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Multiplying Fractions Calculator

The multiplying fractions calculator multiplies straight across, 2/3 x 9/10 = 18/30, then divides top and bottom by 6 to give the product in lowest terms, 3/5.

When rewriting over a denominator, the denominator to rewrite the first fraction over.

Answer3/5

As a mixed number Already a proper fraction: smaller than one, so there is no whole part.
3/5
As a decimal Exact.
0.6
The problem
2/3 x 9/10 = 3/5
Multiply across
(2 x 9) / (3 x 10) = 18/30
Reduced No common denominator is needed to multiply. Only addition and subtraction require one.
divide top and bottom by 6 to get 3/5
As a percentage
60%
Comparison Compared by cross-multiplying rather than by converting to decimals, so the answer is exact even when the decimals are not.
2/3 is smaller than 9/10
  • Every answer is exact and in lowest terms. No step converts to a decimal, which is what lets 1/3 + 1/6 come out as exactly 1/2.
  • A mixed number's sign applies to the whole quantity: -2 1/3 means -(2 + 1/3), which is -7/3.

How the Fraction Calculator works

Multiplication is the easiest operation on fractions, because no common denominator is needed. Multiply the numerators together and the denominators together, then simplify.

The example, 2/3 x 9/10. Numerators: 2 x 9 = 18. Denominators: 3 x 10 = 30. The product is 18/30, and since 18 and 30 share a greatest common factor of 6, it simplifies to 3/5.

Cancel first to keep numbers small. Before multiplying, any numerator can be canceled against any denominator. The 3 in the first denominator divides the 9 in the second numerator, leaving 3; the 2 in the first numerator divides the 10, leaving 5. Then 1/1 x 3/5 = 3/5 directly. Same answer, smaller numbers, and with large fractions it is the difference between easy arithmetic and an overflow.

Whole numbers. Write the whole number over 1. 4 x 2/3 = 4/1 x 2/3 = 8/3, or 2 2/3. Enter it here as whole number 4 with numerator 0 and denominator 1.

Mixed numbers. Convert to improper fractions first. 1 1/2 x 2 2/3 = 3/2 x 8/3 = 24/6 = 4. Multiplying the whole parts and the fraction parts separately (1 x 2 and 1/2 x 2/3) gives 2 1/3, which is wrong.

What "of" means. Multiplying by a fraction takes that fraction of the number: 2/3 of 9/10 is 2/3 x 9/10. That is why multiplying by a proper fraction makes a positive number smaller, the reverse of what multiplying by a whole number does.

Fraction Calculator FAQ

How do you multiply fractions?

Multiply the numerators, multiply the denominators, and simplify. 2/3 x 9/10 = 18/30 = 3/5.

Do you need a common denominator to multiply fractions?

No. Common denominators are only needed to add or subtract. Multiplication works straight across.

How do you multiply a fraction by a whole number?

Write the whole number over 1 and multiply across. 4 x 2/3 = 4/1 x 2/3 = 8/3, which is 2 2/3.

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