GED LESSON: Pre-Algebra: Multiplying with Negative Numbers

SuccessGED Pre-Algebra: Multiplying with Negative Numbers

POSITIVE X POSITIVE = POSITIVE
      +   X   +    =  +

NEGATIVE X NEGATIVE = POSITIVE 
    -    X   -    =   +

POSITIVE X NEGATIVE = NEGATIVE

     +    X   -     =   -

NEGATIVE X POSITIVE  = NEGATIVE
    -  X   +   = -

(If there are an even number of negatives, the answer is POSITIVE; if there are an odd number of negatives the answer is NEGATIVE) 

POSITIVE  ÷  POSITIVE = POSITIVE
      +   ÷   +    =  +

NEGATIVE ÷ NEGATIVE = POSITIVE 
    -    ÷   -    =   +

POSITIVE ÷ NEGATIVE = NEGATIVE

     +    ÷   -     =   -

NEGATIVE ÷ POSITIVE  = NEGATIVE
    -  ÷   +   = -
         

GED LESSON: EXPONENTS

EXPONENTS 

FULL PURPLE MATH ARTICLE HERE

Exponents are shorthand for repeated multiplication of the same thing by itself. For instance, the shorthand for multiplying three copies of the number 5 is shown on the right-hand side of the "equals" sign in (5)(5)(5) = 5³. The "exponent", being 3 in this example, stands for however many times the value is being multiplied. The thing that's being multiplied, being5 in this example, is called the "base".
This process of using exponents is called "raising to a power", where the exponent is the "power". The expression "5³" is pronounced as "five, raised to the third power" or "five to the third". There are two specially-named powers: "to the second power" is generally pronounced as "squared", and "to the third power" is generally pronounced as "cubed". So "5³" is commonly pronounced as "five cubed".

GED LESSON: Permutations and Combinations

From http://www.regentsprep.org/regents/math/algtrig/ats5/lcomb.htm

Permutation:  A set of objects in which position (or order) is important.To a permutation, the trio of Brittany, Alan and Greg is DIFFERENT from Greg, Brittany and Alan.  Permutations are persnickety (picky).Combination:  A set of objects in which position (or order) is NOT important. To a combination, the trio of Brittany, Alan and Greg is THE SAME AS Greg, Brittany and Alan.

Khan Academy Permutations Introduction

GED LESSON Statistics: Measures of Central Tendency, Mean, Median and Mode

FULL PURPLE MATH ARTICLE HERE

Mean, median, and mode are three kinds of "averages". There are many "averages" in statistics, but these are, I think, the three most common, and are certainly the three you are most likely to encounter in your pre-statistics courses, if the topic comes up at all.

The "mean" is the "average" you're used to, where you add up all the numbers and then divide by the number of numbers. 

The "median" is the "middle" value in the list of numbers. To find the median, your numbers have to be listed in numerical order, so you may have to rewrite your list first. 

The "mode" is the value that occurs most often. If no number is repeated, then there is no mode for the list.

Find the mean, median, mode, and range for the following list of values: 13, 18, 13, 14, 13, 16, 14, 21, 13 The mean is the usual average, so: (13 + 18 + 13 + 14 + 13 + 16 + 14 + 21 + 13) ÷ 9 = 15 Note that the mean isn't a value from the original list. This is a common result. You should not assume that your mean will be one of your original numbers. The median is the middle value, so I'll have to rewrite the list in order: 13, 13, 13, 13, 14, 14, 16, 18, 21 There are nine numbers in the list, so the middle one will be the (9 + 1) ÷ 2 = 10 ÷ 2 = 5th number: 13, 13, 13, 13, 14, 14, 16, 18, 21 So the median is 14.   Copyright © Elizabeth Stapel 2004-2011 All Rights Reserved The mode is the number that is repeated more often than any other, so 13 is the mode. The largest value in the list is 21, and the smallest is 13, so the range is 21 – 13 = 8. mean: 15 median: 14 mode: 13 range: 8

Tables, Pictographs, Bar Graphs, Line Graphs and Circle Graphs on the GED Lesson

In statistics, pictograms are charts in which icons represent numbers to make it more interesting and easier to understand. A key is often included to indicate what each icon represents. All icons must be of the same size, but a fraction of an icon can be used to show the respective fraction of that amount.^[6]

For example, the following table:

Day	Letters sent
Monday	10
Tuesday	17
Wednesday	29
Thursday	41
Friday	18

can be graphed as follows:

Day	Letters sent
Monday
Tuesday
Wednesday
Thursday
Friday

Key:  = 10 letters

As the values are rounded to the nearest 5 letters, the second icon on Tuesday is the left half of the original.

GED Simple Interest (Introduction) Lesson

From Khan Academy

From FULL Wikipedia Article

Interest is money paid by a borrower to a lender for a credit or a similar liability. Important examples are bond yields, interest paid for bank loans, and returns on savings. Interest differs from profit in that it is paid to a lender, whereas profit is paid to an owner. In economics, the various forms of credit are also referred to as loanable funds.

When money is borrowed, interest is typically calculated as a percentage of the principal, the amount owed to the lender. The percentage of the principal that is paid over a certain period of time (typically a year) is called the interest rate. Interest rates are market prices which are determined by supply and demand. They are generally positive because loanable funds are scarce.

Interest is often compounded, which means that interest is earned on prior interest in addition to the principal. The total amount of debt grows exponentially, and its mathematical study led to the discovery of the number e.^[1] In practice, interest is most often calculated on a daily, monthly, or yearly basis, and its impact is influenced greatly by its compounding rate.

From Khan Academy

Five percent problems

GED LESSON: Unit Conversion Explanation and Practice

Convert Pounds to Ounces Video PRESS HERE

There are 16 ounces in 1 pound. To convert pounds into ounces MULTIPLY the number of pounds by 16.

Example:
How many ounces are there in 10 pounds?
Answer: 10 pounds X 16 (ounces per pound) = 160 ounces

Convert Gallons to Quarts, Pints, and Cups Video PRESS HERE

1. Convert Gallons to Quarts 
There are 4 quarts per 1 gallon. To convert gallons into quarts MULTIPLY  the number of gallons by 4.

Example
How many quarts are there in 10 gallons?
Answer: 10 gallons X 4 (quarts per gallon) = 40 quarts

2. Convert Gallons to pints
There are 8 pints in 1 gallon. To convert gallons into pints MULTIPLY the number of gallons by 8.

Example:
How many pints are there in 10 gallons?
Answer: 10 gallons X 8 (pints per gallon) = 10

3. Convert Gallons to cups
There are 16 cups in each gallon. To convert gallons to cups MULTIPLY the number of gallons by 16.

Example:
How many cups in 10 gallons?
Answer: 10 gallons X 16 (cups per gallon) = 160 cups

Converting Yards to Inches Video PRESS HERE

There are 36 inches in 1 yard. To convert yards to inches, MULTIPLY the number of yards by 36.

Example:

How many inches are there in 10 yards?
Answer: 10 yards X 36 (inches per yard) = 36 inches.