Fraction Calculator

Adding and subtracting need a common denominator: a/b + c/d = (ad + cb) / bd. Multiplying goes straight across: a/b x c/d = ac / bd. Dividing flips the second fraction and multiplies: a/b / c/d = ad / bc. The answer is then divided by the greatest common divisor of top and bottom, which is what puts it in lowest terms.

How do I add fractions with different denominators?

Give them the same denominator first. Multiply each fraction by whatever makes the bottoms match - for 3/4 and 2/5 that is 15/20 and 8/20 - then add the tops and keep the bottom.

What does simplifying mean?

Dividing the top and bottom by the largest number that goes into both. 8/12 divides by 4 to give 2/3. The value is unchanged; only the way it is written is smaller.

What is a mixed number?

A whole number with a fraction beside it, like 1 3/20 instead of 23/20. Recipes and tape measures use mixed numbers; algebra almost always prefers the improper fraction.

Why does dividing by a fraction make the answer bigger?

Because you are asking how many of the small thing fit into the big one. 2 divided by 1/4 asks how many quarters are in 2, and the answer is 8. Flipping and multiplying is the shortcut for that question.