Transcript Math 35 Introduction - Mt. San Jacinto College

Review of Math50:
Whole Number Arithmetic
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1.2 Addition
Remember?
1.3 Subtraction
Whole #s = {0,1,2,3,…}
There are no negative
1.4 Multiplication
numbers or negative
results!
1.5 Long Division
1.6 Rounding and Estimating
1.7 Solving Equations
1.9 Exponents and Order of Operations
1.2 Addition
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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:
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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:
1.2 Addition
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Perimeter is the distance around a diagram:
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Each side has a number
Add up the sides
Include the measurement units in your answer
1.3 Subtraction
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Is neither Commutative nor Associative:
3–2≠2–3
3 – (2 – 1) ≠ (3 – 2) – 1
Vertical Subtraction showing Borrows:
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Larger over Smaller
Start at the right
Show the Borrows
One digit at a time, L←R
Put in commas last
You try it:
Check with addition :
2897
 5 1 48
80 45
1.4 Multiplication
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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:
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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:
1.5 Long Division
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Is NOT Commutative nor Associative:
126 ≠ 612
(126)2 ≠ 12(62)
Long Division digit by digit:
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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:
r 15
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26
 2
52
26
 4
1 04
26
 5
1 30
26
 8
2 08
1.6 Rounding …
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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).
Round 2 2, 8 5 1 to the nearest ten.
2 2, 8 5 0 is the answer.
+1
6 5 0 0
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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 … and Estimating
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Estimating always involves two or more numbers:
First: Round each number to the same position,
Then: Do the arithmetic using the rounded numbers.
Common error:
First doing precise arithmetic,
then rounding the answer.
+1
+1
38, 7 0 0
 2 4, 5 0 0
1 4, 2 0 0
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You try it:
400
Actual :
7 00
Actual :
14,103
2 8 0, 0 0 0
296,208
1.7 Solving Equations
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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:
 47
 47
x  45
46
46
n 8
 24
0 x
 24
1.9 Exponents…
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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
 25  5  5
63  6  6  6
 125  5
 36  6
 625
 216
You try it:
1.9 … and the Order of Operations
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P E MD AS (Please Excuse My/Dear Aunt/Sally)
Parentheses, Exponents, Multiplication/Division, Addition/Subtraction
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Which operation comes first?
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6–1•4 = 6–4 = 2
12  3 • 4 = 4 • 4 = 16
5 + 2 • 32 = 5 + 2 • 9 = 5 + 18 = 23
8 – 2 + 5 = 6 + 5 = 11
8 – (2 + 5) = 8 – 7 = 1
1.9 More Order of Ops
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Show each step:
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10  24  20  4  2
240  5  2
235  2
233
You try it:
Average of n items is (sum of items) / n
You try: