Multiplying Three Fractions
Learn to multiply three fractions by converting to improper fractions, canceling common factors across numerators and denominators, then multiplying the remainders.
Key Concepts
Property To multiply three or more fractions: 1. Write all numbers in fraction form. 2. Cancel common factors between any numerator and any denominator. 3. Multiply the remaining numerators and denominators.
Examples $\frac{1}{2} \times \frac{2}{3} \times \frac{3}{4} = \frac{1}{4}$ $3 \times \frac{2}{5} \times \frac{1}{6} = \frac{1}{5}$ $1\frac{1}{4} \times \frac{2}{5} \times 2 = 1$.
Explanation Multiplying three fractions is just a bigger version of multiplying two! The coolest part is canceling. You can cancel a numerator from the first fraction with a denominator from the last one. It’s a free for all that makes the final multiplication step way, way easier and faster!
Common Questions
How do you multiply three fractions together?
To multiply three fractions, first write all numbers in fraction form, including any whole numbers or mixed numbers as improper fractions. Then cancel common factors between any numerator and any denominator across all three fractions, and finally multiply the remaining numerators and denominators together.
Can you cancel common factors across different fractions when multiplying?
Yes! When multiplying three or more fractions, you can cancel common factors between any numerator and any denominator, even if they are in different fractions. For example, in 1/2 × 2/3 × 3/4, the 2s and 3s cancel across fractions, leaving just 1/4.
How do you multiply a whole number and a mixed number with a fraction?
First convert the whole number and mixed number into improper fractions before multiplying. For instance, in 1¼ × 2/5 × 2, convert 1¼ to 5/4 and 2 to 2/1, then cancel common factors to simplify the multiplication and get the final answer.
Why is canceling common factors important when multiplying three fractions?
Canceling common factors before multiplying keeps the numbers small and makes calculations much easier and faster. It works as a free-for-all across all numerators and denominators, so you avoid dealing with large numbers and reduce the need to simplify at the end.