**Order of Operations**

**A Journey through Operations**

The Order of Operations

Time to Practice!

In order to evaluate a numerical expression containing multiple operations, operations are done in the following order from left to right.

Do the operations in parentheses first. This also includes any other grouping symbols like brackets and radicals.

P - Parentheses

The next operation to evaluate is exponents.

E - Exponents

The next two operations that you evaluate in a numerical expression is multiplication and division. These operations are calculated as they appear in the expression left to right.

MD - Multiplication and Division

Click on the following link to practice evaluating numerical expressions using the order of operations.

Fraction Bars

When you have multiple operations in the numerator and/or denominator of a fraction, you follow the order of operations to simplify the numerator and denominator separately. Then you divide.

Exponent Review #1

When evaluating exponents, remember that an exponent represents repeated multiplication of the base.

Ex:

A and S - Addition and Subtraction

The next two operations to evaluate are addition and subtraction. These operations are also calculated left to right, just like multiplication and division.

Mnemonics

To help remember this important mathematical rule, there are different mnemonic devices to help you remember!

PEMDAS

BEDMAS (Canada)

BODMAS (UK)

PEMA (New Zealand)

Around the World

In Canada and other English speaking countries, Parentheses may be called Brackets, or symbols of inclusion and Exponentiation may be called either Indices, Powers or Orders, which have the same precedence as Roots or Radicals. Therefore, some of the words in PEMDAS are different for other countries around the world.

Parentheses (Grouping Symbols)

Exponents

Multiplication and Division

Addition and Subtraction

Tutorials

Here are some examples that range in difficulty level to see the order of operations in motion!

Challenge!

Try this challenging game where you have to figure out the order of operations with the given digits to get the answer!

http://www.funbrain.com/cgi-bin/alg.cgi?A1=s&A2=3

o

Keep following the footprints!

http://www.learnalberta.ca/content/mejhm/index.html?ID1=AB.MATH.JR.NUMB&ID2=AB.MATH.JR.NUMB.INTE&lesson=html/object_interactives/order_of_operations/use_it.html

Exponent Review #2

Be careful when identifying the base! If a base has more than one term, we use parentheses to identify it.

Why follow the order of operations?

Just like following directions to get to a destination, if you do not follow the order of operations, you will not arrive at the correct answer! This basic math principle has been officially used for over 500 years and has been proven to simplify numerical expressions correctly.