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Welcome to OSA Training 2014
Basic Math
By:
Greg Hinckson
Renaldo Hylton
Irena Nedeljkovic
Curriculum
I. WHOLE NUMBERS
-Def of various terms
-Oder of Operations
II.
DECIMALS
-Adding, Subtracting, Multiplying,
Dividing
-Decimals to Percents to Fractions
III.
FRACTIONS
-Proper and Improper
-Mixed Numbers
-Adding, Subtracting, Multiplying,
Dividing
IV.
PERCENTS
-Finding Percents (Three types of
questions)
-Proportions
-Finding Percent Increase/Decrease
V.POWERS, EXPONENTS
-Squares and Cubes
-Operations with Powers and Exponents
VI.
SCIENTIFIC NOTATION
-Multiplication and Division
-Large Numbers to Scientific Notation
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VII. MEASUREMENTS
-Basic Formulas
-Area and Perimeter (Polygons)
-Circumference and Area (Circles)
-Angles Measures and Types
-Place Value of Numbers
VIII. GRAPHS
-Bar and Histogram Graphs
-Line Graphs
-Pie Charts
-Coordinate Graphs
IX.
WORD PROBLEMS
-Solving various types of Word
Problems
-Two Variables Word Problems
-Using Algebraic Expressions to Solve
Problems
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Terms and Definitions
• Q: What is a whole number?
• Term: a combination of numbers and or letters
connected by only multiplication.
– Numeric Terms: Only have numbers.
– Algebraic Terms: May have both letters and numbers
• Examples
(a) 2
(b)2x
(c)3xy
(d)-3m2n
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Order of Operations
•
Order of Operations: Tell us the sequence of
operations when simplifying any expression.
–
PEMDAS (parenthesis, exponents,
multiplication, division, addition and
subtraction)
caveats:
- Work from left to right if multiplication and division
- Addition and subtraction follows one after the other
• Examples: Evaluate each
(a) 10 – 2 + 8 x 2 – 3 / 3 = ??
(b) 16 x 4 / 4 x 16 /4 x 2 = ??
(c) 42 + 3 – 52 x 2 = ??
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Adding and Subtracting DECIMALS
• Q: What are decimals?
• Name the digit in the decimal number below:
492.01385
Rule: To Add/Subtract decimals vertically, first
line up the digits then perform regular addition
and subtraction.
Examples: Perform the indicated operations
(a) 123.098
+ 90.567
(b) 12.77
– 3.88
(c) 123.540
+ 554.908
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Multiplying and Dividing Decimals
• Rule: To Multiply decimals vertically, first line up
the digits, use zeros as place holders if necessary,
then multiply one digit at a time.
• Rule: To divide decimals, you may first covert to
whole numbers by moving the decimal point to the
right, then divide as normal.
• Examples: Perform the indicated Operations
(a) 12.093
(b) 12.04 / 4.1
(c) 183.09
x 2.01
x 23.4
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Decimals to Fractions to Percents
• To convert from percents to
fractions, divide by 100 then
reduce.
• To convert from percents to
decimals, move decimal point
two places to the left.
• To convert from fractions to
decimals, first convert to
percents, then decimals.
• Examples: See board
• Complete the table. Write each
fraction in lowest terms and
round each decimal to the
nearest tenth.
Percents
Fractions
Decimals
90%
_______
_______
_______
¼
_______
_______
_______
0.55
_______
2/3
_______
150%
_______
_______
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Performing Operations on Fractions
• Proper Fractions: The numerators are greater
than the denominators
¼
⅔
⅜
⅞
• Improper Fractions: The numerator is greater
than the denominator.
5/2
6/4
10/3
15/4
We simplify improper fractions as mixed numbers.
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Mixed Number Definition
• Mixed Numbers: Have a whole part and a
fractional part.
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Examples of Mixed Numbers and their
conversion
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Performing Operations on Mixed Numbers
Addition/Subtracting
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Multiplying Mixed Numbers
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Dividing Mixed Numbers
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Percents
• Def: In mathematics, a percentage is a number
or ratio expressed as a fraction of 100. It is often
denoted using the percent sign, "%", or the
abbreviation "pct." For example, 45% is equal to
45/100, or 0.45.
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Percent Formula
• In any percent problem, one of
these three questions is asked:
▫ Find the Part
▫ Find the Whole
▫ Find the %
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Percent Examples
You are at a fancy restaurant with your significant
other, your bill is $210 and you want to tip 20%.
Is $20 enough?
How much is the tip?
(For more practice, see the percent page in your
packet)
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Finding Percent Increase
Ann works in a staff analyst for $40K per year. If her pay is increased to $44K,
then what is her percent increase in pay?
Analysis: When finding the percent increase, we take the absolute value of the
difference and divide it by the original value. The resulting decimal is then
converted to a percent.
Solution:
44 – 40 = _4_ = _1_ = 0.1 = 10%
40
40
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Answer: The percent increase in Ann's pay is 10%.
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Finding Percent Decrease
Department of Investigation hired 120 investigators in 2013. Of that group,
24 investigators transferred or resigned their positions. What is the percent
decrease in investigators who were hired in 2013?
Analysis: When finding the percent decrease, we take the absolute value of the
difference and divide it by the original value. The resulting decimal is then
converted to a percent.
Solution: Absolute value of the difference is 24
_24_ = _2_ = 0.2 = 20%
120
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Answer: 20% of investigators hired in 2013 left by 2014. [Retention rate is
80%.]
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Powers and Exponents
• A power is the product of multiplying a
number by itself
– a base number and an exponent.
– The base number tells what number is being
multiplied.
– The exponent tells how many times the base
number is being multiplied
– Ex.
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Exponents and Powers
• Special rules of Exponents
– If the exponent is 1, then the answer is the number itself
(example 91 = 9)
– If the exponent is 0, then the answer is just 1 (example 90 =
1)
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Powers and Exponents -Examples
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Powers and Exponents - Operations
• Multiplying Power you ADD exponents
32 x 33 = 35 = 243
• Dividing Powers you SUBTRACT the exponents
35 ÷ 33 = 32 = 9
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Scientific Notation
• Scientific Notation (also called Standard Form) is
a special way of writing numbers which are often
very long:
▫ Expressed as a number (between 1 and 10) times a power of 10.
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Scientific Notation
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Measurements
Definition: Dimensions, quantity, or capacity as
ascertained by comparison with a standard.
Most Common Measurements:
•
•
•
•
•
Mass and Weight
Distance and Length
Capacity and Volume
Temperature
Time
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Basic U.S. Measurement
Conversions
• Length
1 foot = 12 inches
1 yard = 3 feet
1 mile = 5280 feet
• Time
▫ 1 hour = 60 minutes
▫ 1 minute = 60 seconds
• Volume
▫ 8 ounces
▫ 4 cups
▫ 2 pints
▫ 4 quarts
= 1 cup
= 1 pint
= 1 quart
= 1 gallon
• Weight
▫ 16 ounces = 1 pound
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Checking for Understanding
1) How many cups are in 1 gallon? _____
3) How many pints are in 1 gallon? _____
2) How many ounces are in 1 quart? _____
4) How many second are in 1 hour? _____
5) How many feet are in 1 mile? _____
6) How many inches are in 1 yard? _____
7) How many ounces are in 2 pounds? _____
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Graphs
• Diagram showing a relationship between two
variable quantities
• Y-axis: dependent variable
• X-axis: independent variable
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Bar Graphs
• Use rectangular bars to show how large a value is
▫ Amounts
▫ Characteristics
▫ Times and Frequency
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Line Graphs
• Use points connected by lines to show changes
in value over time
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Pie charts
• Circular chart, divided into sectors illustrating
numerical proportion
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Coordinate Graphs
• Describe position along the axis