GED Math : Order of Operations
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Example Questions
Example Question #11 : Complex Operations
Evaluate:
Do not use a calculator.
In the order of operations, multiplications and divisions have equal rank and, collectively, are carried out from left to right, as follows:
Example Question #11 : Order Of Operations
Which of the following operations might yield a negative result?
Dividing the square of a positive number by a positive number.
Multiplying the square of a positive number by a positive number.
Adding the square of a positive number to a positive number.
Subtracting the square of a positive number from a positive number.
Subtracting the square of a positive number from a positive number.
The square of a positive number, as the product of two positive factors, must be positive.
Adding the square of a positive number to a positive number is adding two positive numbers; the sum must be positive. The same happens when multiplying and dividing; in both cases, both numbers are positive and the result must be positive.
Subtracting the square of a positive number from a positive number can yield a negative result. For example:
Example Question #12 : Order Of Operations
In order to calculate
what step must you take first?
Adding six and four
Subtracting two hundred from two hundred fifty
Squaring four
Dividing two hundred by six
Adding six and four
By the order of operations, the operation(s) within grouping symbols - here, the addition of six and four - must be carried out first.
Example Question #13 : Order Of Operations
Jeff went to the casino with $1,000 in his pocket. He lost $400 of it playing blackjack, won $900 playing craps, then left the casino. How much money did he leave with?
Do not use a calculator.
A loss is a subtraction; a win is an addition. Jeff leaves the casino with
Example Question #14 : Order Of Operations
Suppose the values of all of the variables in the expression
are known. In order to evaluate this expression, what would be the first step?
Multiplication
Subtraction
Addition
Division
Division
In the absence of grouping symbols, the first operations that should be carried out are exponentiations, of which there are none here.
The next operations to be carried out are the multiplications and divisions, from left to right. The division is to the left, so it is executed first.
Example Question #16 : Order Of Operations
Define an operation 
Evaluate 
Substitute 7 for 
By order of operations, square, then add, then subtract.
Example Question #11 : Order Of Operations
Solve:
Simplify the parentheses first. Notice that there is an exponent in the first parentheses.
The expression becomes:
Simplify the terms inside the parentheses by subtraction.
Multiply the terms.
The answer is:
Example Question #11 : Complex Operations
Simplify:
Evaluate the terms of the inner parentheses.
The inner parentheses become:
Replace the terms.
The answer is:
Example Question #11 : Order Of Operations
Solve:
Simplify by distributing the coefficient through the binomial.
Distribute the negative through the second binomial.
Combine the terms.
The answer is:
Example Question #20 : Order Of Operations
Evaluate for 
Substitute 12 for 
By the order of operations, multiplication precedes addition and subtraction, so multiply first:
Addition and subtraction are worked from left to right, so add next, then subtract:
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