In a division problem, such as a ÷ b, a is the dividend, and b is the divisor. To divide fractions, you need to find the reciprocal of the divisor. The reciprocal is the fraction upside down, or reversed. In a/x ÷ b/y, the reciprocal of the divisor is y/b.
To divide a simple fraction by another simple fraction, such as 2/5 ÷ 3/5, find the reciprocal of the divisor (5/3) and multiply: 2/5 * 5/3. To do so, multiply the two numerators, or top numbers, to get the numerator of the answer: 2 * 5 = 10. Multiply the two denominators, or bottom numbers, to find the denominator of the answer: 5 * 3 = 15. The answer is 10/15, or 2/3 when simplified. Another example: 1/3 ÷ 2/5 = 1/3 * 5/2 = 5/6.
Dividing Mixed Fractions
If you have a mixed fraction, such as 2 1/3, first change it to an improper fraction. Multiply the denominator by the whole number and then add the numerator to get the numerator of improper fraction: (3 * 2) + 1 = 7. Use the denominator of the mixed fraction as the denominator in the improper fraction: 7/3. Once you have converted all mixed fractions into improper fractions, you can divide as usual. If the answer is an improper fraction, convert it to a mixed fraction. Example: 3 1/4 ÷ 2/7 = 13/4 ÷ 2/7 = 13/4 * 7/2 = 91/8 = 11 3/8.