## Lesson: Multiplying and Dividing Fractions and Mixed Numbers

Developing the Concept

Students can relate their understanding of the multiplication of fractions to the division of fractions and mixed numbers. Having students estimate and discuss answers will also help them gain a better understanding of the division of fractions.

**Materials:** paper and pencil

**Preparation:** none

**Prerequisite Skills and Background:** Students should be able to multiply and divide whole numbers. They should be able to multiply two fractions and be able to find the prime factorization for a number.

**Wrap-Up and Assessment Hints**

Having students estimate the product or quotient of two fractions before adding or subtracting will help them recognize unreasonable answers. For example, if they divide
by
, they should recognize that division is counting how many one-fourths are in
. Since
>
, which is equivalent to
, there are at least 2 one-fourths in
. Also, since
<
, there are not 3 one fourths in
. So the answer lies between 2 and 3.

Have students do pattern activities such as the following and then write on a bulletin board some of the things they discover. These activities will help them see patterns in multiplication, such as the following.

Ask what happened to the answer each time? (It was cut in half.)

Thus, the answer here must be 3. So what happens when we multiply a number by a fraction less than one? (The answer is less than the other number.)

To challenge some of your best students, ask them open-ended questions such as, “If the product of two fractions is when simplified, what could those two fractions be?” ( x , x , and so on) and “If the quotient of two fractions is 2, what could those two fractions be?” ( ÷ , ÷ , and so on)