Order of Operations
 Home > Lessons > Order of Operations Search | Updated August 9th, 2017
Introduction

This lesson page will inform you how to evaluate expressions. Here are the sections within this lesson page:

Before continuing with this lesson, it is important that you understand how to deal with operations on Integers. Use this lesson before proceeding. esson: Operations on Integers

When we try to solve a variety of real-world problems, we inevitably face situations that require calculations. Whether it is calculating the amount of wall area to be painted, how much a client should be billed for a roofing job, or how much money we will receive in bank interest over twenty years time, there will be formulas to face.

These formulas require us to insert sometimes several values and use multiply operations. Knowing the order in which to proceed to arrive at the correct solution is vital for being accurate. It will be the difference in ordering the right amount of paint, being able to run a successful business, and determining how to plan for the future.

The next sections will inform you how to evaluate expressions.

An operation is some well defined process that we do with numbers. Here are some operators as symbols and what they mean.

 + Addition - Subtraction • Multiplication ÷ Division 2 Exponents √ Radicals

In grammar school and junior high school, a considerable amount of time is spent learning about these operators. The following sections will inform you how to put them together when more than one operator is present in a problem.

So that everyone calculates expressions the same, there is an agreed order to use. To help understand the order, we will use the acronym PEMDAS as a memory aid. This is what PEMDAS means.

 P () Parentheses E 2 Exponents M • Multiplication D ÷ Division A + Addition S - Subtraction

When a problem contains more than one operator, simply approach the order of operations using a top-down process using the table above. This means we do operations inside parentheses first. Next, we work on exponents.

If multiplication and division are present, do the operations in a left-to-right fashion (which is why they are the same color in the table). Likewise, if addition and subtraction are present, do them in a left-to-right fashion. They, too, have the same color in the table to indicate that they are linked in that way.

Use the three examples below to see exactly how expressions are evaluated.

Problem: 42 - 2 + 10 ÷ 2

 Expression Reason 42 - 2 + 10 ÷ 2 Given 16 - 2 + 10 ÷ 2 Perform exponent first. 16 - 2 + 5 Division is next. 14 + 5 Perform addition/subtraction left-to-right. 19 Perform the last operation.

The place people usually have an issue is the place where subtraction is listed first and then addition.

16 - 2 + 5

The problem has to be done left-to-right because addition and subtraction are considered equal operators within the PEMDAS-described system. So, keep this in mind when calculating expressions.

View this instructional video and then try the interactive quiz to determine if you understand this material. ideo: Order of Operations uiz: Order of Operations

Problem: 3(1 - 32) ÷ 2 • 3

 Expression Reason 3(1 - 32) ÷ 2 • 3 Given 3(1 - 9) ÷ 2 • 3 Within the parentheses, the exponent is performed before the subtraction. 3(-8) ÷ 2 • 3 The subtraction within the parentheses was performed. -24 ÷ 2 • 3 When multiplication and division are present, perform them from left-to-right. -12 • 3 We must continue operations from left-to-right. -36 The last step requires multiplication.

The place people usually have an issue with this problem is the place where division is listed before multiplication.

-24 ÷ 2 • 3

The problem has to be done left-to-right because multiplication and division are equal operators within the PEMDAS system.

View this instructional video and then try the interactive quiz to determine if you understand this material. ideo: Order of Operations uiz: Order of Operations

Try this instructional video to gain a more personalized view on this topic. ideo: Order of Operations

Try this interactive quiz to determine if you understand how to evaluate expressions. uiz: Order of Operations

Try this lesson, which is related to the sections above. esson: Functions