Alex is trying to simplify the expression $- 1 \frac { 1 } { 4 } + ( 2 \frac { 1 } { 2 } ) + ( 3 \frac { 1 } { 4 } )$. He started by rewriting it like this:

$\left. \begin{array} { l } { - 1 + ( - \frac { 1 } { 4 } ) + 2 + \frac { 1 } { 2 } + 3 + \frac { 1 } { 4 } } \\ { ( - 1 + 2 + 3 ) + ( - \frac { 1 } { 4 } + \frac { 1 } { 4 } + \frac { 1 } { 2 } ) } \end{array} \right.$

1. Why might he have regrouped the expression in this way?

   Hint (a):

   What are the differences between the two groups of numbers?

   More Help (a):

   Does it make the equation any easier to solve?

   Answer (a):

   Regrouping simplifies the arithmetic.

2. Simplify the expression. What is the result?

   Hint (b):

   First simplify the terms in parentheses.

   Answer (b):

   $4 \frac{1}{2}$

3. What property was Alex using when he rewrote the problem?

   Hint (c):

   What mathematical actions did Alex take?
   What property is this?

   Answer (c):

   The Associative Property of Addition.

4. Use this strategy to regroup the expression $\frac { 3 } { 10 } + 2 \frac { 1 } { 10 } + ( - 1 \frac { 2 } { 5 } )$ and find the result.

   Hint (d):

   Remember, when adding, you can separate the whole numbers from the fractions.