A mathematical expression came up during class that GDT should have spent more time discussing.

Evaluate: 20 - 10 + 6 Subtraction and addition have equal precedence; therefore, evaluate left-to-right. step 1) 20 - 10 = 10 step 2) 10 + 6 = 16 20 - 10 + 6 = 16Order of operations are still applicable when processing operators of equal precedence.

Evaluate: 20 - 10 + 6 If the addition is done before the subtraction, then the expression becomes 20 - (10 + 6). step 1) 10 + 6 = 16 step 2) 20 - 16 = 4 20 - 10 + 6 != 20 - (10 + 6) In English, 20 minus 10 plus six is not equal to 20 minus the quantity 10 + 6.Writing subtraction as addition can help ensure operations are executed in the correct order.

20 - 10 + 6 = 20 + (-10) + 6 Because the commutative and associative properties hold true for addition, order of operations is not significant. Commutative property: a + b = b + a Associative property: a + (b + c) = (a + b) + c Some examples... 20 + ((-10) + 6) = (20 + (-10)) + 6 20 + ((-10) + 6) = 20 + (6 + (-10)) = ((-10) + 6) + 20

**Creator:** Gerald Thurman
[gthurman@gmail.com]

**Created:** 07 February 2007

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