Fraction Calculator guide
How to Multiply Fractions
To multiply fractions, multiply the numerators together and the denominators together, then simplify. For 2/3 × 3/4, that is (2 × 3) ÷ (3 × 4) = 6/12, which simplifies to 1/2. No common denominator is needed.
The good news
Multiplying is the easiest of the four fraction operations, and it often comes as a relief after addition.
You do not need a common denominator. Just multiply straight across: top by top, bottom by bottom.
A common mix-up is to find a common denominator out of habit, because that is what addition drilled in. It is not wrong exactly — you would still get a correct answer eventually — but it is unnecessary work.
A worked example
Take 2/3 × 3/4.
Multiply the numerators: 2 × 3 = 6.
Multiply the denominators: 3 × 4 = 12.
That gives 6/12, which simplifies to 1/2.
Cross-cancelling saves work
You can simplify before multiplying, which keeps the numbers small and often removes the need to simplify at the end at all.
In 2/3 × 3/4, the 3 on top of the second fraction and the 3 on the bottom of the first cancel each other out. That leaves 2/1 × 1/4 = 2/4 = 1/2.
You can cancel any numerator against any denominator, including diagonally across the multiplication sign. What you cannot do is cancel two numerators against each other, or two denominators.
For larger numbers this is a significant saving. 15/16 × 8/25 becomes 3/2 × 1/5 after cancelling, which is far easier than multiplying out to 120/400.
Why "of" means multiply
When a question asks for "two thirds of three quarters", it is asking you to multiply. That word is the giveaway.
It works because taking a fraction of something is exactly what multiplication by a fraction does. Half of 8 is 8 × ½ = 4, which matches your intuition. Half of ¾ is ¾ × ½ = ⅜, which follows the same rule.
This is also why multiplying by a fraction less than 1 makes things smaller, which can feel wrong the first time. Multiplication does not always increase — it increases only when you multiply by something greater than 1.
Multiplying mixed numbers
Convert to improper fractions first. Do not try to multiply the whole numbers and the fractions separately — that method works for addition and fails badly here.
For 1½ × 2⅓: convert to 3/2 and 7/3. Multiply straight across: 21/6, which simplifies to 7/2, or 3½.
If you had multiplied the parts separately you would have got 2 × 1 = 2 and ½ × ⅓ = ⅙, giving 2⅙. The right answer is 3½, so the error is substantial.
