GED LESSON: Introduction to Ratios

KHAN ACADEMY INTRODUCTION TO RATIOS VIDEO 

FULL WIKIPEDIA ARTICLE

In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second.^[1] For example, if a bowl of fruit contains eight oranges and six lemons, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Thus, a ratio can be a fraction as opposed to a whole number. Also, in this example the ratio of lemons to oranges is 6:8 (or 3:4), and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7).

The numbers compared in a ratio can be any quantities of a comparable kind, such as objects, persons, lengths, or spoonfuls. A ratio is written "a to b" or a:b, or sometimes expressed arithmetically as a quotient of the two.^[2]When the two quantities have the same units, as is often the case, their ratio is a dimensionless number. A rate is a quotient of variables having different units. But in many applications, the word ratio is often used instead for this more general notion as well.^[3]

The ratio of numbers A and B can be expressed as:^[4]

• the ratio of A to B
• A is to B (followed by "as C is to D")
• A:B
• A fraction that is the quotient: A divided by B: , which can be expressed as either a simple or a decimal fraction.^[5]

The numbers A and B are sometimes called terms with A being the antecedent and B being the consequent.^[6]

The proportion expressing the equality of the ratios A:B and C:D is written A:B = C:D or A:B::C:D. This latter form, when spoken or written in the English language, is often expressed as

A is to B as C is to D.

A, B, C and D are called the terms of the proportion. A and D are called the extremes, and B and C are called the means. The equality of three or more proportions is called a continued proportion.^[7]

Ratios are sometimes used with three or more terms. The ratio of the dimensions of a "two by four" that is ten inches long is 2:4:10. A good concrete mix is sometimes quoted as 1:2:4 for the ratio of cement to sand to gravel.^[8]

For a mixture of 4/1 cement to water, it could be said that the ratio of cement to water is 4:1, that there is 4 times as much cement as water, or that there is a quarter (1/4) as much water as cement.

GED LESSON: Success GED Absolute Value Lesson

Khan Academy Full Course on Absolute Value

Read full Eduplace article here

Absolute Value

Absolute value describes the distance of a number on the number line from 0 without considering which direction from zero the number lies. The absolute value of a number is never negative.

• The absolute value of 5 is 5.
distance from 0: 5 units

• The absolute value of 5 is 5.
distance from 0: 5 units

• The absolute value of 2 + 7 is 5.
distance of sum from 0: 5 units

• The absolute value of 0 is 0. (This is why wedon't say that the absolute value of a number is positive: Zero is neither negative nor positive.)

The symbol for absolute value is two straight lines surrounding the number or expression for which you wish to indicate absolute value.

• |6| = 6 means the absolute value of 6 is 6.
• |6| = 6 means the absolute value of 6 is 6.
• |2 - x| means the absolute value of 2 minus x.
• |x| means the negative of the absolute value of x.

GED LESSON: Robert Kiyosaki How to Make Money or Get Rich

Robert Kiyosaki From YouTube 

Watch this video about making money and getting rich. You should do your own thinking about this subject. One of the main reasons people have for taking the GED is to make more money. Start thinking about that now, even before you take the test. Press the subject buttons on the right or look at the posts other posts in the blog to work on specific GED subjects.

Full Wikipedia Article

Robert Toru Kiyosaki (born April 8, 1947) is an American businessman, investor, self-help author, motivational speaker, financial literacy activist, financial commentator, and radio personality. Kiyosaki is the founder of the Rich Dad Company.^[3] He has written over 15 books which have combined sales of over 26 million copies.^[4]

A financial literacy advocate, Kiyosaki has been a proponent of entrepreneurship, business education, investing, and that comprehensivefinancial literacy concepts should be taught in schools around the world.^[5] Kiyosaki also maintains a monthly column on Yahoo Finance.^[6][7]

Full Article

GED LESSON: What the hell are negative numbers, and why do I need to learn about them

Video below from Khan Academy

Full article from Wikipedia here

In mathematics, a negative number is a real number that is less than zero. Negative numbers represent opposites. If positive represents movement to the right, negative represents movement to the left. If positive represents above sea level, then negative represents below level. If positive represents a deposit, negative represents a withdrawal. They are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset, a decrease in some quantity may be thought of as a negative increase. If a quantity may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. In the medical context of fighting a tumor, an expansion could be thought of as a negative shrinkage. Negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. The laws of arithmetic for negative numbers ensure that the common sense idea of an opposite is reflected in arithmetic. For example, − − 3 = 3 because the opposite of an opposite is the thing you started with.

Negative numbers are usually written with a minus sign in front. For example, −3 represents a negative quantity with a magnitude of three, and is pronounced "minus three" or "negative three". To help tell the difference between a subtraction operation and a negative number, occasionally the negative sign is placed slightly higher than the minus sign (as a superscript). Conversely, a number that is greater than zero is called positive; zero is usually^[1] thought of as neither positive nor negative.^[2] The positivity of a number may be emphasized by placing a plus sign before it, e.g. +3. In general, the negativity or positivity of a number is referred to as its sign.

GED LESSON: Multiplying with Negative numbers

Success GED Multiplying with Negative numbers 

Watch the Khan Academy Video below 

The Multiplication Rules: 

Positive times a positive = Positive
Negative times a negative = Positive 
Positive times a negative = Negative
Negative times a Positive = Negative

Theory        ,    Examples 

+ x + = +,   +5 x +2 = +10
- x - = +,      -5 x -2 = +10
+ x - = -,      +5 x -2 = -10
- x + = -,      -5 x +2 = -10

Why is negative times a negative a positive?

-1 x +2 = -2 (Negative means, "No, you have to change!" The negative sign is very negative!) 

-1 x -2 = +2 (Because the negative sign of the -1 forcing the -2 to change signs. Bossy!)

Lets get deeper... 

-1 x -2 x -3 = ??

Okay, first things first: Take -1 x -2 first. We know that negative is going to make the -2 positive, so -1 x -2 = +2.
Take the +2 x -3. The rule  is positive is cool if you keep your sign. So +2 x -3 = -6. So -1 x -2 x -3 = -6. 

So the more useful rule is that if there are an odd number of negative numbers you're multiplying, the answer will be negative. If there are an even number, the answer will be positive. 

GED LESSON: Pre-Algebra: Adding and Subtracting Negative Numbers

ADDITION WITH NEGATIVE NUMBERS 


When adding numbers with the same signs (the signs of both numbers are positive or the signs of both numbers are negative),

Adding numbers with SAME SIGNS

1. Add the numbers
2. The answer keeps the same sign

For instance:      

         +2  +  +7  = +9
         -2  +  -7  = -9

When adding numbers with the different signs (if the first number is positive and the second number is negative, or the first number is negative and the second number is positive)

Adding numbers with DIFFERENT SIGNS

1. SUBTRACT the smaller number from the larger number regardless of signs)
2. Get the answer
3. Apply the sign of the larger number to the answer.

For instance:

         +2  +  -7  =  

          Step #1: Subtract the smaller number (2) from (7): 7 - 2 = 5 
          Step #2 The answer is 5
          Step #3 Since 7 is larger than 2 and 7 is negative, turn 5 into negative 5, so
       -5 is the answer. 

+2  +  -7  = -5

SUBTRACTION WITH NEGATIVE NUMBERS 

Subtraction is easy. Just change the sign of the SECOND number, then ADD using the additions rules above.

Examples:

Example one:           +2  -  -7  = +2  +  +7 = +9

Example two:           -2  -  +7  = -2  +  -7  = -9

Example three:               +2  -  +7  = +2  +  -7 = -5 

Example four:               -2  -  -7  = +2  +  +7 = +5 

FURTHER EXPLANATION AND PRACTICE CLICK HERE

GED LESSON: Negative Numbers (SuccessGED)

From Wikipedia

In mathematics, a negative number is a real number that is less than zero. Negative numbers represent opposites. If positive represents movement to the right, negative represents movement to the left. If positive represents above sea level, then negative represents below level. If positive represents a deposit, negative represents a withdrawal. They are often used to represent the magnitude of a loss or deficiency. A debt that is owed may be thought of as a negative asset, a decrease in some quantity may be thought of as a negative increase. If a quantity may have either of two opposite senses, then one may choose to distinguish between those senses—perhaps arbitrarily—as positive and negative. In the medical context of fighting a tumor, an expansion could be thought of as a negative shrinkage. Negative numbers are used to describe values on a scale that goes below zero, such as the Celsius and Fahrenheit scales for temperature. The laws of arithmetic for negative numbers ensure that the common sense idea of an opposite is reflected in arithmetic. For example, − − 3 = 3 because the opposite of an opposite is the thing you started with.

Negative numbers are usually written with a minus sign in front. For example, −3 represents a negative quantity with a magnitude of three, and is pronounced "minus three" or "negative three". To help tell the difference between a subtraction operation and a negative number, occasionally the negative sign is placed slightly higher than the minus sign (as a superscript). Conversely, a number that is greater than zero is called positive; zero is usually^[1] thought of as neither positive nor negative.^[2] The positivity of a number may be emphasized by placing a plus sign before it, e.g. +3. In general, the negativity or positivity of a number is referred to as its sign.

Every real number other than zero is either positive or negative. The positive whole numbers are referred to as natural numbers, while the positive and negative whole numbers (together with zero) are referred to as integers.

In bookkeeping, amounts owed are often represented by red numbers, or a number in parentheses, as an alternative notation to represent negative numbers.

GED LESSON: Reducing Fractions and Equivalent Fractions

Practice by pushing on this button-->Fractions: Lowest Common Multiple/Denominator

Article from Wikipedia: 

In mathematics, the lowest common denominator or least common denominator (abbreviated LCD) is the least common mulitiple of the denominators of a set of fractions. It simplifies adding, subtracting, and comparing fractions.

Role in arithmetic and algebra

The same fraction can be expressed in many different forms. As long as the ratio between numerator and denominator is the same, the fractions represent the same number. For example:

.

It's usually easiest to add, subtract, or compare fractions when each is expressed with the same denominator, called a "common denominator". For example, it's obvious that  and that , since each fraction has the common denominator 12. But it's not obvious what  equals, or whether  is greater than or less than , because the denominators are different. Any common denominator will do, but usually the least common denominator is desirable because it makes the rest of the calculation as simple as possible.

The least common denominator of a set of fractions is the least number that is a multiple of all the denominators: their "least common multiple". The product of the denominators is always a common denominator, as in:

but it's not always the least common denominator, as in:

Here, 36 is the least common multiple of 12 and 18. Their product, 216, is also a common denominator, but calculating with that denominator involves larger numbers: .

With variables rather than numbers, the same principles apply:

Practice by pushing on this button-->Fractions: Lowest Common Multiple/Denominator

Success GED Multiplication

Multiplication Tables  <--- Click Here to practice 

You will probably want to sign in so that the program can remember all of your accomplishments. Once you get to the site, hit the sign in button.

Click on button above to practice your basic multiplication facts. It is absolutely essential that you memorize these multiplication facts. You sign up for this FUN (non-childish) game that will painlessly help you work this important tool of multiplication. This will help you with every math test that you will need to take, including the GED. Knowing the multiplication rules will also help you in real life and higher math.

Just so you know, the practice means practice with problems like  4 X 8 = 32 and 7 X 9 = 63.

I'll put up much more sophisticated GED-type questions as a I post more videos. To repeat an important fact about the GED, you need to MEMORIZE these facts. You can do this by practicing about 15 minutes a day. Use this software and if you are feeling ambitious, make your own flash cards by putting the question on the front, like 6 X 3 and put the answer 18 on the back of the card. Practice by looking on the front before flipping over the card to look at the answer. You will need 144 cards. Get two packs of 100 index cards (200 total) because you will probably make some mistakes. With left over cards you can create harder problems like 13 X 13 = 169,  14 X 14 = 196 and so on.