High School Math : How to use the order of operations in pre-algebra

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : How To Use The Order Of Operations In Pre Algebra

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, subtract, cube

Multiply, subtract, add, cube

Cube, multiply, add, subtract

Cube, multiply, subtract, add

Multiply, add, subtract, cube

Correct answer:

Multiply, subtract, add, cube

Explanation:

By order of operations, always carry out any operations within grouping symbols first. Since there are nested grouping symbols, work from the inside (the parentheses) outward. Within the parentheses, there is a multiplication and a subtraction; do them in that order. Going outward, there is a subtraction within the brackets, so do that next. A cube remains, so do that last.

In summary: Multiply, subtract, add, cube

Example Question #21 : High School Math

Evaluate the following expression:

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we must follow the order of operations. That is: Parentheses, Exponent, Multiply, Divide, Addition, Subtraction (PEMDAS).

First, we evaluate the parentheses:

Next, we evaluate the exponents:

Next, we complete the multiplication and division from the left to the right of the expression:

Finally, we complete the addition:

Example Question #1 : How To Use The Order Of Operations In Pre Algebra

Evaluate the following expression:

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we must follow the order of operations. That is: Parentheses, Exponent, Multiply, Divide, Addition, Subtraction (PEMDAS).

First, we evaluate the parentheses:

Next, we complete the multiplication:

Finally, we evaluate the addition and subtraction from left to right in the expression:

Example Question #1 : How To Use The Order Of Operations In Pre Algebra

Evaluate the following expression:

Possible Answers:

Correct answer:

Explanation:

To solve this problem, we must follow the order of operations. That is: Parentheses, Exponent, Multiply, Divide, Addition, Subtraction (PEMDAS).

First, we evaluate the parentheses:

Next, we evaluate the exponents:

Next, following PEMDAS, we evaluate the multiplication and division from left to right in the expression:

Finally, we evaluate the subtraction:

 

Example Question #1 : 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 #1 : Multiplication And Division

Express in degrees:  radians

Possible Answers:

Correct answer:

Explanation:

Since , we can convert as follows:

Example Question #1 : How To Use The Order Of Operations In Pre Algebra

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

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

Possible Answers:

Multiply, add, subtract, divide

Divide, multiply, subtract, add

Multiply, subtract, add, divide

Add, subtract, multiply, divide

Subtract, add, multiply, divide

Correct answer:

Multiply, subtract, add, divide

Explanation:

A fraction bar in an expression acts as both a division symbol and a grouping symbol, so we evaluate the numerator first. Within the numerator, there is a multplication, a subtraction, and an addition, so, by order of operations, we multiply first. Addition and subtraction are carried out right to left; the subtraction is left of the addition, so we subtract next, then add. Finally, we divide the numerator by the denominator.

In summary: Multiply, subtract, add, divide

Example Question #1 : 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, square, multiply, divide

Multiply, divide, add, square

Add, square, divide, multiply

Add, multiply, divide, square

Multiply, add, divide, 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 #1 : Operations And Properties

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, square, multiply, subtract

Multiply, square, add, subtract

Square, add, multiply, subtract

Square, multiply, add, subtract

Multiply, add, square, 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 #1 : 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.

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