With our free evaluating numerical expressions using PEMDAS worksheets, not only do students steer clear of the confusion about which math operation to start with while simplifying a numerical expression, they also have a crystal-clear picture of which order to follow while at it. "PEMDAS" in an acronym for parentheses, exponents, multiplication, division, addition, subtraction. Think of the mnemonic phrase "Please Excuse My Dear Aunt Sally", and the operations will be at your service one after another. Explore the full gamut of PEMDAS with our pdf worksheets presenting expressions with either both parentheses and exponents or one of them at play.
These printable worksheets are ideal for students in grade 5, grade 6, grade 7, and grade 8.
CCSS: 5.OA, 6.EE
Numerical Expressions involving Four Operations
Evaluate expressions like you have been at it for ages, with this printable worksheet! Incorporate the DMAS rule, perform the four arithmetic operations in the order, and find the value of the expressions. Prove your numerical mettle!
Expressions with Parentheses | Easy
With this pdf worksheet on, recognizing a numerical expression with parentheses won't be half as challenging for 5th grade and 6th grade students. Perform the operations within the parentheses first; move on to the other parts to evaluate them.
Expressions with Parentheses | Moderate
In this free moderate practice resource on PEMDAS, students face off against expressions with multiple parentheses. Reduce the expressions inside the parentheses to a number and then proceed with the other operations in the appropriate order.
Expressions involving Exponents | Easy
The defiant and resolute students in grade 6 and grade 7 have a refreshing resource to practice simplifying arithmetic expressions involving exponents. This easy exercise includes two operators per expression so working with powers is easy.
Expressions involving Exponents | Moderate
In this printable PEMDAS worksheet, learners are up against arithmetic expressions involving three to four operations and two exponential notations. By solving the problems here, they hone in on simplifying numerical expressions involving exponents.
PEMDAS | Parentheses and Exponents
Linked here is an all-in-one pdf that the fledgling PEMDAS practitioners in 7th grade and 8th grade will hold dear for a long time. Evaluate expressions with parentheses, exponents, multiplication/division, and addition/subtraction, all at once!
Using the Order of Operations - Also Known as PEMDAS
How many times have you evaluated a numerical expression, and even though you know your addition, subtraction, multiplication, and division is correct, you still have the wrong answer?
If this has happened to you, then you probably haven't used the Order of Operations correctly.
What is the Order of Operations?
The order of operations is a set of rules that you must follow in order to correctly evaluate a numerical expression that contains multiple operations (a combination of addition, subtraction, multiplication, and division).
Using the Order of Operations
In order to evaluate an expression with more than one operation, you must:
1. Evaluate expressions inside of grouping symbols (parenthesis or brackets).
2. Evaluate powers (think exponents).
3. Multiply and/or divide from left to right.
4. Add and/or subtract from left to right.
In order to remember this set of rules, many people remember the acronym, PEMDAS. Check it out:
PEMDAS - How to Remember the Order of Operations
Ok, now let's use this set of rules to evaluate numerical expressions.
Example 1 - Using PEMDAS
Tip
If you find that you are having trouble, use colored pencils to help color code your work as I have done in the example above.
This will help you to organize your work and make sure that you follow the rules correctly.
Many people get confused because you may start computing in the middle of the numerical expression.
You can color code by underlining the part of the problem that you are focusing on. Take a look at Example 2.
Example 2 - Color Coding
One last example with a power to evaluate. Take a look....
Example 3 - Evaluating Powers Within a Problem
The order of operations can easily be remembered by thinking of the acronym, PEMDAS: Parentheses, Exponents, Multiplication or Division and Addition or Subtraction.
If you perform the operations within a problem in this order, then you will be sure to arrive at the correct solution. However, if you do not perform the operations in this order, then you will most likely end up with an incorrect solution!
We will continue our study of the order of operations in our next lesson, as we focus on alternative grouping symbols.
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