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Algebra for every one

Basic Rules that must be abided by.

Order of Operations

1. Grouping like the use of Parenthesis
2. Exponents
3. Multiply and Divide
4. Add and Subtract
 
Example: A. 2 + 7 * 6 = 44
B. 2 + 7 * 6 = 54
What's your answer?

Answer:

A. 

 
Variables Normally letters, that represent numbers
Example:

2 + y = 5

y = 3.  It just has to be.  The equal sign is the key.
2 + y = 5  Isolate 'y'
Subtract 2 from each side of the equal sign so that the statement remains true.
 2 + y = 5
-2
 y = 5 is wrong
      -2
 y = 3.  This is correct

  

 2 + y = 5
-2         -2    keep statement
------------  equal
  0 + y = 3    or
         y = 3   
2 + 3 = 5

3 is y

All math boils down to simple addition and subtraction.

Addition is adding single units together
Multiplication is adding groups of the same size together

2 * 5  (2 times 5) means one of two things
there are 2 5's (two 5's) or there are 5 2's (five 2's).
5 + 5                                 2 + 2 + 2 + 2 + 2
Normally you would pick the easiest one to work with.  I like the 2 5's
5 + 5 = 10 therefore 2 * 5 = 10

Now you have seen it in addition form you might agree with my above statement.

Addition and Subtraction are the back bone of the numbers' game.

All number can be expressed in fraction form making fractions simple and easy.
just as long as you remember the rules that deal with fractions.

Addition and Subtraction
Here, the weird thing is the denominator

This is the case of the old and ever famous common denominator syndrome.

1\2 + 1\4 = ?
you could use money and say 2 quarters make a half and one more quarter makes 75 so a half a dollar plus a quarter of a dollar makes 3 quarters of a dollar.  You still created the common denominator when you made two quarts instead of a fifty cent piece. 

Looks like this:
1       1             the denominators are 
2       4             different.

we have to change the 1\2 (one half)
into 2\4 (two quarters) to match the one quarter.  Now it looks like this:
2        1             Now the denominators
4        4             are the same.

Now we may add or subtract.
2\4 + 1\4 = 3\4  or  2\4 - 1\4 = 1\4
Notice common denominators before and after the equal sign.  This is correct.

Multiplication and Division
Here, the only weird thing is division

1\2    1\4    or

        take reciprocal of last
                and change the sign to
                Multiplication

1\2  x  4\1  4\1 is the reciprocal of 1\4.

Now we can solve the equation by multiplying straight across.

Bonus round

(1\5 * 10) + 7 * 4 = ?

Start with the rules
1> groups

1\5 * 10 = 1\5 * 10\1 = 10\5 = 2
2 + 7 * 4 = ?

Rule 3. Multiply before adding
7 * 4 = 28

2 + 28 = 30

(1\5 * 10) + 7 * 4 = 30

Math rules must be followed Negative numbers

The Quadratic Formula

A famous Equation:

If ax2 + bx + c = 0, then

                       -b    sqrt(b2  -  4ac)
            x  =  ------------------------------
                                   2a

The Quadratic Formula always has two answers.  Only one answer will fit the sinario.
 

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