## Multiplying and Dividing Fractions

Problem – Basic Math/Algebra – Multiplication and Division of Fractions This is a video session on how to multiply and divide fractions, as how students generally encounter it in Pre-Algebra and early Algebra courses.

Notice that the illustration starts off with some relatively simple multiplication problems, and ultimately ends with some more complex division of mixed numbers. This wasn’t an accident. It illustrates that these types of problems can be as easy as a 3 step process:

1. Multiply across to calculate the new numerator and denominator;
2. Use the prime factorization process to identify and eliminate common factors in the numerator and denominator; and
3. Multiply-out to find the final answer;

or as complex as a 6 step process:

1. Convert mixed numbers to improper fractions;
2. Convert “division by a fraction” to “multiplication by the reciprocal of the fraction”;
3. Multiply across to calculate the new numerator and denominator;
4. Use the prime factorization process to identify and eliminate common factors in the numerator and denominator;
5. Multiply-out to find the final answer, possibly as an improper fraction; and
6. Convert the improper fraction to a mixed number, if necessary.

When we teach this skill, we use a building approach in which we make sure that you feel comfortable first with problems requiring the simple process, and then move on to the more complex. From there, we help you become fluent in the simple ones before moving on to master the more complex.