Rules for Fractions, Integers, Equations, & Inequalities

All students may be responsible for memorizing the following material on fractions/integers and may be quizzed on the same.

Fractions & Mixed Numbers:

Adding & Subtracting fractions:

1) Rewrite with a common denominator

2) Keep denominator

3) Combine numerator (add or subtract)

4) Simplify

Multiplying fractions:

1) Change any mixed numbers to improper fractions

2) Simplify

3) Multiply top & bottom straight across

4) Simplify again if necessary

Dividing fractions:

1) Change any mixed numbers to improper fractions

2) Multiply by the Reciprocal

3) Simplify

4) Multiply top & bottom straight across

5) Simplify again if necessary

Integers:

Subtracting Integers:

1) Change subtraction to addition and change the sign of the next number

Adding Integers:

1) Same Sign - Keep the sign and Add

2) Different sign - Keep the sign of the larger digit and Subtract

Multiplying & Dividing Integers:

1) Same Sign - Positive

2) Different Sign – Negative

Order of Operations (GEMDAS):

1) G Parenthesis or other Groupings

2) E Exponents

3) M Multiplication & D Division

4) A Addition & S Subtraction

Equations:

1) Simplify (Distributive property, then combine like terms)

2) Variable on one side

3) Variable by itself

Notes:

* Get rid of terms using inverse operations

* Undo the equation in reverse order of operations (Up the GEMDAS), (usually furtherest from the variable)

* Whatever you do to one side of the equation you've always got to do to the other side (Golden Rule)

* Do the top and the bottom of a fraction individually before combining

Inequalities:

Same as equations except:

Whenever you multiply or divide both sides by a negative number, you have to flip the inequality symbol.