How to Solve a Math Problem Using PEMDAS

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Take a look at the following equality:

x = 7 + 2 • (11 - 5) ÷ 3

Solve for x by working through the mathematical operations in order from left to right and you'll get 18, which is the wrong answer. To get the right answer, which is 11, you have to follow the correct order of operations. If you can't remember the proper order, PEMDAS can help. It's an acronym that stands for Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

As a word, PEMDAS isn't that difficult to remember, but if you can't do it, a couple of catchphrases might help. One of them is "Please Excuse My Dear Aunt Sally." The first letter in each of the words of this phrase is one of the letters in PEMDAS. If you prefer to call parentheses brackets, remember the acronym BEDMAS and the catchphrase "Big Elephants Destroy Mice and Snails" instead. This phrase reverses the D and the M, but that's okay. When you get to multiplication and division, you usually do the one that comes first in the expression.

Some people who have trouble remembering PEMDAS look for order of operations by searching for PADMAS math. This won't help. It ignores E for exponents, and exponents are an important operation that must be done before you get to any of the other arithmetical operations.

How to Apply the Order of Operations

Whenever you have a long string of operations to perform, the rules of mathematics are clear. You always start by performing operations in parentheses (brackets), and then you solve exponents, which are numbers in the form xa. The next two operations are multiplication and division. If a division comes first in the expression, you do it first. Similarly if a multiplication comes first, do that first. The same is true for the final two operations, addition and subtraction. Perform subtractions before additions if they come first in the expression and vice versa.

A Sample Calculation

Take another look at the expression at the beginning of this article. Applying PEMDAS, you solve it like this:

  1. Start With the Numbers in Brackets

  2. 11 - 5 = 6, so the expression now becomes x = 7 + 2 • 6 ÷ 3

  3. Perform the Multiplication and Division

  4. The multiplication comes first, so start with that. The expression is now x = 7 + 12 ÷ 3. Now do the division to end up with: x = 7 + 4.

  5. Finish up With Addition and Subtraction

  6. There is only one addition to perform, which produces the final answer:

    x = 11

    Sometimes you'll see more than one set of brackets or parentheses. The rule is to simplify everything inside the brackets, starting with the inner ones, before you get to the rest of the arithmetical operations. Remember to follow PEMDAS or BEDMAS even when working with numbers in brackets. That means to solve exponents before you move on to the other operations.

More Examples for How to Use PEMDAS or BEDMAS

15 - [5 + (7 -4)]

  1. Start with the inner brackets: 15 - [5 + 3}
  2. Now do the outer brackets: 15 - 8
  3. Do the subtraction, and the answer is 7. 

(5 - 3)2 + {10 ÷ (7 - 2)}2 • 4

  • P – Start with numbers in parentheses, beginning with inner parentheses:

(5 - 3)2 + {10 ÷ 5}2 • 4

22 + 22 • 4

  • E – Solve all the exponents:

4 + 4 • 4

  • M, D – Do the multiplications and divisions:

4 + 16

  • A, S – Do the additions and subtractions:

The final answer is 20.

References

About the Author

Chris Deziel holds a Bachelor's degree in physics and a Master's degree in Humanities, He has taught science, math and English at the university level, both in his native Canada and in Japan. He began writing online in 2010, offering information in scientific, cultural and practical topics. His writing covers science, math and home improvement and design, as well as religion and the oriental healing arts.

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