1/15
00:00

O.3 Multiply three fractions

Loading questions...

What does it mean to multiply fractions?

When you multiply fractions, you find a part of a part. Multiplying three fractions means you are finding a fraction of another fraction, and then of another. The product will usually be smaller than any of the original fractions if all are less than one.

Example:
  • 12 × 13 × 14 = 124
Note

Each multiplication step makes the result a smaller part of the whole if the fractions are less than one.

How to multiply three fractions

To multiply three fractions, multiply all the numerators (top numbers) together and then multiply all the denominators (bottom numbers) together. Simplify the final fraction if possible.

Steps:
  • Write the problem: 23 × 34 × 12
  • Multiply the numerators: 2 × 3 × 1 = 6
  • Multiply the denominators: 3 × 4 × 2 = 24
  • Write the product: 624
  • Simplify: 624 = 14
Note

You can multiply in any order. It is often easier to simplify before multiplying to make the numbers smaller.

Simplifying before multiplying

Before multiplying, you can cross-cancel (simplify) any numerator and denominator that share a common factor. This helps you work with smaller numbers and reduces the final fraction more easily.

Example:
  • 35 × 109 × 12
  • Cross-cancel 10 and 5 (divide both by 5): 10 → 2, 5 → 1
  • Now multiply: 3 × 2 × 11 × 9 × 2 = 618
  • Simplify: 618 = 13
Note

Cross-canceling makes multiplication faster and prevents large numbers that are harder to simplify later.

Checking your work

Always check your product by making sure you multiplied all numerators and denominators correctly and simplified completely. You can also estimate whether your answer makes sense — the product of three fractions less than one should be smaller than each of them.

Example:
  • 12 × 23 × 34 = 624 = 14
  • The product (14) makes sense because it is smaller than all three fractions.
Note

Always simplify your final answer to its lowest terms. A simplified fraction is easier to understand and compare.