Welcome to OSA Training Basic Math

CurriculumI. WHOLE NUMBERS-Order of OperationsII. DECIMALS-Decimals to Percents to FractionsIII. FRACTIONS-Adding, Subtracting, Multiplying,

DividingIV. PERCENTS-Finding Percents (Three types of

questions)-Proportions-Finding Percent Increase/DecreaseV. POWERS, EXPONENTS-Squares and Cubes-Operations with Powers and ExponentsVI. SCIENTIFIC NOTATION-Multiplication and Division-Large Numbers to Scientific Notation

VII. MEASUREMENTS-Basic Formulas-Area and Perimeter (Polygons)-Circumference and Area (Circles)-Angles Measures and Types-Place Value of NumbersVIII. GRAPHS-Bar and Histogram Graphs-Line Graphs-Pie Charts-Coordinate GraphsIX. WORD PROBLEMS-Solving various types of Word

Problems-Two Variables Word Problems-Using Algebraic Expressions to Solve

Problems

Check In

There are ten students in a classroom. If each student shakes each other’s hands exactly once, how many handshakes would be shared among them?

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 DivisionOR 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 = ??

Adding and Subtracting DECIMALS• Q: What are decimals?• Name the digit in the decimal number below:492.01385Rule: To Add/Subtract decimals vertically, first

line up the digits then perform regular addition and subtraction.

Examples: Perform the indicated operations

(a)123.098 (b) 12.77 (c) 123.540+ 90.567 – 3.88 + 554.908

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) 183.09x 2.01 x 23.4

Performing Operations on Fractions• Proper Fractions: The numerators are lesser

than the denominators¼ 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.

Mixed Number Definition

• Mixed Numbers: Have a whole part and a fractional part.

Examples of Mixed Numbers and their conversion

Performing Operations on Mixed NumbersAddition/Subtracting

Multiplying Mixed Numbers

Dividing Mixed Numbers

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.

Percent Formula• In any percent problem, one of

these three questions is asked:

▫ Find the Part▫ Find the Whole▫ Find the %

Percent ExamplesSam is at a fancy restaurant with his significant

other. His bill is $210 and he wants to tip 20%. Sam left $20.

Is Sam being cheap??

How much is the tip?

Finding Percent IncreaseDeirdre works as 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 10

Answer: The percent increase in Deirdre's pay is 10%.

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 10

Answer: 20% of investigators hired in 2013 left by 2014. [Retention rate is 80%.]

Finding Percent Decrease

Decimals to Fractions to Percents

• To convert from percents to fractions, divide by 100 then reduce.

• To convert from to fractions to percents, multiply by 100 then simplify.

• 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% _______ _______

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.

Powers and Exponents

• 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)

Powers and Exponents -Examples

Powers and Exponents - Operations

• Multiplying Power you ADD exponents32 x 33 = 35 = 243

• Dividing Powers you SUBTRACT the exponents

35 ÷ 33 = 32 = 9

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.

Scientific Notation

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

Basic U.S. Measurement Conversions

• Length1 foot = 12 inches1 yard = 3 feet1 mile = 5280 feet

• Time▫ 1 hour = 60 minutes▫ 1 minute = 60 seconds

• Volume▫ 8 ounces = 1 cup▫ 2 cups = 1 pint▫ 2 pints = 1 quart▫ 4 quarts = 1 gallon

• Weight▫ 16 ounces = 1 pound

Checking for Understanding

1) How many cups are in 1 gallon? _____2) How many pints are in 1 gallon? _____3) 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? _____

Graphs

• Diagram showing a relationship between two variable quantities

• Y-axis: dependent variable• X-axis: independent variable

Bar Graphs

• Use rectangular bars to show how large a value is▫ Amounts▫ Characteristics▫ Times and Frequency

Line Graphs

• Use points connected by lines to show changes in value over time

Pie charts

• Circular chart, divided into sectors illustrating numerical proportion

Coordinate Graphs

• Describe position along the axis

Word Problems (page13)

Word Problem (page 13)

Word Problems (page 14)

Word Problem (page 24)