In Lesson 11.1.2 you will focus on multiplying and dividing rational expressions. Recall what you learned about multiplying and dividing fractions in a previous course as you answer the questions below. To help you, the following examples have been provided.

$\frac { 9 } { 16 } \cdot \frac { 4 } { 6 } = \frac { 36 } { 96 } = \frac { 3 } { 8 } \quad \text { and } \quad \frac { 5 } { 6 } \div \frac { 20 } { 12 } = \frac { 5 } { 6 } \cdot \frac { 12 } { 20 } = \frac { 60 } { 120 } = \frac { 1 } { 2 }$

1. Without a calculator, multiply $\frac { 2 } { 3 } \cdot \frac { 9 } { 14 }$ and reduce the result. Describe your method for multiplying fractions.

   Hint (a):

   Multiply the numerators together to find the numerator of the final answer, and multiply the denominators together to find the denominator of the final answer.

   More Help (a):

   Do $2$ and $14$ have a common factor? Do $3$ and $9$ have a common factor? It is possible to reduce before multiplying across? Use whichever method is easiest for you.

   Answer (a):

   $\frac{3}{7}$

2. Without a calculator, divide $\frac { 3 } { 5 } \div \frac { 12 } { 25 }$ and reduce the result. Then use a calculator to check your answer. Describe your method for dividing fractions.

   Hint (b):

   Take the reciprocal of the divisor, and multiply the two resulting fractions.