Basic Arithmetic : Operations in Expressions

Study concepts, example questions & explanations for Basic Arithmetic

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Example Questions

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Example Question #1 : Order Of Operations And Pemdas

Solve:

Possible Answers:

Correct answer:

Explanation:

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:

Possible Answers:

Correct answer:

Explanation:

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. 

 and 

Therefore the following happens:

Then add and subtract.

Example Question #1 : Operations In Expressions

Possible Answers:

Correct answer:

Explanation:

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 #1 : Order Of Operations And Pemdas

Simplify

Possible Answers:

Correct answer:

Explanation:

We start with what is inside the parentheses, so  becomes .

Next, we take care of any exponents, giving us .

Next, we take care of multiplication/division, giving us  or .

Finally, we carry out our addition/subtraction, leaving us with .

Example Question #1 : Order Of Operations And Pemdas

Solve:

Possible Answers:

Correct answer:

Explanation:

Using PEMDAS, we do the parenthetical bit first:

Now, we do multiplication and division:

Finally, subtract.

Example Question #2 : Order Of Operations And Pemdas

Possible Answers:

Correct answer:

Explanation:

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  into , which gives us

The last step is to add and subtract the numbers above, paying careful attention to negative signs.  In the end, we end up with  because  added to  equals , and  minus  equals

Example Question #1 : Operations In Expressions

When evaluating the expression 

,

in which order must you work the three operations?

Possible Answers:

Subtraction, multiplication, addition

Subtraction, addition, multiplication

Multiplication, subtraction, addition

Multiplication, addition, subtraction

Addition, subtraction, multiplication 

Correct answer:

Multiplication, subtraction, addition

Explanation:

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 #1 : Order Of Operations And Pemdas

When evaluating the expression 

,

which of the five operations must be carried out third?

Possible Answers:

Multiplication

Division

Squaring

Addition

Subtraction

Correct answer:

Squaring

Explanation:

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 #2 : Order Of Operations And Pemdas

When evaluating the expression 

,

in which order must you work the three operations?

Possible Answers:

Cubing, subtraction, multiplication

Subtraction, cubing, multiplication

Multiplication, cubing, subtraction

Subtraction, multiplication, cubing

Cubing, multiplication, subtraction

Correct answer:

Cubing, multiplication, subtraction

Explanation:

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.

Example Question #1 : Operations In Expressions

Simplify:

Possible Answers:

Correct answer:

Explanation:

When dividing terms with the same bases, remember to subtract the exponents.

Keep in mind that when there is a negative exponent in the numerator, putting that term in the denominator will make the exponent positive.

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