Multiply & Divide Fractions Calculator

Multiplying and dividing fractions trips up more students than adding them, which feels backwards because the arithmetic is actually simpler. There is no common denominator to hunt for. To multiply two fractions you go straight across: numerator times numerator over denominator times denominator. Two thirds times three quarters is six twelfths, which reduces to one half. That is the whole rule.

Division is multiplication wearing a disguise. To divide by a fraction you flip the second one and multiply, the move every teacher calls keep, change, flip: keep the first fraction, change the divide sign to a multiply, and flip the divisor upside down. So one half divided by three quarters becomes one half times four thirds, which is four sixths, or two thirds. Why does flipping work? Dividing by three quarters asks how many three-quarter pieces fit into your number, and multiplying by its reciprocal answers exactly that.

The part people forget is the cleanup. A correct answer left as twelve over eighteen still loses marks in most classrooms, so this calculator always reduces to lowest terms using the greatest common divisor, then also gives you the mixed number and the decimal so you can check the result against a different representation. If you get three halves from the math and 1.5 from the decimal line, you know the fraction is right.

A couple of notes. You can enter negative numerators, and the sign is carried to the top of the reduced answer the way it is normally written. You cannot divide by zero, so a second fraction of zero in a division returns an error rather than a number. Enter the two fractions, choose multiply or divide, and you get the worked steps, the simplified fraction, the mixed number, and the decimal.