Multiplying two fractions
Multiplying two fractions means multiplying the numerators together to get the new numerator, and the denominators together to get the new denominator: (a/b) × (c/d) = (a×c)/(b×d). In Grade 6 Saxon Math Course 1 (Chapter 3: Number, Operations, and Geometry), students apply this rule directly, then simplify the product to lowest terms. For 3/4 × 2/5: numerators 3 × 2 = 6, denominators 4 × 5 = 20, giving 6/20 = 3/10. Students may also cancel common factors before multiplying to keep numbers smaller, dividing a numerator and a denominator by a shared factor before computing.
Key Concepts
Property When we multiply fractions, we multiply the numerators to find the numerator of the product, and we multiply the denominators to find the denominator of the product.
Examples Find $\frac{2}{5}$ of $\frac{3}{7}$: $\frac{2}{5} \times \frac{3}{7} = \frac{2 \times 3}{5 \times 7} = \frac{6}{35}$ Multiply $\frac{1}{4}$ and $\frac{5}{9}$: $\frac{1}{4} \times \frac{5}{9} = \frac{1 \times 5}{4 \times 9} = \frac{5}{36}$ Calculate $\frac{7}{8} \times \frac{1}{2}$: $\frac{7}{8} \times \frac{1}{2} = \frac{7 \times 1}{8 \times 2} = \frac{7}{16}$.
Explanation Imagine a pizza party! If you have $\frac{3}{4}$ of a pizza left and you eat $\frac{1}{2}$ of that , you're not eating half the whole pizza—just half of the leftovers. Multiplying fractions tells you exactly what portion of the original, entire pizza you just devoured. It keeps track of the pieces for you!
Common Questions
What is the rule for multiplying two fractions?
Multiply the numerators to get the new numerator, and multiply the denominators to get the new denominator: (a/b) × (c/d) = (a×c)/(b×d).
Multiply 2/3 × 3/4.
Numerator: 2 × 3 = 6. Denominator: 3 × 4 = 12. Result: 6/12 = 1/2.
Do you need a common denominator to multiply fractions?
No. Unlike addition and subtraction, multiplication of fractions does not require common denominators—you simply multiply across.
What does it mean to cancel before multiplying fractions?
Before multiplying, divide a numerator of one fraction and a denominator of either fraction by a shared common factor. This simplifies calculations. For 2/3 × 3/4: cancel the 3s to get 2/1 × 1/4 = 2/4 = 1/2.
What is 3/5 × 5/9 simplified?
Numerator: 3 × 5 = 15. Denominator: 5 × 9 = 45. Simplify 15/45: GCF = 15, giving 1/3.