Working With Fractions

Introduction

Fractions show parts of a whole. Each fraction has a numerator (top number) and a denominator (bottom number that tells into how many parts the whole is split).

How Do We Calculate With Fractions?

• Addition/Subtraction: use a common denominator.
  a/b + c/d = (a*d + b*c) / (b*d)
a/b - c/d = (a*d - b*c) / (b*d)
• Multiplication: multiply numerators and denominators.
  a/b * c/d = (a*c) / (b*d)
• Division: multiply by the reciprocal of the second fraction.
  a/b / c/d = a/b * d/c = (a*d) / (b*c)
  (All denominators must be nonzero.)

Practical Tips

• Simplify first by dividing top and bottom by a common factor (gcd).
• For different denominators, find the LCM to create a common denominator.
• Sketches/visuals can make concepts clearer.

Where Are Fractions Used?

Everywhere: cooking, measurement, percentages, probability. Mastering fractions is key for school math and everyday tasks, and it builds problem‑solving skills.