How do you divide a mixed number by a fraction?

To divide a mixed number by a fraction, change the mixed number to an improper fraction. Write the reciprocal of the divisor. Simplify the fractions if possible. Multiply the numerators and then the denominators.

Example:

To divide a mixed number by a fraction:

Ms. Butler has packages of art paper containing 20 sheets each. She determined that packages were enough to give each student in her class 3 sheets, or of a package. To find how many students are in her class, divide packages by .

First, write the mixed number as an improper fraction.

Then, write the reciprocal of the divisor by switching the numerator and denominator.

Before multiplying the fractions, check if you can simplify the fractions: divide any numerator and denominator by their greatest common factor. The greatest common factor of 4 and 20 is 4, so cross out and divide both numbers by 4.

The greatest common factor of 15 and 3 is 3, so cross out and divide both numbers by 3.

Now, multiply the numerators and denominators of the simplified fractions.

Write the product as a whole number by dividing the numerator by the denominator. The improper fraction equals 25.

There are 25 students in Ms. Butler's class.