4b) - (a/2b) = (a/4b)
(v) (x/5) - (2x/10) = (x/10)
C. Multiplication of Algebraic Fractions
(i) (2x/3y) × (9y/4x) = 3/2
(ii) (a/b) × (b/c) = a/c
(iii) (3m/2n) × (4n/9m) = 2/3
(iv) (x/5y) × (10y/3x) = 2/3
(v) (4p/9q) × (3q/2p) = 2/3
D. Division of Algebraic Fractions
(i) (x/y) ÷ (2/3) = (x/y) × (3/2) = 3x/2y
(ii) (a/b) ÷ (c/d) = (a/b) × (d/c) = ad/bc
(iii) (4p/3q) ÷ (2p/q) = (4p/3q) × (q/2p) = 2/3
(iv) (5x/2y) ÷ (10x/4y) = (5x/2y) × (4y/10x) = 1
(v) (2m/n) ÷ (m/3n) = (2m/n) × (3n/m) = 6
E. Simplifying Algebraic Fractions
(i) (6x²/3x) = 2x
(ii) (x² + 2x)/x = x + 2
(iii) (12a²b/4ab) = 3a
(iv) (15x³y/5xy) = 3x²
(v) (4m²n/2mn) = 2m
6. Key Points / Points to Remember
• Denominator cannot be zero.
• Always factorize before simplifying.
• Use LCM for addition and subtraction of fractions.
• Multiply by reciprocal when dividing.

3. • Simplify the final answer by cancelling common factors.
• Keep algebraic signs with their terms.
7. MCQs Test – Algebraic Fractions and Operations
1. In the fraction 4x/9, the numerator is:
A) 9
B) x
C) 4x
D) None
Answer: C
2. In a proper fraction, the numerator is:
A) Greater than denominator
B) Smaller than denominator
C) Equal to denominator
D) Zero
Answer: B
3. Which of the following is an algebraic fraction?
A) 5
B) x + y
C) (x+2)/3y
D) 7a
Answer: C
4. Simplify: (3x/y + 2x/y)
A) 5x/y
B) x/y
C) 6x/y
D) 5/y
Answer: A
5. Simplify: (2/x + 3/y)
A) 5/xy
B) (2y + 3x)/xy

4. C) (3x + 2)/xy
D) (2 + 3)/xy
Answer: B
6. Multiply: (2x/3y × 9y/4x)
A) 18xy/12xy
B) 3/2
C) 2/3
D) 1
Answer: B
7. Division of (x/y ÷ 2/3) gives:
A) 2x/3y
B) 3x/2y
C) x/2y
D) y/x
Answer: B
8. Simplify: (6x²/3x)
A) 2x
B) 3x
C) x²
D) 2
Answer: A
9. The reciprocal of (3a/4b) is:
A) 4b/3a
B) 3a/4b
C) a/b
D) b/a
Answer: A
10. The denominator of a fraction can never be:
A) 1

5. B) Negative
C) 0
D) A variable
Answer: C