Fraction multiplication
Mixed numbers are pleasant to read and awkward to multiply — so the first job is converting them. Rewrite each one as an improper fraction, multiply across, then bring the answer back to mixed form: 1 1/2 × 2 1/3 = 3/2 × 7/3 = 21/6 = 3 1/2. This page walks through every step, shows where cancelling saves the most work, and explains the mistake that causes most lost marks.
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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
7/2
= 3 1/2
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
3/2 x 7/3
Simplify first
1/2 x 7/1
Before final simplify
7/2
Mixed-number form
3 1/2
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 1/2 × 2 1/3 = 3/2 × 7/3 = 21/6 = 7/2 = 3 1/2
The full pipeline. Convert each mixed number: 1 1/2 becomes 3/2 and 2 1/3 becomes 7/3. Multiply across — 3 × 7 = 21 over 2 × 3 = 6 — then bring the improper product back to mixed form: 7/2 is 3 wholes with 1/2 left over. The answer 3 1/2 is readable; 21/6 is not.
Worked example
1 1/4 × 1 1/5 = 5/4 × 6/5 = 1/2 × 3/1 = 3/2 = 1 1/2
Converting to improper fractions does more than make the shape uniform — it exposes the cancellations. The 5s cancel across the fractions, then 6 and 4 share the factor 2. Without cancelling you would multiply 5 × 6 = 30 over 4 × 5 = 20 and reduce 30/20 to 3/2 afterwards. Same answer, bigger detour.
Worked example
2 1/2 × 1 1/3 = 5/2 × 4/3 = 20/6 = 10/3 = 3 1/3
The 4 and the 2 share a factor, so cancel first: 5/2 × 4/3 becomes 5/1 × 2/3, which is 10/3. In mixed form that is 3 wholes and 1/3. Notice the product lands bigger than either factor — both mixed numbers are greater than 1, so their product must be greater than both.
Worked example
3 1/2 × 2 = 7/2 × 2/1 = 14/2 = 7
Mixed number times a whole number uses the same method. Rewrite 2 as 2/1, convert 3 1/2 to 7/2, and the 2s cancel completely: the answer is exactly 7. Three and a half, twice, is seven.
A mixed number names a single amount: 2 1/3 is not “two, and separately a third.” The multiply-across rule needs one numerator and one denominator per factor, and mixed-number form does not show either — the whole part has no denominator. Converting merges the two parts into one fraction: 2 × 3 + 1 = 7 over 3, so 2 1/3 becomes 7/3.
Once every factor is a fraction, the problem is ordinary fraction multiplication — the same rule as 2/3 × 4/5, with nothing new to remember. The conversions at each end are bookkeeping; the multiplication in the middle never changes.
The tempting shortcut is to multiply the whole-number parts and the fraction parts separately. For 2 1/2 × 1 1/2, that gives 2 × 1 = 2 and 1/2 × 1/2 = 1/4, so the answer looks like 2 1/4. The real product is 5/2 × 3/2 = 15/4 = 3 3/4 — the shortcut misses by more than a whole. The whole parts of the two factors interact: the full 2 multiplies the full 1 1/2, and 2 1/2 multiplies the half as well.
A quick estimate catches this before it happens. 2 1/2 is a little more than 2, and 1 1/2 is a little more than 1, so the product should sit a little above 2 × 1 1/2 = 3 — 2 1/4 is too small. Estimating first, then computing, is the cheapest insurance in this topic.
Improper fractions have large numerators — a 1 1/4 quietly becomes 5/4, and 2 1/3 becomes 7/3. Larger numbers mean more chances that a numerator shares a factor with some denominator, so cancelling pays off more often here than in plain fraction-times-fraction problems. In 1 1/4 × 1 1/5, the hidden 5s cancel the moment the mixed numbers become improper.
The reverse also matters: cancel in improper form only. Cancelling “part of a mixed number” — reducing the fraction piece while ignoring the whole — changes the value. Convert first, then cancel, then multiply.
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