# PEMDAS with Fractions, Decimals, Exponents Worksheets

The basic concept of determining which operator to give priority to when you are confronted with a series of available operators to process is tough enough for students. When you compound that with other features of these values such as a fractional and decimal values, it can really begin to confuse students. Exponents should not throw them from much of a loop because they are part of the standard operation priority system of procedures (PEMDAS). These worksheets and lessons teach students how to power through the order of operations regardless of the values that are present and their form. This will help make students ready to work with more complex equations and expressions.

### Aligned Standard: 5.OAT.1, 6.EE.1

- PEMDAS with Fractions Lesson- Many students lose their minds when they see operations and fractions in the same place.
- PEMDAS with Decimals Lesson - Decimals don't seem to scare as many people.
- Nested Tables Worksheet 1 - There are parentheses everywhere.
- Order of Operations with Fractions and Exponents - Make sure to cover exponents before you go here.
- Quick Operations - The focus here is on a mix of skills.
- The Closer- Look very carefully at this one and note where the parentheses are.

- Answer Keys - These are for all the unlocked materials above.

### Homework Sheets

It does make a difference whether you are solving an expression or an equation.

- Homework 1 - We realize right away that this is an order of operations problem.
- Homework 2 - You will need to reduce fractions to the lowest terms to help process these problems.
- Homework 3 - The order is key here. There are two operations present at each level
- Homework 4 - Solve. Round your answers to the nearest hundredths place.

### Practice Worksheets

You can do some really heavy lifting here.

- Practice 1 - This is where it gets tough. You find situations where you need to solve brackets found within one another.
- Practice 2 - We have to remember that when we are deciding between processing a division operation and a multiplication operation, we always process these operations left to right.
- Practice 3 - The M and D are equal, so you go left to right. I would encourage you to number the order in which you go through the operators.
- Practice 4 - The last practice worksheet for you. There are many instances where you will need to evaluate subtracting a negative value.

### Math Skill Quizzes

The quizzes were built to progress in a rhythm.

- Quiz 1 - My favorite of all the quizzes here. That is because of the placement of brackets and the adjacent exponents.
- Quiz 2 - Lots of space to work with here. There are three operators involved in all of the equations.
- Quiz 3 - No bones about it, this is a quiz. Take a look at the placement of the parathesis due to the stretched layout.

### When Does PEMDAS Confuse Students?

Once children have mastered four basic mathematical operations, they move on to learning advanced mathematical concepts. One of the firsts advanced mathematical concepts that they encounter is of PEMDAS. PEMDAS or BODMAS is a universally accepted concept for solving mathematical problems with more than one mathematical operation. The acronym PEMDAS stands for parentheses, exponents, multiplication, division, addition, and subtraction. When applying PEMDAS to any problem, we look for parentheses and solve them first. Next, we solve for exponents, multiplication and division come next, and addition and subtraction are solved last.

However, this widely accepted concept sometimes stirs confusion among students. Most confusion arises when solving for the four basic operations. Students find it difficult to figure out whether to apply division first or multiplication. Both the operations are given the same priority, but the solution should be carried out in left to right order. The same applies to addition and subtraction. These two are also given the same priority and need to be solved in the right to left order, when they are present at the same level. Unfortunately, this concept is often taught literally, which leaves students confused. Students tend to solve all the division before multiplication, and all addition is solved before subtraction. To be honest, we get roughly a teacher or two a month contacting us to tell us our solutions on these answer keys are incorrect because they feel that this order of operations should also be followed literally. When exploring this concept, it should be pointed out that those operation pairs are found at the same level and those have the same level of priority and should be followed in the same direction that we read English (left to right).