 A – Addition  B – Subtraction  C – Multiplication  D – Long Division  E – Rounding and Estimating  F – Exponents and Order of Operations  G – Solving Equations Review of Math50: Whole Number Arithmetic Remember? Whole #s = {0,1,2,3,…} There are no negative numbers or negative results!

A – Addition  Commutative Property: = =113  Associative Property: 3 + (9 + 7) = (3 + 9) + 7 =19  Additive Identity is 0: = =47  Vertical Addition showing Carries:  Line up neatly  Start at the right  Show the carries  One digit at a time, L ← R  Put in the commas last You try it:

A – Addition  Perimeter is the distance around a diagram:  Each side has a number  Add up the sides  Include the measurement units in your answer

B – Subtraction  Is neither Co mm utative nor Associative: 3 – 2 ≠ 2 – 3 3 – (2 – 1) ≠ (3 – 2) – 1  Vertical S ub traction showing Borrows:  Larger over Smaller  Start at the right  Show the Borrows  One digit at a time, L ← R  Put in commas last You try it:

C – Multiplication  Commutative and Associative: 6(12) = 12(6) =72 (2 3) 4 = 2 (3 4) =24  Multiplicative Identity is 1: 14 1 = 1 14 =14  Vertical Multiplication showing Carries:  Longer over shorter  Start with rightmost digit  Show multiplication carries  New shifted line for each lower digit  Add product lines, show carries  Use a - as a spacer You try it:

D – Long Division  Is NOT Commutative nor Associative: 12  6 ≠ 6  12 (12  6)  2 ≠ 12  (6  2)  Long Division digit by digit:  Set up long division work area  Find the place for the 1 st quotient digit  Use a work area for test products  Show work step by step L → R  Build the quotient one digit at a time  Show the Remainder like this: r15  You try it: ˄

E – Rounding …  When Rounding is done, a rounding place must be given. The check digit is the next digit right of the rounding place: If it’s 0-4, round off the number; If it’s 5-9, round up (+1).  Underline the leading digits that include the rounding position,  Then circle the check digit.  Replace all digits to the right of the rounding position with 0’s. If rounding up, add +1 to the rounding position digits.  You try it: Round 2 2, to the nearest ten. 2 2, is the answer.

 Estimating always involves two or more numbers: First: Round each number to the same position, Then: Do the arithmetic using the rounded numbers.  You try it: E – … and Estimating +1 Common error: First doing precise arithmetic, then rounding the answer.

F – Exponents…  Exponents are shorthand for multiplication: 8 3 = = 64 8 = 512  5 1 or x 1 are not in simplest form: 5 or x  Zero th power: 5 0 = = 1 0 = x 0 = 1  You try it:

F – … and the Order of Operations  P E MD AS (Please Excuse My/Dear Aunt/Sally) Parentheses, Exponents, Multiplication/Division, Addition/Subtraction  Which operation comes first? 6 –  – – (2 + 5) = 6 – 4 = 2 = 4 4 = 16 = = = 23 = = 11 = 8 – 7 = 1

F – More Order of Ops  Show each step:  You try it:  Average of n items is (sum of items) / n  You try:

G – Solving Equations  Equations usually have a variable in place of a number. Solving an equation finds that number.  Equations remain true when exactly the name thing (+, –,,  ) is done to both sides.  You try: