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Printable Version of Leroy's Rules

Leroy's Rules
Algebra for the Numb Mind
by Leroy
(My Mind was Numb)

(Must memorize to successfully use - otherwise will be lost like time)

Equation:

Farmer A has 2 cows and Farmer B has 3 cows.  How many cows does Farmer A & B have?

 A = 2 B = 3             A + B = ? 2 + 3 = 5 For Add & Subtract = Equal (Same) Farmer A Cows = A Farmer B Cows = B     Sell means subtract And means add Loss means subtract Buy means add Look for other words that mean multiply & divide

Multiplication and Division Rules

A x B = AB

(A) x (B) = AB

A * B = AB

Rule 1:

Do equals unto equals to get equals.                           (equals)(=)

Examples:

A = A
+1 = +1
A + 1 = A + 1

A = A
B = B
A x B = A x B

A = B
A + 2 = B + 2

Rule 2:

The sign of the Biggest group in addition or substraction is the correct sign for the answer.
Group all (+), then total them;  Group all (-), then total them.  The group with the biggest sign, carries their sign over to the answer

Examples:

(-11) + (+13) = +2
13 is bigger

(-11) + (-13) = -24
13 is bigger

In multiplication and division, the signs follow this pattern.  (Combine only 2 signs at a time).
(+) is forward and (-) is reverse.

Sign                          Sign 2                              Outcome
+                                +                                        +
+                                -                                         -
-                                 +                                        -
-                                 -                                         +

Examples:

(-3) x (-4) = +12
(-3) x (+4) = -12
(+3) x (-4) = -12
(-3) x (-4) = +12 or 12 (assumed +)

*Example Problems for Positive and Negative Symbol Allocation

Rule 3:

(Order of Operations)
Please Excuse My Dear Aunt Sally

P - everything in parenthesis first
E - exponents do second
M - multiplication do third
D - division do fourth
S - subtraction do last

Example Problems for Order of Operations

Rule 4:

Isolation:  Isolate to one side of an equal sign what you want to find.  You do this by doing equals to both sides

Example:

x + 1 = y + 2
If you want to find x, subtract 1 from both sides
x + 1 = y + 2
- 1         - 1
x = y + 1

If you want to find y, subtract 2 from both sides
x + 1 = y + 2
- 2         - 2
x  - 1 = y

Example Problems for Isolation

Rule 5:

Powers and Exponents give us a handle on big and small numbers and some equations in science.

x2 = x * x

x1/2 = x .5 = square root of x

x5 = x * x * x * x * x

x2 * x3 = x5

Division (subtract) exponents

Example Problems for Power and Exponents

Rule 6:

Convert Fraction to Decimal

Convert Decimal to Fraction of nearest 16th is:

Decimal is .64

Multiply by 16

.64  x  16 = 10.24

Suppose decimal is .500:

.500  x  16  =  8

Example Problems for Conversions

Rule 7:

% Fractions Decimal

50% is the number

Example Problems for Percents

Rule 8:

Ratio and Proportions

Ratios and proportions are fractions, division problems, and/or decimal values.

Ratios:

Ratios are derived from no more than two values that are not like terms. The terms in ratios are arranged in a manner where the term that increases the decimal value of the ratio is the numerator of the ratios fraction value and the term that diminishes the decimal value of the ratio is the denominator of the ratios fraction value. For example: speed is a ratio of distance over time because a greater distance traveled would indicate a greater speed while a greater value of time to travel that distance would diminish the value of the speed.

Proportions:

Proportions are derived from two or more values that are like terms. The terms in a proportion are arranged to find the value of an isolated term compared to the sum of all terms inclued in the proportion where the isolated term is the numerator of the proportions fraction value and the sum of all terms (including the isolated term) included in the proportion is the denominator of the proportions fraction value. Note that the decimal value of a proportion is always a decimal percentage. For example: if a dough base mixture calls for 1 part water for every 2 parts flour, to find the proportion of water in the recipe, make the parts of water used in the mixture the numerator and the sum of the parts of water and parts of flour the denominator.

Rule 9:

If all other rules fail, I'm here to help.
*More of Leroy's Rules to follow.

*If you have any questions, please feel free to e-mail Jay Blevins at
Mountain Empire Community College