Fraction multiplication
Three fractions do not need a new rule. Multiply every numerator, multiply every denominator, then simplify: 1/2 × 2/3 × 3/4 = 6/24 = 1/4. The extra work is the extra numbers — products grow quickly, so cancelling shared factors across all three fractions is the difference between a short calculation and a large one.
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Type the problem directly or adjust the factors below. The tool rewrites mixed numbers and whole numbers, simplifies when possible, and shows every multiplication step.
Result
5/12
Multiply fractions by multiplying across. Multiply the numerators, multiply the denominators, and simplify at the end.
Treat each fraction as equal-size pieces. Count how many pieces stay selected after multiplying, then simplify if possible.
Rewritten
2/3 x 3/4 x 5/6
Simplify first
1/1 x 1/2 x 5/6
Before final simplify
5/12
Mixed-number form
Not needed
Formula flow
Step by step
Multiply across
Multiply across: Fraction multiplication does not need common denominators. The operation tracks part of a part, so multiplying across keeps the size relationship intact.
Worked example
1/2 × 2/3 × 3/4 = (1 × 2 × 3)/(2 × 3 × 4) = 6/24 = 1/4
Three fractions, one rule. Multiply every numerator (1 × 2 × 3 = 6) and every denominator (2 × 3 × 4 = 24), then simplify 6/24 to 1/4. You could also cancel first: the 2s cancel, the 3s cancel, and you are left with 1/4 without ever building 6/24.
Worked example
2/3 × 3/4 × 5/6 = 1/1 × 1/2 × 5/6 = 5/12
A numerator can cancel with any of the three denominators, not only the one next to it. The first 3 cancels the second 3, and the 2 cancels with the 4. After cancelling, the leftover product is 1 × 1 × 5 over 1 × 2 × 6 = 5/12.
Worked example
3/5 × 1/2 × 4/9 = 1/5 × 1/2 × 4/3 = 4/30 = 2/15
The 3 in the first numerator shares a factor with the 9 in the third denominator, so cancel those first. Then 4 and 2 share a factor of 2. The leftover product 1 × 1 × 2 over 5 × 1 × 3 is 2/15 — much smaller than multiplying 3 × 1 × 4 = 12 over 5 × 2 × 9 = 90 and reducing 12/90 afterwards.
Worked example
1/2 × 1/3 × 1/4 = 1/24
Unit fractions have 1 in every numerator, so there is nothing to cancel on top. Multiply the denominators: 2 × 3 × 4 = 24, and the product is 1/24. That picture is useful: each extra unit fraction cuts the previous piece into smaller equal parts, so the whole ends up in 24 pieces.
Multiplying two fractions takes a part of a part. Adding a third fraction takes a part of that result. 1/2 × 1/3 × 1/4 means one half of one third of one fourth: each extra fraction cuts the previous piece again, so the denominators multiply (2 × 3 × 4 = 24) and you keep 1 × 1 × 1 of those pieces. The picture scales; the rule does not change.
That is also why grouping does not matter. Compute 1/2 × 2/3 first to get 1/3, then multiply by 3/4 to get 1/4 — or multiply all three at once. Both paths land on the same product, because multiplication is associative.
With two fractions, cancelling looks like a diagonal. With three, it is easier to forget that a factor in the first numerator can cancel a factor in the third denominator. Write every numerator in one list and every denominator in another, then strike matching factors wherever they sit.
2/3 × 3/4 × 5/6
= (2 × 3 × 5) / (3 × 4 × 6)
= (1 × 1 × 5) / (1 × 2 × 6)
= 5/12
The 3s cancel, then 2 and 4 reduce to 1 and 2. Nothing in 5/12 still shares a factor, so that is the finished answer. Skipping the cancel step would send you through 30/72 first — the same fraction, much more arithmetic.
Homework often mixes types: 2 × 3/4 × 5/6, or 1 1/2 × 2/3 × 4/5. Rewrite the odd one out first. A whole number becomes a fraction over 1, and a mixed number becomes an improper fraction. After that, the expression is three ordinary fractions again, and the same cancel-then-multiply path applies.
Do not multiply the two fractions and then try to handle the mixed number as a leftover. Convert first so every factor is in the same form; mixing formats is where most three-factor mistakes start.
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