Maria and Jorge were trying to simplify the expression $1 \frac { 2 } { 5 } \cdot ( - \frac { 3 } { 4 } ) \cdot ( - \frac { 4 } { 3 } )$. Maria started by rewriting $1 \frac { 2 } { 5 }$ as $\frac { 7 } { 5 }$. Her work is below.

$\left. \begin{array} { c } { 1 \frac { 2 } { 5 } \cdot ( - \frac { 3 } { 4 } ) \cdot ( - \frac { 4 } { 3 } ) } \\ { \frac { 7 } { 5 } \cdot ( - \frac { 3 } { 4 } ) \cdot ( - \frac { 4 } { 3 } ) } \\ { ( - \frac { 21 } { 20 } ) \cdot ( - \frac { 4 } { 3 } ) } \end{array} \right.$
$\frac { 84 } { 60 } = 1 \frac { 24 } { 60 } = 1 \frac { 2 } { 5 }$

Jorge had a different idea. He multiplied $( - \frac { 3 } { 4 } ) \cdot ( - \frac { 4 } { 3 } )$ first.

1. Simplify the expression $1 \frac { 2 } { 5 } \cdot ( - \frac { 3 } { 4 } ) \cdot ( - \frac { 4 } { 3 } )$ using Jorge's method. Is your answer equal to Maria's?

   Help (a):

   What do you get when you multiply $\left(-\frac{3}{4}\right) \cdot \left(-\frac{4}{3}\right)$?
   Does this answer make sense and match Maria's answer?

   Hint (a):

   Since you are multiplying by reciprocal fractions, the fractions reduce to $1$.

   Answer (a):

   $\text{Yes, }1\frac{2}{5} \cdot \left(-\frac{3}{4}\right) \cdot \left(-\frac{4}{3}\right) = 1\frac{2}{5}$

2. Why might Jorge have decided to multiply $( - \frac { 3 } { 4 } ) \cdot ( - \frac { 4 } { 3 } )$ first?

   Help (b):

   As you found in part (a), $\left(-\frac{3}{4}\right)\left(-\frac{4}{3}\right)$ is $1$, due to the multiplicative property.

3. In a multiplication problem, the factors can be grouped together in different ways. This is called the Associative Property of Multiplication. Read the Math Notes box for this lesson, then show that $( \frac { 3 } { 4 } \cdot \frac { 2 } { 5 } ) \cdot ( - 2 ) = \frac { 3 } { 4 } \cdot ( \frac { 2 } { 5 } \cdot ( - 2 ) )$.

   Help (c):

   Solve each equation. What do you get?
   Are the answers equal?

   Answer (c):

   $-\frac{12}{20} = -\frac{12}{20}$

4. Simplify each expression. First, decide if you want to group some factors together.