Math101 · Independent Ontario learning library
Math101Multiplying Fractions
Multiplying fractions finds a fraction **of** another quantity. The product $\frac ab\cdot\frac cd=\frac{ac}{bd}$ follows from taking $a/b$ of $c/d$ of one whole.
Fraction multiplication models portions, probabilities, scale factors, area, and rate calculations. Cancellation builds number sense and prepares learners to simplify algebraic products.
Intuition and core definition
Multiplying fractions finds a fraction of another quantity. The product $\frac ab\cdot\frac cd=\frac{ac}{bd}$ follows from taking $a/b$ of $c/d$ of one whole. Denominators $b$ and $d$ must be nonzero. Unlike addition, common denominators are not required.
Notation, language, and conditions
A whole number $n$ may be written $n/1$, and a mixed number must be converted before multiplication. Cancellation divides a numerator and a denominator by the same nonzero common factor; it is simplification of the overall product, not deletion of nearby digits.
Why this idea matters
Multiplying fractions scales a quantity by a part, and factor cancellation reveals the size of that scaling without producing unnecessarily large intermediate numbers.
A dependable method
- Convert mixed numbers to improper fractions and attach the product’s sign.
- Factor numerators and denominators enough to see common factors.
- Cancel common factors across any numerator–denominator pair.
- Multiply remaining numerators and remaining denominators.
- Reduce, convert form if requested, and estimate the size.
