How to solve it
- Multiply the numerators together.
- Multiply the denominators together.
- Simplify the result. You can also cross-cancel before multiplying.
2/3 × 3/8 = 6/24 = 1/4
Result: 1/4
Common mistake:Wrong: 1/2 × 1/3 = 1/5.Right: 1/2 × 1/3 = 1/6.Multiplication needs no common denominator, and the denominators are multiplied, not added.
Multiplying fractions does not need a common denominator: you work directly with the top numbers and the bottom numbers. Below you will find a full example, two ways to read the product, the cases that change the calculation and one very common mistake. If you are wondering why the result can be smaller than the factors, see the guide on multiplying by a fraction less than one.
Worked example: 2/3 × 9/10
A piece of fabric is 9/10 of a yard long and you use 2/3 of it. What part of a yard did you use?
- Multiply the numerators. 2 × 9 = 18.
- Multiply the denominators. 3 × 10 = 30, so the product is 18/30.
- Reduce. The greatest common factor of 18 and 30 is 6, and 18/30 = 3/5.
Answer: 3/5 of a yard.
Check: 0.667 × 0.9 ≈ 0.6 (error less than 0.001), which matches 3/5 = 0.6.
What multiplying fractions means
The product of two fractions is a part of a part. Half of a third is 1/2 × 1/3 = 1/6: splitting a whole into three parts and each third into two gives sixths. That is why you multiply the denominators, which count how many parts the whole is split into, and the numerators, which count how many parts you take.
The same calculation is an area. A rectangle 3/4 yd by 2/3 yd has an area of 3/4 × 2/3 = 6/12 = 1/2 square yard. Inside a square 1 yd on a side, the rectangle covers 3 of 4 columns and 2 of 3 rows, which is 6 of the 12 cells.
Cancelling before multiplying
You can divide a numerator and a denominator by the same number before multiplying, even if they belong to different fractions. In the example, the 2 and the 10 are divided by 2, and the 9 and the 3 by 3. That leaves (1 × 3)/(1 × 5) = 3/5, without going through 18/30.
Another case: 6/35 × 14/15 gives 84/525 if you multiply straight across, and 4/25 after reducing. Cancelling first, 6 and 15 are divided by 3, and 14 and 35 by 7, and the calculation is 2/5 × 2/5 = 4/25. The calculator cancels the common factors between numerators and denominators first, shows it in the steps, and then reduces the result. You can only cancel a numerator with a denominator, never two numerators with each other or a term in a sum.
Cases that change the calculation
A whole number, a mixed number, a sign or a zero needs a small adjustment before multiplying. The table shows what to do in each case.
| Case | What you do | Calculation |
|---|---|---|
| Whole number times a fraction | Write the whole number over 1 | 4 × 3/8 = 12/8 = 3/2 |
| Mixed number | Convert to an improper fraction | 2 1/2 × 4/5 = 5/2 × 4/5 = 2 |
| One negative factor | The product is negative | −5/6 × 3/10 = −15/60 = −1/4 |
| A factor of zero | The product is zero | 0 × 5/7 = 0 |
The sign follows a simple rule: with an odd number of negative factors the product is negative, and with an even number it is positive. For more sign cases across all operations, see negative fractions.
When to use another page
If your product includes sums or parentheses, fraction expressions follow the order of operations. For the inverse operation, which multiplies by the reciprocal of the divisor, there is dividing fractions. If you want to reduce a result you already have, use simplify fractions, and to practice with answers, try the multiplication worksheets.
The calculator accepts up to 100 digits per number and rejects any denominator equal to zero. OpenStax covers multiplying fractions in detail (accessed October 16, 2026).
Frequently asked questions
Can I multiply three or more fractions at once?
Yes. Multiply all the numerators and all the denominators, then reduce. With 3/4 × 4/9 × 2/7 you get 24/252, which reduces to 2/21. The calculator's "Mixed numbers and decimals" mode accepts 2 to 20 factors, and the order does not change the result.
How do I multiply a fraction by a decimal?
Write the terminating decimal as a fraction and multiply as usual. With 0.125 × 4/5, the decimal is 125/1000 = 1/8, so the product is 4/40 = 1/10, which is 0.1 as a decimal. The calculator accepts a period or a comma as the separator and returns an exact fraction, never a rounded value.
When is the product of two fractions a whole number?
When the denominator disappears after cancelling. In 3/10 × 20/3, the 3 cancels with the 3 and the 20 with the 10, leaving 2. It happens when the numerators contain all the factors of the denominators.
What happens if a denominator is zero?
A fraction with a zero denominator is undefined, so it cannot be multiplied and the calculator asks you to fix the entry. A zero numerator is fine: any product with a factor equal to zero is 0, as in 0 × 9/4.
How do I find a fraction of an amount?
Multiply the fraction by the amount. For 3/8 of 40, calculate 3/8 × 40 = 120/8 = 15. That is the same as dividing 40 by 8 and taking 3 parts. The fraction of a number page solves it with units.