Multiplying Fractions Calculator
Enter two or three fractions (or mixed numbers) to multiply them together. The calculator shows the simplified fraction result, the equivalent mixed number, and the decimal value. Toggle "show a third fraction" to chain three fractions in one calculation, and flip on "mixed number" mode to enter whole-number parts alongside the fractions. A step-by-step panel walks through each stage of the multiplication so you can follow along or check your work.
Formula
Worked example
To multiply 2/3 by 3/4: multiply the numerators (2 × 3 = 6) and multiply the denominators (3 × 4 = 12) to get 6/12. The GCD of 6 and 12 is 6, so divide both by 6 to get 1/2. The decimal equivalent is 0.5.
How to multiply fractions
Multiplying fractions is the simplest of the four fraction operations. The rule is: multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator. So (a/b) x (c/d) = (a x c) / (b x d). After that single step, simplify the result by dividing both the numerator and denominator by their greatest common divisor (GCD). For example, (2/3) x (3/4) = 6/12. Because GCD(6, 12) = 6, you divide both by 6 to get 1/2. You do not need a common denominator for multiplication, which is why it is easier than addition or subtraction of fractions.
Cross-cancellation: simplify before you multiply
When the numbers are large, it helps to simplify before multiplying rather than after. Look diagonally: check whether the numerator of one fraction shares a common factor with the denominator of the other. For (4/9) x (3/8), notice that 4 and 8 share a factor of 4 (divide to get 1 and 2), and 3 and 9 share a factor of 3 (divide to get 1 and 3). After cross-cancellation you multiply (1/3) x (1/2) = 1/6, reaching the same answer with far smaller numbers. This technique, called cross-cancellation or cross-reduction, avoids big intermediary products and lowers the chance of arithmetic errors.
Multiplying mixed numbers
A mixed number like 2 3/4 has a whole-number part and a fractional part. Before multiplying, convert it to an improper fraction: multiply the whole number by the denominator and add the numerator. So 2 3/4 becomes (2 x 4 + 3)/4 = 11/4. Once every mixed number is an improper fraction, apply the standard rule: multiply numerators, multiply denominators, simplify. For example, 1 1/2 x 2 2/3 = (3/2) x (8/3) = 24/6 = 4. Converting first keeps the process mechanical and avoids confusion.
Multiplying three or more fractions
The same rule extends naturally to three or more fractions: multiply all the numerators together, multiply all the denominators together, and simplify the resulting fraction. For (1/2) x (2/3) x (3/4), the numerators give 1 x 2 x 3 = 6 and the denominators give 2 x 3 x 4 = 24, producing 6/24. The GCD of 6 and 24 is 6, giving a final answer of 1/4. Cross-cancellation across multiple fractions can also reduce the work significantly: any numerator can be cancelled against any denominator before multiplying.
Common fraction multiplication results
| Expression | Raw product | Simplified | Decimal |
|---|---|---|---|
| 1/2 × 1/2 | 1/4 | 1/4 | 0.25 |
| 1/2 × 1/3 | 1/6 | 1/6 | 0.1667 |
| 2/3 × 3/4 | 6/12 | 1/2 | 0.5 |
| 3/4 × 4/5 | 12/20 | 3/5 | 0.6 |
| 1/3 × 1/3 | 1/9 | 1/9 | 0.1111 |
| 2/5 × 5/6 | 10/30 | 1/3 | 0.3333 |
| 3/5 × 2/3 | 6/15 | 2/5 | 0.4 |
| 7/8 × 4/7 | 28/56 | 1/2 | 0.5 |
These standard products are useful reference points when checking your work.
Frequently asked questions
Do I need a common denominator to multiply fractions?
No. A common denominator is only needed for addition and subtraction of fractions. For multiplication, you simply multiply numerator by numerator and denominator by denominator - no adjustment to the denominators is required beforehand.
How do I simplify a fraction after multiplying?
Find the greatest common divisor (GCD) of the resulting numerator and denominator, then divide both by that number. For example, 6/12 has a GCD of 6, so 6 / 6 = 1 and 12 / 6 = 2, giving 1/2. You can also use prime factorization or the Euclidean algorithm to find the GCD.
What is cross-cancellation and how does it help?
Cross-cancellation means simplifying diagonally across fractions before you multiply: divide a numerator from one fraction by a factor shared with the denominator of another fraction. For (6/7) x (14/9), you can cancel 6 and 9 by 3 (getting 2 and 3) and cancel 14 and 7 by 7 (getting 2 and 1), leaving (2/1) x (2/3) = 4/3. The final answer is the same but the intermediate numbers are smaller and easier to handle.
How do I multiply a fraction by a whole number?
Write the whole number as a fraction with denominator 1, then apply the standard rule. For example, 3 x (2/5) = (3/1) x (2/5) = 6/5, which simplifies to 1 1/5 as a mixed number. Equivalently, you can just multiply the numerator by the whole number and keep the denominator unchanged.
Why is the product of two proper fractions smaller than either fraction?
A proper fraction is less than 1, so multiplying by it scales the other fraction down. For example, 1/2 of 3/4 means you are taking half of something already smaller than a whole, giving 3/8 - smaller than both 1/2 and 3/4. Mathematically, if 0 < a/b < 1 and 0 < c/d < 1, then the product (ac)/(bd) is smaller than both fractions.
How do I multiply mixed numbers?
Convert each mixed number to an improper fraction first. For a mixed number W N/D, the improper fraction is (W x D + N)/D. Once both are improper fractions, multiply numerators together and denominators together, then simplify and convert back to a mixed number if needed.