Class Notes 1.1: Order of Operations
Essential Understanding:
1. When evaluating an expression involving more than one operation, we must follow a
certain order. The order of operations is a set of rules for simplifying expressions that
have two or more operations. A common mistake students make is to perform all
operations in order from left to right, regardless of the proper order.
2. Perform all multiplication and division in order from left to right. Then, perform all
addition and subtraction in order from left to right.
3.Operations are things like adding, subtracting, multiplying, and dividing.
Examples:
You have 2 objectives:
1. Pick the correct operation in the correct order
2. Calculate accurately
PEMD AS
P Parenthesis or grouping symbols ( ), [ ], { }, fraction bars (work from the
inside out)
E Exponents
MD Multiply and divide (FROM LEFT TO RIGHT)
AS Add and subtract (FROM LEFT TO RIGHT – WHEN THERE IS NO MORE
MULTIPLICATION OR DIVISON)
Class Notes 1.2: Order of Operations with Grouping Symbols
Essential Understanding:
1. If an expression contains grouping symbols, the order of operations requires that
whatever part of the expression is contained in the grouping symbols be simplified
first. A common mistake of students is to ignore the grouping symbols when
simplifying.
2. Grouping symbols are sometimes used to enclose an expression. There are several
types of grouping symbols, including parentheses, brackets, and the fraction bar
(vinculum). Parentheses are the most common.
3. For example, 3 × (4+2) means 3 groups of 6 which equals 18. This is quite different
from 3 × 4 + 2, which means 3 groups of 4 plus 2 more and is equal to 14.
4. All operations inside of parentheses should be done first. When simplifying inside of
parentheses, you follow the order of operations.
Examples:
Class Notes 1.3: Order of Operations with Nested Grouping Symbols
Essential Understanding:
1. If an expression has nested grouping symbols—one or more sets of grouping
symbols inside another—some students ignore the innermost symbols. They then go
on to simplify the expression incorrectly.
2. Grouping symbols help to indicate what operations to do first when simplifying
expressions. Always work from the innermost group, then outward.
Examples: