Basic Arithmetic : Order of Operations and PEMDAS
Study concepts, example questions & explanations for Basic Arithmetic
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Example Questions
Example Question #1 : Operations In Expressions
Solve:
Use the order of operations: PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction).
We want to solve what's in the parentheses first.
Now, do the division and the multiplication.
Therefore our equation becomes:
Finally, subtract.
Example Question #1 : Order Of Operations And Pemdas
Solve:
Use order of operations, PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) to solve.
Since there are no parentheses or exponents we can go straight to multiplication and division.
Therefore the following happens:
Then add and subtract.
Example Question #2 : Order Of Operations And Pemdas
Using order of operations, we need to solve whatever is in the parentheses first.
Next, do the multiplication and division.
Finally, add and subtract.
Example Question #2 : Order Of Operations And Pemdas
Simplify
We start with what is inside the parentheses, so 
Next, we take care of any exponents, giving us 
Next, we take care of multiplication/division, giving us 
Finally, we carry out our addition/subtraction, leaving us with 
Example Question #3 : Order Of Operations And Pemdas
Solve:
Using PEMDAS, we do the parenthetical bit first:
Now, we do multiplication and division:
Finally, subtract.
Example Question #1 : Real Numbers
This is a classic order of operations question, and if you are not careful, you can end up with the wrong answer!
Remember, the order of operations says that you have to go in the following order of operations: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction (also known as PEMDAS). In this equation, you will start with the parentheses. In the parentheses, we have
But within the parentheses, you still need to follow PEMDAS. First, we will solve the exponent, and the square of 2 is 4. Then, we'll divide 16 by 4, which gives us 4, so we can rewrite our original equation as
We can now divide 
The last step is to add and subtract the numbers above, paying careful attention to negative signs. In the end, we end up with 
Example Question #3 : Operations In Expressions
When evaluating the expression
in which order must you work the three operations?
Subtraction, addition, multiplication
Subtraction, multiplication, addition
Addition, subtraction, multiplication
Multiplication, addition, subtraction
Multiplication, subtraction, addition
Multiplication, subtraction, addition
By the order of operations, in the absence of grouping symbols, multplication must be worked before adding or subtracting. Then the addition and subtraction must be worked in left-to-right order; the subtraction is at left, so the subtraction is worked next, followed by the addition.
Example Question #4 : Operations In Expressions
When evaluating the expression
which of the five operations must be carried out third?
Division
Squaring
Addition
Subtraction
Multiplication
Squaring
By the order of operations, any operations within parentheses must be carried out first; there are two here, the addition and the subtraction. After this is done, the exponent, or squaring, must be worked before the other operations. Squaring, the third operation, is therefore the correct answer.
Example Question #3 : Order Of Operations And Pemdas
When evaluating the expression
in which order must you work the three operations?
Subtraction, multiplication, cubing
Subtraction, cubing, multiplication
Cubing, multiplication, subtraction
Cubing, subtraction, multiplication
Multiplication, cubing, subtraction
Cubing, multiplication, subtraction
By the order of operations, in the absence of grouping symbols, the exponent (represented here by cubing) must be worked first. The multiplication must be worked second, followed by the subtraction.
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