Module 1: Adding & Subtracting Integers
 Adding integers with the SAME signs: add & keep the signs the same
(*Remember: If you’re adding & the signs are the SAME, keep the SAME
signs & ADD.)
+ + + = +
positive + positive = positive
negative
- + - = negative + negative =
 Adding integers with DIFFERENT signs: subtract & take the sign of
the number farthest from 0
(*Remember: If you’re adding & the signs are DIFFERENT take the
DIFFERENCE (subtract).)
 Subtracting integers: add the opposite
(Keep the first number the same, change the subtraction sign to addition,
and change the second number to its opposite; if it’s positive, make it
negative & if it’s negative, make it positive.)
Module 2: Multiplying & Dividing Integers
 If the signs are the SAME, your answer is POSITIVE
 If the signs are DIFFERENT, your answer is NEGATIVE
Module 3: Rational Numbers (Rational Numbers are numbers that can be written as a
fraction.)
 Fractions to Decimals: divide numerator (top) BY denominator (bottom)
(Calculator: numerator (top), division sign, denominator (bottom), equals)
(Long Division: DIVIDE Denominator INTO Numerator;
denominator on OUTSIDE of the house, numerator on INSIDE of the house)
 Adding or Subtracting Rational Numbers:
o Fractions must have a common denominator (Find the least common
multiple and make equivalent fractions)
o You must line up the decimals
o *Don’t forget the rules of integers for adding & subtracting
fractions and decimals
 Writing Mixed Numbers as Decimals
o “MAK” (multiply, add, keep) the mixed number & divide
numerator by denominator
o Separate whole number from fraction & change fraction to a
decimal. Rejoin it with the whole number.
 Multiplying Rational Numbers:
o Fractions- cross cancel (if you want), multiply straight across &
simplify
o Decimals- do not line up the decimals. Multiply as normal. Count
how many numbers are after the decimal(s) in the problem & put
the decimal (in the answer) that many places (going from right to left)
o *Don’t forget the rules of integers for multiplying
 Dividing Rational Numbers:
o Fractions- SAME, CHANGE, FLIP. Next, cross cancel (if you want),
multiply straight across.
o Decimals- the divisor (number that’s doing the dividing; the number outside
the house) cannot be a decimal. So, move the decimal out of the
divisor. You must also move the decimal in the dividend (number
that’s being divided; the number inside the house) the same number of
places you moved it in the divisor. Divide as normal.
o *Don’t forget the rules of integers for dividing
Module 6: Expressions and Equations
 Algebraic Expressions:
o Combining like terms: variables with variables (letters) & constants
with constants (numbers)
o Distributive Property: When you have a number on the outside
of parenthesis, multiply that by each term in the parenthesis.
o Factoring Expressions: Pull out (divide by) the GCF of the terms
and write it on the outside of parenthesis.
o REMEMBER- If you see the word “than”, switch the order of the
terms.
 Equations:
o Whatever you do to one side of the equals sign, you must do to
the other.
o The goal is to get the variable alone (solve for the variable).
Undo every operation that is being done to the variable by doing the inverse
(opposite) operation.
Module 7: Inequalities
 Solve inequalities exactly like you solve an equation (see the steps
above).
 The difference is you use an inequality sign (>, <, ≥, ≤, =)
 When you multiply or divide by a negative number, REVERSE the
direction of the inequality sign.
 Graphing solutions of inequalities:
o OPEN CIRCLE – greater than or less than (> or <)
o CLOSED CIRCLE – greater than or EQUAL to OR less than or
EQUAL to (≥ or ≤)
o SHADE in the direction that the arrow points (from the
inequality sign).
*The VARIABLE must be on the LEFT.