How to Multiply Fractions
Multiply fractions straight across, simplify to lowest terms, cross-cancel first, and handle whole numbers and mixed numbers, then check the answer with a quick estimate.
You will end up able to multiply fractions, simplify the answer, handle whole numbers and mixed numbers, and check the result with a quick estimate. Multiplying is simpler than adding or subtracting fractions, because there are no common denominators to find. You multiply straight across.
The details are where answers go wrong: when to simplify, what to do with a mixed number, and how cross-canceling keeps the numbers small. Each one has its own step below, with a worked example you can check.
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 The same rule gives 1/4 × 3/7 = 3/28. You do not need a common denominator and you do not flip anything. Multiply straight across, top and bottom.
Good to know: Dividing fractions uses the same rule with one extra move. Flip the second fraction (swap its top and bottom), then multiply straight across. For example, 1/2 ÷ 1/4 = 1/2 × 4/1 = 4/2 = 2. That flip is the only step multiplication does not have.
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 In a second example, 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. As a second 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. Skipping the conversion gives the wrong answer shown in the warning below.
Heads up: Do not multiply 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 rounds to 1/2. 2/3 rounds to 1/2 as well, though it sits a fair way above it. 1/2 × 1/2 = 1/4. The actual answer is 5/12, which is a good deal bigger than 1/4. Both fractions rounded down, so the estimate came in low, and that is normal rather than a sign of a mistake. An estimate tells you the size of the answer, not its value. 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. Two proper fractions (both less than 1) always multiply to something smaller than either one, as FAQ 2 below explains, so an answer bigger than either fraction is a mistake.
If an answer will not reduce the way you expect, find the greatest common factor again (step 2), or cross-cancel before you multiply next time (step 3). If the product of two proper fractions comes out bigger than either one, check whether a top and bottom got swapped, then run the estimate from step 6. If a problem with mixed numbers comes out smaller than your estimate, check that you converted each mixed number before multiplying (step 5). If you need to turn a fraction into a decimal, our guide on how to do long division walks through it.
Questions we get asked about this
Answers from experience, not a textbook.
Turn the decimal into a fraction first, then multiply as usual. Drop the decimal point and write the number over 10, 100, or 1,000, with one zero for each digit after the point. Then simplify, so 0.35 becomes 35/100, which is 7/20. For example, 3/4 × 0.4 = 3/4 × 2/5 = 6/20 = 3/10, which is 0.3 as a decimal. To go the other way and turn a fraction answer into a decimal, divide the top by the bottom.
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.