Pre-Algebra : Order of Operations

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

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Example Question #1 : Order Of Operations

Simplify the expression below.

Possible Answers:

Correct answer:

Explanation:

First, distribute the negative sign into the parentheses.

Next, combine like terms.

Note that all operations in this problem are addition and subtraction; there is no need to FOIL or multiply.

Example Question #2 : Order Of Operations

Solve the following problem:

Possible Answers:

Correct answer:

Explanation:

First, work from left to right completing multiplication and division, then work from left to right completing addition and subtraction. 

Example Question #3 : Order Of Operations

Suppose you know the value of , and you want to evaluate the expression:

In which order would you carry out the four operations in the expression?

Possible Answers:

Add, multiply, divide, square

Add, square, divide, multiply

Multiply, add, divide, square

Add, square, multiply, divide

Multiply, divide, add, square

Correct answer:

Add, square, multiply, divide

Explanation:

By order of operations, always carry out any operations within parentheses first; this is the addition.  This removes the parentheses; what remains is a square, a multiplication, and a division. Since there are no more grouping symbols, square next. The multiplication is done next, as multiplications and divisions are performed in left-to-right order.

In summary: Add, square, multiply, divide

Example Question #4 : Order Of Operations

Suppose you know the value of , and you want to evaluate the expression:

In which order would you carry out the four operations in the expression?

Possible Answers:

Multiply, add, square, subtract

Square, multiply, add, subtract

Square, add, multiply, subtract

Add, square, multiply, subtract

Multiply, square, add, subtract

Correct answer:

Add, square, multiply, subtract

Explanation:

By order of operations, always carry out any operations within parentheses first; this is the addition. This removes the parentheses; what remains is a square, a multiplication, and a subtraction. This is the correct order in the absence of grouping symbols.

In summary: Add, square, multiply, subtract

Example Question #5 : Order Of Operations

Simplify the expression.

Possible Answers:

Correct answer:

Explanation:

The order of operations is parenthesis, exponents, multiplication, division, addition, subtraction (PEMDAS).

First, we will evaluate the parentheses. Within the parentheses, we need to solve the exponent, then multiply,

Now that the parenthesis is evaluated, we need to multiply.

Finally, we add and subtract. We can arrange the terms in any order.

Example Question #6 : Order Of Operations

Simplify:

Possible Answers:

Correct answer:

Explanation:

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

 

Example Question #7 : Order Of Operations

Simplify:

Possible Answers:

Correct answer:

Explanation:

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

 

Example Question #8 : Order Of Operations

Simplify:

Possible Answers:

Correct answer:

Explanation:

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses: 

Example Question #9 : Order Of Operations

Simplify:

Possible Answers:

Correct answer:

Explanation:

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

 

 

 

 

 

 

 

Example Question #10 : Order Of Operations

Simplify:

Possible Answers:

Correct answer:

Explanation:

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

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