Rational Numbers in Fraction Form

A rational number written in fraction form looks like a/b, where a and b are integers and b is not zero. Fractions are the natural way to express parts of a whole — a quantity like "three quarters of a cup" — and many real-world problems involving ratios, recipes, and measurements are easiest to solve by staying in fraction form throughout, though the same value could also be written as a decimal and compared to other rational numbers.

To add or subtract fractions, they need a common denominator. Once the denominators match, add or subtract the numerators and keep the denominator the same. If the denominators are already equal, this is a single step.

To multiply fractions, multiply the numerators together and the denominators together — no common denominator needed. To divide by a fraction, multiply by its reciprocal instead (flip the second fraction and multiply).

Fraction word problems often involve scaling a recipe, splitting a quantity, or combining parts. Convert any mixed numbers (like 1½) to improper fractions first, then apply the right operation: multiplying scales a quantity up or down, while dividing splits a quantity into equal parts.

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