Distance Learning Math Index
Websites for Those Who Need Help
Homepage

Printable Version of Leroy's Rules
 

Add and Subtract Rules

 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 +) 
 
 

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 
A - addition do fifth 
S - subtraction do last 
 
 

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 
 
 

Rule 5: 

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

x² = x * x 

x^1/2 = x ^.5 = square root of x 

x⁵ = x * x * x * x * x 
 

Multiplication (add) exponents

    x² * x³ = x⁵
 

Division (subtract) 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 

Rule 7:

% Fractions Decimal

50% is the number 

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.

Example Problems for Ratio and Proportions

Rule 9:

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