Order of Operations

Intro

In life there are some things that must be done in a specific order or you won’t obtain a good result. For example, you must put on your socks before putting on your shoes, you cannot do it the other way around. When evaluating mathematical expressions you must also do it in a correct order. To remember this order there is an acronym known as PEMDAS. You must first solve, Parentheses. You must perform the action inside the parentheses () or inside the brackets [] first. Once you evaluate inside the parentheses or brackets then the parentheses or brackets will disappear and you will be left with a simpler problem. Next you must evaluate the Exponents. Third, you must evaluate all Multiplication and Division, in order from left to right. Lastly, you must evaluate all Addition and Subtraction, in order from left to right. As you are evaluating the expression and writing down each step, you should see an upside down pyramid forming, as your expression slowly becomes only one number.

Sample Problem

Same problem, different ways of expressing them:
(5-2)+2•6/3-1
(5️⃣➖2️⃣)➕2️⃣✖️6️⃣➗3️⃣➖1️⃣

Solution

**Use PEMDAS**
Worked Out Solution:
(5-2)+2•6/3-1
3+2•6/3-1
3+12/3-1
3+4-1
7-1
6
Written Out Explanation:
Step 1: Parentheses
5-2=3 so (5-2)+2•6/3-1 becomes 3+2•6/3-1

Step 2: Exponents
Check to see if the problem contains exponents. This one does not so keep going.

Step 3: Multiplication and Division From Left to Right
In this example, multiplication of 2•6 comes before division so we have to start with this one. 2•6=12. So now the problem becomes 3+12/3-1. Now we must do division, 12/3=4 so now the problem becomes 3+4-1.

Step 4: Addition and Subtraction From Left to Right
In this example, addition of 3+4 comes before the subtraction, so we must start by getting the addition. 3+4=7. Now the problem becomes very simple into 7-1, and by subtracting we know our final answer is 6.



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