What Is the Order of Operations in Math?

These acronyms will help you solve any equation

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This tutorial is designed to help you solve problems correctly by using the 'Order of Operations'. When there is more than one operation involved in a mathematical problem, it must be solved by using the correct order of operations. A number of teachers use acronyms with their students to help them to retain the order. Remember, calculators/spreadsheet programs will perform operations in the order which you enter them, therefore, you will need to enter the operations in the correct order for the calculator to give you the right answer.

Rules to the Order of Operations

In mathematics, the order in which mathematical problems are solved is extremely important.

  1. Calculations must be done from left to right.
  2. Calculations in brackets (parenthesis) are done first. When you have more than one set of brackets, do the inner brackets first.
  3. Exponents (or radicals) must be done next.
  4. Multiply and divide in the order the operations occur.
  5. Add and subtract in the order the operations occur.

In addition, you must always remember to:

  • Simplify inside groupings of parentheses, brackets, and braces first. Work with the innermost pair, moving outward.
  • Simplify the exponents.
  • Do the multiplication and division in order from left to right.
  • Do the addition and subtraction in order from left to right.

Acronyms to Help you Remember

So, how will you remember this order? Try the following acronyms:

Please Excuse My Dear Aunt Sally
(Parenthesis, Exponents, Multiply, Divide, Add, Subtract)

or

Pink Elephants Destroy Mice And Snails
(Parenthesis, Exponents, Divide, Multiply, Add, Subtract)

and

BEDMAS
(Brackets, Exponents, Divide, Multiply, Add, Subtract)

or

Big Elephants Destroy Mice And Snails
(Brackets, Exponents, Divide, Multiply, Add, Subtract) 

Does It Really Make a Difference Whether You Use the Order of Operations?

Mathematicians were very careful when they developed the order of operations.

 Without the correct order, watch what happens:

15 + 5 x 10 = Without following the correct order, we know that 15+5=20 multiplied by 10 gives us the answer of 200.

15 + 5 x 10 = Following the order of operations, we know that 5 x 10 = 50 plus 15 = 65. This gives us the correct answer, while the first answer is incorrect.

So, you can see that it is absolutely critical to follow the order of operations. Some of the most frequent errors students make occur when they do not follow the order of operations when solving mathematical problems. Students can often be fluent in computational work yet do not follow procedures. Use the handy acronyms outlined above to ensure that you never make this mistake again. 

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Russell, Deb. "What Is the Order of Operations in Math?" ThoughtCo, Jan. 8, 2018, thoughtco.com/order-of-operations-2312083. Russell, Deb. (2018, January 8). What Is the Order of Operations in Math? Retrieved from https://www.thoughtco.com/order-of-operations-2312083 Russell, Deb. "What Is the Order of Operations in Math?" ThoughtCo. https://www.thoughtco.com/order-of-operations-2312083 (accessed April 21, 2018).