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.
