← Chapter 50 Chapter 51: Algebraic Fractions (Basic) Chapter 52 →

Chapter 51: Algebraic Fractions (Basic)

✏️ Explanation

Algebraic fractions have variables in numerator or denominator. Simplify by cancelling common factors, just like with number fractions.

🔍 Why It Matters

Appears in advanced algebra, calculus, and scientific formulas.

✏️ Worked Example

Simplify: 6x/8x
Step 1: Identify common factors in numerator and denominator
6x = 2 × 3 × x
8x = 2 × 4 × x
Step 2: Cancel the common factor x
6x/8x = 6/8
Step 3: Simplify the remaining fraction
6/8 = 3/4

🔢 Practice Exercises

1. Simplify: 4x/6x
Answer:
2. Simplify: 15a/10a
Answer:
3. Simplify: 12xy/8x
Answer:
4. Simplify: (x+2)/(x+2)
Answer:
5. Add: x/3 + x/6
Answer:

⚠️ Common Mistakes

  • Cancelling terms instead of factors
  • Not finding common denominators for addition
  • Cancelling when you shouldn't

✨ Quick Summary

Cancel common factors only. Treat like number fractions with variables.