Algebra is fundamental to GMAT Quant. A great way to get started on your GMAT prep is to refresh your skills in simplifying algebraic expressions!
PEMDAS is an acronym for the order of operations, which are the basic rules which govern the simplification of algebra. Notice how division/subtraction is always done in order from left to right.
Addition and multiplication are both “commutative” which means it doesn’t matter the order in which the operation is performed. This means that A + B = B + A, and A x B = B x A.
The Associative Property for addition and multiplication means that the numbers can be re-grouped in parentheses without a different outcome. For example, 2 + (3 + 7) = (2 + 3) + 7. Like the Commutative law, this is ONLY true for addition and multiplication.
The Distributive law allows us to “distribute” a factor among terms being added or subtracted. That is, a(b + c) = ab + ac. This law, along with the commutative and associative laws, will become second-nature to you the more you practice!
Remember this rule: you can ONLY cancel factors. Try to simplify the numerator and the denominator as much as possible if you’re looking for things to cancel.
Notice that algebraic expressions can be made more complicated with exponents, including negative exponents. Remember your exponent rules! When you have the same base in the numerator and the denominator, you can subtract the exponents.
Watch some video walk-throughs of some GMAT algebra problems involving order of operations and algebraic expressions on the GMAT – Simplifying Algebraic Expressions learnboard.