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# Order of Operations Help

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By McGraw-Hill Professional
Updated on Sep 21, 2011

## Order of Operations

In the English language, we have punctuation symbols to clarify the meaning of sentences. Consider the following sentence:

John said the teacher is tall.

This sentence could have two different meanings depending on how it is punctuated:

John said, "The teacher is tall."

or

"John," said the teacher, "is tall."

In mathematics, we have what is called an order of operations to clarify the meaning when there are operations and grouping symbols (parentheses) in the same problem.

The order of operations is

1. Parentheses
2. Exponents
3. Multiplication or Division, left to right
4. Addition or Subtraction, left to right

Multiplication and division are equal in order and should be performed from left to right. Addition and subtraction are equal in order and should be performed from left to right.

Math Note: The word simplify means to perform the operations following the order of operations.

#### Example 1

Simplify 18-6×2-16÷2.

#### Example 2

Simplify 5 + 2 3 - 3 × 4.

#### Example 3

Simplify 42 - (8 - 6) × 2 2 .

#### Example 4

Simplify 19 + (6 - 3) 2 18 ÷ 2.

### Order of Operations Practice Problems

#### Practice

Simplify each of the following:

1. 3 - 2 2 + 5

2. 6 ÷ 3 × 2

3. 32 - (6 × 2) 2 + 15 ÷ 3

4. 8 2 - 3 × 4 ÷ 2

5. 7 3 + (2 × 5 2 -4) ÷ 2

1. 4

2. 4

3. -107

4. 58

5. 366

More practice problems for this concept can be found at: Integers Practice Test.

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