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: 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:

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 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:

5408

8415

7982

:

additionwithCheck

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:

126 ≠ 612 (126)2 ≠ 12(62) 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:

˄

25

2

62

031

5

62

401

4

62

802

8

62

15r

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:

+1

6 5 0 0

Round 2 2, 8 5 1 to the nearest ten.

2 2, 8 5 0 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

002,41

005,42

007,83

000,082

007

004

103,14

:Actual

208,296

:Actual

+1 +1

Common error: First doing precise arithmetic, then rounding the answer.

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:625

5125

5525

216

636

66663

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

F – More Order of Ops Show each step:

You try it: Average of n items is (sum of items) / n You try:

233

2235

25240

24202410

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:

45

4747

x8

4646

n

x

0

2424