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Order of Operations
A Review
 Improving Math Skills • Adding & Subtracting • Polynomials • Algebra Tutorials • Polynomial Worksheets • Polynomial Identities • Test Preparation
 Order of Operations •  • More Exercises • Operation Order Game • Tutorial • Several Examples • Calculator Examples

Tutorial

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 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.

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

Rules

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.

 Rememer 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.

How will you remember this order?
Try the following Acronyms:

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

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

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

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

Examples

 12 ÷ 4 + 32 12 ÷ 4 + 9 3 + 9 12 Rule 3: Exponent first Rule 4: Multiply or Divide as they appear Rule 5: Add or Subtract as they appear (42 + 5) - 3 21 - 3 18 Rule 2: Everything in the brackets first Rule 5: Add or Subtract as they appear 20 ÷ (12 - 2) X 32 - 2 20 ÷ 10 X 32 - 2 20 ÷ 10 X 9 - 2 18 - 2 16 Rule 2: Everything in the brackets first Rule 3: Exponents Rule 4: Multiply and Divide as they appear Rule 5: Add or Subtract as they appear

Does It Make a Difference? What If I Don't 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, I know that 15+5=20 multiplied by 10 gives me the answer of 200.

15 + 5 X 10 -- Following the order of operations, I know that 5X10 = 50 plus 15 = 65. This is the correct answer, the above is not!

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 to ensure that you never make this mistake again.

Deb Russell