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Divide Fractions Calculator

Fraction division in one step.

How it is calculated

The tool divides the first fraction by the second using keep-change-flip: n1/d1 ÷ n2/d2 = (n1·d2) / (d1·n2). It then divides top and bottom by their greatest common divisor, so the answer is always in lowest terms. Order matters: the first fraction is the one being divided. All four boxes must be whole numbers (no more than 3 billion in size); a decimal such as 0.5 gives no result. The second numerator cannot be 0, because dividing by zero has no answer, and neither denominator can be 0; in those cases there is no result either. Negative numbers are fine and the sign is moved to the front. A whole-number answer is shown over 1, and a zero numerator in the first fraction gives 0/1.

Worked example

Divide 3/4 by 5/6. Flip the second fraction to 6/5 and multiply: top 3 × 6 = 18, bottom 4 × 5 = 20, giving 18/20. The greatest common divisor of 18 and 20 is 2, so divide both by 2. The calculator shows 9/10. As a check, 9/10 × 5/6 = 45/60 = 3/4, the starting fraction.

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Common mistakes

  • Flipping the first fraction instead of the second. Only the divisor (the second fraction) is inverted.
  • Swapping the two fractions. 3/4 ÷ 5/6 is 9/10, while 5/6 ÷ 3/4 is 10/9.
  • Putting 0 in the second numerator. Dividing by 0/x has no answer and the tool returns nothing.
  • Entering decimals in the boxes. Convert to whole numbers first, for example 0.5/3 becomes 1/6; the tool rejects the decimal rather than rounding it.
  • Expecting the answer to be smaller. Dividing by a fraction below 1 makes the number larger: 3/4 ÷ 5/6 = 9/10 is larger than 3/4.

About this calculator

Dividing one fraction by another follows the keep-change-flip method: keep the first fraction as it is, change the division sign to multiplication, and flip (take the reciprocal of) the second fraction — so a/b divided by c/d becomes a/b multiplied by d/c. The result is then simplified by dividing the numerator and denominator by their greatest common divisor.

This method works because dividing by a number is mathematically identical to multiplying by its reciprocal, the same principle behind the reciprocal calculator; it is one of the core skills taught in elementary and middle-school arithmetic, and it underlies later topics like solving rational equations and simplifying complex fractions in algebra.

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