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Review of Math50: Whole Number Arithmetic

Review of Math50: Whole Number Arithmetic. A – Addition B – Subtraction C – Multiplication D – Long Division E – Rounding and Estimating F – Exponents and Order of Operations G – Solving Equations. Remember? Whole #s = {0,1,2,3,…}

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Review of Math50: Whole Number Arithmetic

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

  2. A– Addition • Commutative Property: 14 + 99 = 99 + 14 =113 • Associative Property: 3 + (9 + 7) = (3 + 9) + 7 =19 • Additive Identity is 0: 0 + 47 = 47 + 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:

  3. 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

  4. B – Subtraction • Is neither Commutative nor Associative:3 – 2 ≠ 2 – 3 3 – (2– 1) ≠(3 – 2) – 1 • Vertical Subtraction 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:

  5. 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:

  6. 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 1st 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: ˄

  7. 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, 8 5 1 to the nearest ten. 2 2, 8 5 0 is the answer. +1 6 5 0 0

  8. E – … and Estimating • 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: Common error: First doing precise arithmetic, then rounding the answer. +1 +1

  9. F – Exponents… • Exponents are shorthand for multiplication:83 = 8•8•8 = 64•8 = 512 • 51 or x1 are not in simplest form: 5 or x • Zeroth power: 50 = 1420 = 10 = x0 = 1 • You try it:

  10. 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 – 1 • 4 • 12  3 • 4 • 5 + 2 • 32 • 8 – 2 + 5 • 8 – (2 + 5) = 6 – 4 = 2 = 4• 4 = 16 = 5 + 2 • 9 = 5 + 18 = 23 = 6 + 5 = 11 = 8 – 7 = 1

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

  12. 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:

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