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

## 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?

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:

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:

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

Evaluate the following expression:

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:

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:

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

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?

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?

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?

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.