Multiplying Fractions Calculator

Multiply two fractions or mixed numbers to get the simplified product, its mixed-number form, and its decimal equivalent, using (a/b) × (c/d) = (a×c)/(b×d).

Quick Facts

Multiplication rule
(a/b) × (c/d) = (a×c)/(b×d)
Multiply numerators together and denominators together — no common denominator needed.
Mixed numbers
Convert to improper fractions first
Multiply the whole number by the denominator, then add the numerator.
Simplifying
Divide by the GCD
Reduce the numerator and denominator by their greatest common divisor.

Your Results

Calculated
Simplified Product
-
(a×c)/(b×d), reduced to lowest terms
As a Mixed Number
-
Whole number plus remaining fraction
Decimal Equivalent
-
Simplified product written as a decimal
Unsimplified Product
-
Straight across, before reducing

Ready

Enter two fractions (or mixed numbers) and press Calculate.

How to Multiply Fractions

Multiplying fractions is the most direct of the four fraction operations because, unlike addition or subtraction, it never requires a common denominator. To multiply two fractions a/b and c/d, multiply the numerators together to get the new numerator, and multiply the denominators together to get the new denominator: (a/b) × (c/d) = (a×c)/(b×d). The result is then simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).

How the calculation works

If either fraction is written as a mixed number (a whole number plus a fraction, such as 1 1/2), the calculator first converts it to an improper fraction by multiplying the whole number by the denominator and adding the numerator — for example, 1 1/2 becomes (1×2+1)/2 = 3/2. Once both fractions are in a/b form, it multiplies straight across: numerator × numerator, and denominator × denominator. It then finds the GCD of the resulting numerator and denominator using the Euclidean algorithm and divides both by it to produce the simplified product, which is also shown as a mixed number and as a decimal.

Common mistakes

  • Finding a common denominator first: that step is required for addition and subtraction, not multiplication — multiplying fractions works directly on the numbers as given.
  • Forgetting to convert mixed numbers: multiplying the whole-number parts and fraction parts separately (e.g., treating 1 1/2 × 2/3 as 1 × 2/3 plus 1/2 × 2/3 incorrectly) gives the wrong answer — always convert to an improper fraction first.
  • Leaving the answer unsimplified: 6/12 and 1/2 are the same value, but 1/2 is the standard, fully reduced form expected in most answers.

Real-world applications

  • Scaling a recipe up or down, such as multiplying 2/3 cup of an ingredient by 1/2 to make half a batch.
  • Finding a fraction of a fraction, such as determining what portion of a workday (e.g., 3/4) is spent on a task that takes 1/3 of that time.
  • Converting between units or scales that are expressed as fractions, such as architectural or map scale drawings.
  • Computing probabilities of independent events, which multiply together as fractions (e.g., 1/2 chance times 1/6 chance).

Frequently Asked Questions

How do you multiply two fractions?
Multiply the numerators together and the denominators together: (a/b) × (c/d) = (a×c)/(b×d). For example, 2/3 × 3/4 = (2×3)/(3×4) = 6/12, which simplifies to 1/2.
Do I need a common denominator to multiply fractions?
No. Unlike adding or subtracting fractions, multiplying fractions does not require a common denominator — simply multiply straight across the numerators and denominators, then simplify the result.
How do you multiply mixed numbers?
Convert each mixed number to an improper fraction first (multiply the whole number by the denominator and add the numerator), then multiply the two improper fractions as usual. For example, 1 1/2 × 2/3 = 3/2 × 2/3 = 6/6 = 1.
How do I simplify the product of two fractions?
Divide the numerator and denominator of the result by their greatest common divisor (GCD). For example, 6/12 has a GCD of 6, so it simplifies to 1/2.

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