Multiplying fractions is one of the simplest fraction operations because you do not need a common denominator. You multiply straight across the top and bottom, then reduce the answer to its simplest form.
Step by step
- Write the fractions side by sideSet up the problem as two fractions being multiplied, for example 2/3 times 4/5.
- Convert any whole or mixed numbersTurn a whole number into a fraction over 1, and change a mixed number like 1 1/2 into an improper fraction such as 3/2 before multiplying.
- Multiply the numeratorsMultiply the two top numbers together. In the example, 2 times 4 gives 8, which becomes the new numerator.
- Multiply the denominatorsMultiply the two bottom numbers together. Here 3 times 5 gives 15, which becomes the new denominator, so you have 8/15.
- Simplify the resultDivide the top and bottom by their greatest common factor. If they share no common factor, as with 8/15, the fraction is already in simplest form.
Handy tips
- You can cancel common factors between a top and a bottom number before multiplying to keep the numbers small.
- The word of usually means multiply, so half of a quarter is 1/2 times 1/4.
- Multiplying by a fraction less than 1 gives an answer smaller than the number you started with.
FAQ
Do I need a common denominator to multiply fractions?
No. Common denominators are only needed for addition and subtraction. To multiply, you simply multiply across the tops and across the bottoms.
How do I multiply a fraction by a whole number?
Write the whole number as itself over 1, then multiply across. For example, 5 times 2/3 is 5/1 times 2/3, which equals 10/3.
What about mixed numbers?
Convert each mixed number to an improper fraction first, then multiply as usual and simplify or convert back to a mixed number at the end.