Dividing Fractions Calculator

To divide fractions, use the 'keep, change, flip' method: keep the first fraction as-is, change the division sign to multiplication, then flip (reciprocate) the second fraction. For example, 3/4 ÷ 2/5 becomes 3/4 × 5/2 = 15/8. Finally, simplify the result if possible.

'Keep, change, flip' (also called KCF) is a memory aid for dividing fractions. You keep the first fraction unchanged, change the ÷ operator to ×, and flip the second fraction (swap its numerator and denominator). This works because dividing by a number is the same as multiplying by its reciprocal.

First convert each mixed number to an improper fraction. For example, 2 1/2 becomes 5/2 and 1 1/3 becomes 4/3. Then apply the standard 'keep, change, flip' rule: 5/2 ÷ 4/3 = 5/2 × 3/4 = 15/8 = 1 7/8.

Find the Greatest Common Divisor (GCD) of the numerator and denominator, then divide both by it. For instance, 15/10 has a GCD of 5, so it simplifies to 3/2. This gives you the fraction in its lowest terms.

Yes. Treat the whole number as a fraction with denominator 1. For example, dividing 3/4 by 2 is the same as 3/4 ÷ 2/1. Applying 'keep, change, flip' gives 3/4 × 1/2 = 3/8.

Any non-zero number divided by itself equals 1. So dividing a fraction by the same fraction always results in exactly 1, regardless of what numerator or denominator is used (as long as neither is zero).

Yes. When dividing fractions with negative numbers, follow the normal rules of signs: a negative divided by a positive (or vice versa) gives a negative result, while a negative divided by a negative gives a positive result. Apply 'keep, change, flip' as usual, then determine the sign separately.

Division by zero is undefined in mathematics. A denominator of zero would mean the fraction itself has no meaningful value, so calculators and mathematicians always require the denominator to be a non-zero number.