# GED Math : Order of Operations

## Example Questions

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### Example Question #1 : Complex Operations

Evaluate:

Explanation:

Work the operations in this order: Square first, multiply second, add third.

### Example Question #1 : Order Of Operations

Solve:

Explanation:

When solving this problem, you need to remember order of operations, which tells us which operation has to be done first.

When following order of operations, you complete operations in the following order:

1. Parenthesis - Complete any operation in parenthesis first

2. Exponents - Solve exponents second

3. Multiplication and Division - Multiply or Divide (whichever one comes first from left to right)

4. Addition and Subtraction - Add or Subtract (whichever one comes first from left to right)

Keeping order of operations in mind, the steps to solve are below

### Example Question #3 : Order Of Operations

Define an operation  on the real numbers as follows:

Evaluate

Undefined

Explanation:

Substitute 6 for  and  for :

### Example Question #4 : Order Of Operations

Define an operation  on the real numbers as follows:

Evaluate

Undefined

Undefined

Explanation:

Substitute 7 for  and - for :

Any fraction with a zero denominator - such as this one - is an undefined quantity.

### Example Question #2 : Order Of Operations

Solve:

Explanation:

This problem involves order of operations.

Use the acronym for the correct order:

PEMDAS-Parenthesis, Exponents, Multiply, Divide, Add, Subtract

(Please Excuse My Dear Aunt Sally)

Start by grouping what needs to be solved first.

### Example Question #1 : Complex Operations

In order to calculate

what step must you take first?

Calculating the square of eight

Subtracting twenty from fifty

Dividing twenty by five

Calculating the square of eight

Explanation:

By the order of operations, in the absence of grouping symbols, exponents must be carried out before any other operations. The correct choice is that eight must be squared.

### Example Question #1 : Order Of Operations

Evaluate  for .

Do not use a calculator.

Explanation:

Substitute 0.5 for  and follow the order of operations:

### Example Question #1 : Order Of Operations

Evaluate  for . Do NOT use a calculator.

Explanation:

Substitute  for  in the expression and folllow the order of operations:

### Example Question #3 : Order Of Operations

Evaluate   for

Do not use a calculator.

Explanation:

Substitute 7 for  in the expression and evaluate, paying attention to the order of operations:

### Example Question #3 : Order Of Operations

Evaluate:

Do not use a calculator.