Fraction multiplication
Yes — and you do not need a common denominator either. Unlike denominators only become a problem in addition and subtraction. When multiplying, you multiply straight across: 2/3 × 4/5 = 8/15, no rewriting required. This page explains why the rule works, walks through the steps with worked examples, and shows the shortcuts and mistakes that matter most.
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Interactive tool
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
2/5
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 3/5
Simplify first
2/1 x 1/5
Before final simplify
2/5
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
2/3 × 4/5 = (2 × 4)/(3 × 5) = 8/15
The denominators 3 and 5 are different, so nothing needs fixing first. Multiply the numerators together (2 × 4 = 8) and the denominators together (3 × 5 = 15). The product 8/15 is already in lowest terms, so the work stops there.
Worked example
3/4 × 2/3 = 6/12 = 1/2
Different denominators again — 4 and 3 — and the same rule applies: 3 × 2 = 6 over 4 × 3 = 12. The product 6/12 shares the factor 6, so simplify to 1/2. Notice the 3 that appears in a numerator and a denominator: that pair cancels, which is why the answer comes out so small.
Worked example
5/6 × 3/10 = 5/10 × 3/6 = 1/2 × 1/2 = 1/4
The 5 cancels with the 10 (shared factor 5), and the 3 cancels with the 6 (shared factor 3). Diagonal cancelling works fine even though the denominators are different — it is just simplification done early, and it keeps every number in the problem small.
Worked example
7/8 × 1/2 = 7/16
Nothing cancels here: 7 shares no factor with 8 or 2, and 1 never cancels anything. Multiply straight across — 7 × 1 = 7 over 8 × 2 = 16 — and the fraction 7/16 is already fully simplified.
Common denominators exist for one job: making piece sizes match so amounts can be added or subtracted. You cannot add 1/3 + 1/2 directly because thirds and halves are different sizes of parts — so you rebuild both as sixths first. Multiplication asks a completely different question, so that constraint disappears.
1/2 × 1/3 means one half of one third. Take a whole cut into thirds, then take half of that third: you have cut the whole into 2 × 3 = 6 pieces, and you are holding 1 of them — 1/6. The denominators multiplied each other (2 × 3 = 6), which is exactly why they never needed to match. Different denominators are not an obstacle to work around; they are part of the multiplication itself.
Every fraction-times-fraction problem with different denominators follows the same three steps. For 3/4 × 2/3:
3/4 × 2/3
= (3 × 2)/(4 × 3)
= 6/12
= 1/2
Multiply the numerators (3 × 2 = 6), multiply the denominators (4 × 3 = 12), then simplify 6/12 to 1/2. If both fractions are proper or improper, this is the entire method. Mixed numbers get one extra step at the front: convert each one to an improper fraction first, and the denominators still do not need to match.
With unlike denominators, a numerator often shares a factor with the other fraction’s denominator. In 5/6 × 3/10, the 5 and the 10 share the factor 5, and the 3 and the 6 share the factor 3. Cancel those diagonal pairs first and the problem becomes 1/2 × 1/2 = 1/4 — the same answer as multiplying 5 × 3 = 15 over 6 × 10 = 60 and reducing 15/60, but with far smaller numbers along the way.
Cancelling is optional. It is not a different rule, just simplification performed at the friendliest moment. If no diagonal pair shares a factor — as in 7/8 × 1/2 — skip straight to multiplying across.
Same denominators make multiplication even quicker, not different: keep the shared denominator and multiply the numerators. 2/7 × 3/7 = 6/49. The tempting mistake is to write 6/14 — as if the denominators only counted once — but the rule does not change when the numbers match. The denominators still multiply: 7 × 7 = 49.
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