How to Solve a Math Problem Using PEMDAS

By Tina Molly Lang
Mneumonic devices can help you solve a complicated arithmetic equation.

When you are given a messy arithmetic expression, you will need to remember the order of operations. PEMDAS or the phrase “Please excuse my dear Aunt Sally” is a mnemonic device that with help you remember the order of operations. PEMDAS stands for parentheses, exponents, multiplication and division, addition and subtraction--mathematical operations are done in that order.

To solve a math problem using PEMDAS, pick an example math problem. Let’s use: 10 - 3 x (5-3)^2 + 8 ÷ 2 = ??

Start by solving inside the parentheses.

(5-3) = 2

This give: 10 - 3 x (2)^2 + 8 ÷ 2 = ??

Next, solve the exponents

(2)^2 = 4

This gives: 10 – 3 x 4 + 8 ÷ 2 = ??

Then work on multiplication and division.

3 x 4 = 12 and 8 ÷ 2 = 4

This gives: 10 – 12 + 4 = ??

Finally, work out the addition and subtraction.

10 – 12 + 4 = 2

This means: 10 - 3 x (5-3)^2 + 8 ÷ 2 = 2

Tip

Remember that multiplication and division take equal priority. Exponents always take priority over multiplication or division, but multiplication and division are always done in the same step. Likewise, addition and subtraction are always done in the same step.

You must completely finish one order of operation before moving onto the next. Let’s say the problem had been 10 - 3 x (5^2-3 x 2)^2 + 8 ÷ 2 = ?? The order of operations continues to apply even within an operation. (5^2-3 x 2) would be 5^2 = 25. (25 – 3 x 2). 3 x 2 = 6. (25 – 6). 25 – 6 = 19. Now that you have solved within the parentheses, you can move on to the next order of operation in the problem.

Warning

In any math problem, always remember tp solve the parentheses before solving the exponents. Some textbooks use PPMDAS (“Pretty please, my dear Aunt Sally” or Parentheses, Powers, Multiplication, Division, Addition, and Subtraction) instead of PEMDAS. So sometimes there is a tendency to switch the exponents (powers) for the parentheses.

If you choose to use a calculator to solve the math problem, your calculator must be in scientific notation. Only a calculator in scientific notation will follow PEMDAS and the order of operations. A non-scientific calculator will yield an incorrect answer.

About the Author

Tina Molly Lang is a violinist, freelance writer, and Yale School of Music graduate. She is also a regular news writer for Associated Content, arts writer for the Examiner and has been published in other magazines including The American Thinker. She has been writing on a freelance basis since 2007.