Multiplying Fractions Calculator
Our free fractions calculator solves multiplying fractions problems. Get worked examples, visual aids, and downloadable results.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
a/b x c/d = (a x c) / (b x d)
To multiply fractions, multiply the numerators together for the new numerator and multiply the denominators together for the new denominator. Then simplify the result by dividing both by their greatest common divisor.
Worked Examples
Example 1: Basic Fraction Multiplication
Problem:Multiply 3/4 by 2/5.
Solution:Numerator: 3 x 2 = 6\nDenominator: 4 x 5 = 20\nProduct: 6/20\nGCD of 6 and 20 is 2\nSimplified: 6/2 = 3, 20/2 = 10\nFinal answer: 3/10
Result:3/4 x 2/5 = 6/20 = 3/10 (decimal: 0.3)
Example 2: Fraction Multiplication with Cross Cancellation
Problem:Multiply 5/8 by 4/15.
Solution:Cross cancel: 5 and 15 share factor 5 (become 1 and 3)\nCross cancel: 4 and 8 share factor 4 (become 1 and 2)\nSimplified multiplication: 1/2 x 1/3\nNumerator: 1 x 1 = 1\nDenominator: 2 x 3 = 6\nFinal answer: 1/6
Result:5/8 x 4/15 = 20/120 = 1/6 (decimal: 0.1667)
Frequently Asked Questions
How do you multiply two fractions together?
To multiply two fractions, you simply multiply the numerators together to get the new numerator and multiply the denominators together to get the new denominator. For example, multiplying 3/4 by 2/5 means computing 3 times 2 for the numerator (which equals 6) and 4 times 5 for the denominator (which equals 20), giving the result 6/20. This can then be simplified to 3/10 by dividing both numerator and denominator by their greatest common divisor of 2. Unlike adding or subtracting fractions, you do not need to find a common denominator before multiplying. This straightforward rule makes fraction multiplication one of the simpler fraction operations to perform.
How do you multiply mixed numbers as fractions?
To multiply mixed numbers, you must first convert each mixed number into an improper fraction before performing the multiplication. For example, to multiply 2 1/3 by 1 3/4, convert 2 1/3 to 7/3 (since 2 times 3 plus 1 equals 7) and convert 1 3/4 to 7/4 (since 1 times 4 plus 3 equals 7). Then multiply the improper fractions: 7/3 times 7/4 equals 49/12. Finally, convert back to a mixed number if desired: 49 divided by 12 equals 4 remainder 1, so the answer is 4 1/12. Attempting to multiply the whole numbers and fractions separately produces incorrect results, so always convert to improper fractions first.
Why does multiplying two fractions less than one give a smaller result?
When both fractions are between zero and one, their product will always be smaller than either fraction individually. This is because you are taking a part of a part. For instance, 1/2 times 1/3 equals 1/6, meaning one half of one third is one sixth, which is smaller than both one half and one third. This principle is intuitive when you think about it physically: if you have half a pizza and you eat one third of that half, you have eaten one sixth of the whole pizza. This concept often surprises students who associate multiplication with making numbers bigger, but that rule only applies when multiplying by numbers greater than one.
How do you multiply fractions with different signs (positive and negative)?
The rules for multiplying positive and negative fractions follow the same sign rules as integer multiplication. A positive fraction times a positive fraction gives a positive result. A negative fraction times a negative fraction also gives a positive result, because two negatives cancel out. A positive fraction times a negative fraction (or vice versa) gives a negative result. For example, (-2/3) times (4/5) equals -8/15, while (-2/3) times (-4/5) equals positive 8/15. The magnitude of the result is calculated the same way regardless of signs. Simply determine the sign first based on the rule, then multiply the absolute values of the numerators and denominators as normal.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy