How to Multiply Fractions
Learn how to multiply fractions step by step with simple examples. Covers simplifying, cross-canceling, mixed numbers, and whole numbers.
Multiplying fractions is one of those things that made perfect sense for about five minutes in school and then slowly faded from memory. But here is the good news: it is actually simpler than adding or subtracting fractions. There are no common denominators to worry about. You just multiply straight across.
The tricky part is remembering the small details. When do you simplify? What do you do with mixed numbers? What is cross-canceling and why does everyone keep bringing it up?
This guide walks through it all with clear examples. By the end, you will be able to multiply any two fractions in your head without second-guessing the steps.
Multiply straight across the top and bottom
This is the entire rule. Multiply the numerators (the top numbers) together, then multiply the denominators (the bottom numbers) together. 2/3 × 4/5 Top: 2 × 4 = 8 Bottom: 3 × 5 = 15 Answer: 8/15 One more. 1/4 × 3/7 = 3/28. No common denominators needed. No flipping anything. Just straight across, top and bottom.
Good to know: A helpful way to remember: for addition you need matching denominators, but for multiplication you just go straight across. Multiplication is actually the simpler operation when it comes to fractions.
Simplify the result to lowest terms
After multiplying, check whether your numerator and denominator share a common factor. Divide them both by the largest number that goes into each evenly. That number is called the greatest common factor. 3/4 × 2/6 = 6/24 Both 6 and 24 are divisible by 6. 6 ÷ 6 = 1, and 24 ÷ 6 = 4. Simplified answer: 1/4 Another one. 5/8 × 2/3 = 10/24. The greatest common factor of 10 and 24 is 2. Divide both: 10 ÷ 2 = 5, 24 ÷ 2 = 12. Answer: 5/12. If you cannot spot the greatest common factor right away, start small. Try dividing both numbers by 2, then 3, then 5. Keep going until nothing divides evenly.
Cross-cancel to keep the numbers small
Cross-canceling lets you simplify before you multiply, so you never deal with big numbers in the first place. Look diagonally across the two fractions. If one fraction's numerator and the other fraction's denominator share a common factor, divide them both by that factor before you multiply. 3/8 × 4/9 Look diagonally. 3 and 9 share a factor of 3. Divide: 3 becomes 1, 9 becomes 3. Now look the other way. 4 and 8 share a factor of 4. Divide: 4 becomes 1, 8 becomes 2. You are left with 1/2 × 1/3 = 1/6. That is the same answer you would get by multiplying first (3 × 4 = 12, 8 × 9 = 72, then reducing 12/72), but with much smaller numbers the whole way through.
Good to know: You can only cross-cancel between a numerator and the other fraction's denominator. Never cancel two numerators or two denominators against each other.
Multiply a fraction by a whole number
Any whole number can be written as a fraction by putting it over 1. Once you do that, the normal rule applies. 5 × 2/3 = 5/1 × 2/3 = 10/3 If your answer is an improper fraction (the top number is bigger than the bottom), convert it to a mixed number. Divide 10 by 3. That gives you 3 with a remainder of 1. So 10/3 = 3 1/3. Another example. 4 × 3/8 = 12/8. Simplify by dividing both by 4: 12 ÷ 4 = 3, 8 ÷ 4 = 2. Answer: 3/2 = 1 1/2.
Convert mixed numbers before multiplying
A mixed number is a whole number paired with a fraction, like 2 1/3. You cannot multiply mixed numbers directly. Convert them to improper fractions first. To convert, multiply the whole number by the denominator, add the numerator, and put the result over the original denominator. 2 1/3 = (2 × 3 + 1) / 3 = 7/3 1 1/2 = (1 × 2 + 1) / 2 = 3/2 Now multiply: 7/3 × 3/2. Cross-cancel the 3s: 7/1 × 1/2 = 7/2 = 3 1/2. Always convert first, then multiply, then simplify. Trying to multiply mixed numbers without converting leads to wrong answers.
Heads up: A common mistake is multiplying the whole numbers together and the fractions together separately (2 × 1 = 2, then 1/3 × 1/2 = 1/6, giving 2 1/6). That gives the wrong answer. The correct answer for 2 1/3 × 1 1/2 is 3 1/2.
Check your answer with a quick estimate
Round each fraction to the nearest benchmark: 0, 1/2, or 1. Multiply the benchmarks and see if your answer is in the right neighborhood. 5/8 × 2/3 5/8 is close to 1/2. 2/3 is close to 1/2 (or a bit more). 1/2 × 1/2 = 1/4. Your actual answer of 5/12 is close to 1/4, so you are on track. This catches big mistakes fast. If your estimate says the answer should be near 1/4 but you wrote down 5/2, something went wrong. One more thing to remember: when you multiply two proper fractions (both less than 1), the answer is always smaller than either fraction you started with. You are taking a part of a part. Half of a third is a sixth. If your answer is bigger than what you started with, go back and check your work.
The core rule fits in one sentence: multiply the tops, multiply the bottoms, simplify. Everything else is just a variation on that. Cross-canceling keeps the numbers small. Mixed numbers need to be converted first. Whole numbers go over 1. If you only remember one thing, remember to multiply straight across. That will get you through most fraction problems you run into. And if the answer looks too big or too small, use the estimation trick from the last step to double-check yourself.
Questions we get asked about this
Answers from experience, not a textbook.
No. Common denominators are only needed for adding and subtracting fractions. When multiplying, you go straight across: numerator times numerator, denominator times denominator. The denominators do not need to match.
Because you are taking a fraction of a fraction. Half of a half is a quarter. When both numbers are less than 1, the result is always less than either number you started with. Think of it as a part of a part. 1/2 × 1/3 means one half of one third, which is 1/6.
The same way. Multiply all the numerators together to get the new numerator, and multiply all the denominators together to get the new denominator. For example, 1/2 × 2/3 × 3/4 = 6/24, which simplifies to 1/4. Cross-cancel first if you can spot shared factors across any numerator and any denominator.
Cross-canceling is a shortcut you use before multiplying fractions. You simplify diagonally by dividing a numerator and the other fraction's denominator by their shared factor. Cross-multiplying is a different technique used for comparing fractions or solving equations that have fractions on both sides of an equals sign. They sound similar but do completely different things.
When adding fractions, you need a common denominator and you only add the numerators. When multiplying, you ignore whether the denominators match and multiply straight across, both top and bottom. Multiplying also makes the result smaller (when both fractions are less than 1), while adding makes it larger.