# Order of Operations Worksheets

What are the Common Order of Math Operations? Operations consist of things like add, subtract, divide multiply, or even powered numbers however if you are given all of these within a single expression. Which one will you solve first? A standard method for remembering the order of operations is learning the abbreviation PEMDAS, which perfectly defines the order of operations. The full form of PEMDAS is Parentheses, Exponents, Multiplication, Division, Addition, and subtraction. You must keep in mind that if you do not obey the orders, you will get the wrong answer. Keep in mind the following tips when you are solving an expression that involves every operation. In Parentheses, you need to solve the expression within them. Now you must keep in mind that different types of brackets have different priorities. The round brackets need to be addressed first, then curly brackets and finally the square brackets. Multiplication and Division should get solved from left to right. Addition and Subtraction need to get solved from left to right as well. We use the acronomy PEMDAS to tackle all of these worksheets some will take you a minute others will take you a lot of time.

- 2-Step Order of Operations - You will need to make two checker like moves here. This usually will involve the movement of constant and then splitting a variable product combination.
- 3-Step Order of Operations - You will need to plan this out before you perform these. These can get a bit confusing. It helps if you start by circling the unknown value for yourself.
- 4-Step Order of Operations - You will need to be well organized when solving these problems. Remind yourself that the overall goal is to just isolate one variable for yourself.
- Adding and Subtracting Rational Numbers - These sums and differences are not what really make you understand the process mostly. The goal here is to determine the end value.
- Advanced Real World Math Operations - These are types of problems you will come across in your daily life. You would be surprised at the number of steps you will need to take.
- Advanced Absolute Value Operations - My advice is to address the absolute value first and then move on to step two. Remind yourself of the basic moves that are required here.
- Missing Operations (Add and Subtract) - What symbols are missing to make this correct? We only focus on sums and differences only on this worksheet topic.
- Mixed Basic Operations Word Problems - What will you need to finish this one up? These are more intermediate level problems.
- One and Two Step Addition and Subtraction (Up to 100) Word Problems - In this set of worksheets look for indicators to find which operations you need to use. The keywords will vary, but you have seen them before.
- Parentheses, Brackets, and Braces in Math Expressions - How to use and handle these in your math problems. I find that braces and brackets confuse students the most.
- PEMDAS - The great old acronym that tells us how to approach these types of problems. We need to remember how these calculations are relative to one another.
- PEMDAS with Fractions, Decimals, and Exponents - Just because the form of the value differs does not change how you go after these problems. We see how these different forms of notation complicate things a bit.
- Properties of Math Operations as Problem Strategies - You will take your time and access what is being asked of you and form a plan to complete these problems. It is all about taking your time and making the best choice.
- Very Basic Order of Operations - This is a great introduction for students as to how to approach this topic. Beginners will appreciate all the extra space that they have to work with on these worksheets.

### Tips for Solving These Types of Problems

As with any strategy in math there are instances where it they either do not work or do not apply. These types of rules are very deceptive and can really complicate your life. If you pay attention to when PEMDAS goes a little off the rails, your life with be super easy. The only time you really need to worry is when division and multiplication are found in the same equation. Students may instinctively complete the multiplication operation before division, but since both operations are considered to be on the same level, when presented with a problem like this it is processed as you would read it from right to left. This even confuses trained adults that forget this same thing. Not only that but check most online math calculators that can process multiple operators at the same time. They often neglect this simple rule. Our poor editors are constantly getting emails telling them that their answer keys are incorrect for our four step problems, but every time it is some one who either did not know that this rule even existed or forgot about it. We also find another common speed bump on this topic is the over reliance on mental math. When you are processing calculations that have four or even five steps, it is hard to keep track without writing something out to track it.

### 2 Step Example

**Problem: ** 4 + 8 x 2 =

**Solution: ** We revert to look at the acronym PEMDAS. Multiplication comes before addition, so the answer here can be better illustrated as: 4 + (8 x 2) =. Following this out further 4 + 16 = 20.

### 3 Step Example

**Problem: ** 2 x 8 – 12 ÷ 4 =

**Solution: ** Looking at our original thought process (PEMDAS). We have division, followed by multiplication, and then subtract to finish it off. So it would look like this:

**Division: ** 2 x 8 – 3 =

**Multiplication: ** 16 – 3

**Subtraction** = 13.

### 4 Step Example

**Problem: ** 19 x 4 + 192 ÷ 4^{3}

**Solution: ** This may look like only 3 operators are present, but we need to begin with the exponent, then multiply, then divide, and finally the addition portion. Here is a breakdown of that:

**Exponent: ** 19 x 4 + 192 ÷ 64

**Multiply: ** 76 + 192 ÷ 64

**Divide: ** 76 + 3

**Add: ** 79