Hilda was simplifying some numerical expressions and made each of the following sequences of calculations. Name the mathematical property, operation, or idea that justifies how Hilda went from each step to the next step.

1.  $\left. \begin{array} { l } { 5 \cdot 412 } \\ { = 5 ( 400 + 10 + 2 ) } \\ { = 5 \cdot 400 + 5 \cdot 10 + 5 \cdot 2 } \\ { = 2000 + 50 + 10 } \\ { = 2060 } \end{array} \right.$

   Hint (a):

   If you are having trouble, go back through Chapter 3 and review the mathematical properties before checking the answers.

   Answer (a):

   Decomposed $412$
   Distributive Property
   Multiplied each term
   Added the terms together

2.  $\left. \begin{array} { l } { 17 + 29 + 3 + 1 } \\ { = 17 + 3 + 29 + 1 } \\ { = ( 17 + 3 ) + ( 29 + 1 ) } \\ { = 20 + 30 } \\ { = 50 } \end{array} \right.$

   Hint (b):

   For each step, think about what Hilda did to the expression.
   Was she grouping terms differently?
   Did she move any terms?