Write the expression as improper fraction divided by a mixed number. For an example, let the expression be 15/7 ÷ 1 2/3.
Multiply the whole number part of the mixed number by its denominator, then add that product to the numerator to convert the number into an improper fraction. For example, when the mixed number is 1 2/3, multiplying 1 by 3 results in 3, and adding 3 to 2 equals 5, resulting in 5/3. The expression now reads as 15/7 ÷ 5/3.
Invert the modified mix number and change the division sign to multiplication. In this example, the mixed number 5/3 becomes 3/5 --- so the expression becomes 15/7 --- 3/5.
Compare the factors of each fraction's numerator to the other's denominator, and factor out the largest factor that both possess. In this example, the first fraction's numerator 15 has 1, 3, 5 and 15 as factors and the second fraction's denominator 5 has 1 and 5 as factors --- 5 can be factored out of both, leaving the numerator as 3 and the denominator as 1. The second fraction's numerator 3 has 1 and 3 as factors, and the first fraction's denominator 7 has 1 and 7 as factors --- no real factors can be factored out since factoring out 1 will not affect the numbers, so the numbers remain unchanged. The expression is now 3/7 --- 3/1.
Multiply the numerators and denominators, then write the numerators' product over the product of the denominators. In this example, multiplying 3 and 3 results in 9, and multiplying 7 and 1 results in 7 --- the fraction becomes 9/7.
Convert the answer into a mixed number if it is an improper fraction. Concluding this example, 9/7 is an improper fraction. Divide the fraction's denominator into its numerator, writing the quotient as the whole number and the remainder as a fraction --- 7 divides into 9 once with a remainder of 2, so the improper fraction 9/7 becomes 1 2/7.