Multiplying Fractions Calculator
Our free fractions calculator solves multiplying fractions problems. Get worked examples, visual aids, and downloadable results.
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.
Can you multiply more than two fractions at once?
Yes, you can multiply any number of fractions together by extending the same basic rule. Multiply all the numerators together for the final numerator and all the denominators together for the final denominator. For example, 1/2 times 2/3 times 3/4 equals (1 times 2 times 3) over (2 times 3 times 4), which is 6/24, simplifying to 1/4. When multiplying three or more fractions, cross cancellation becomes especially valuable because there are more opportunities to simplify before multiplying. In the example above, you could cancel the 2 in the numerator with the 2 in the denominator, and the 3 in the numerator with the 3 in the denominator, immediately getting 1/4 without any intermediate large numbers.
What are common mistakes when multiplying fractions and how to avoid them?
The most common mistake is adding the denominators instead of multiplying them, which happens when students confuse the rules for addition and multiplication of fractions. Another frequent error is attempting to find a common denominator before multiplying, which is unnecessary and adds extra steps. Some students forget to simplify the final answer, leaving it in unreduced form like 6/20 instead of 3/10. When working with mixed numbers, a critical mistake is multiplying the whole numbers and fractions separately instead of converting to improper fractions first. To avoid these errors, always remember the simple rule: multiply straight across for both numerators and denominators, then simplify the result by finding the greatest common divisor.