SAT Math : Arithmetic

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #31 : Arithmetic

Possible Answers:

Correct answer:

Explanation:

There is multiplication and addition present. Remember PEMDAS. Multiplication comes first followed by addition. 

Example Question #31 : Arithmetic

When evaluating the expression

what is the third operation that should be performed?

Possible Answers:

Division

Addition

Cubing

Subtraction

Multiplication 

Correct answer:

Multiplication 

Explanation:

The order of operations is:

Exponents

Multiplication and division (left to right)

Addition and subtraction (left to right)

The first operation to be performed is the exponent (the cubing). The next two operations to be performed are the multiplication and the division; since the division is first when read left to right, this is performed second, and the multiplication is performed third.

Example Question #32 : Arithmetic

Consider the expression:

.

Suppose you know the value of each of the four variables. In which order do you work the operations in the expression?

Possible Answers:

Square, multiply, divide, add

Square, multiply, add, divide

Multiply, square, divide, add

Multiply, divide, square, add

Multiply, square, add, divide

Correct answer:

Square, multiply, divide, add

Explanation:

The order of operations is as follows:

Exponents

Multiplication and division (left to right)

Addition and subtraction (left to right)

The expression has an exponentiation - a squaring - so this is done first. It also has a multiplication and a division - the multiplication is to the left, so it is done next, followed by the division. This leaves the addition for last.

Example Question #32 : Order Of Operations

Consider the expression:

.

Suppose you know the value of each of the four variables. In which order do you work the operations in the expression?

Possible Answers:

Add, multiply, square, divide

Add, square, multiply, divide

Square, add, multiply, divide

Multiply, square, add, divide

Multiply, add, square, divide

Correct answer:

Add, square, multiply, divide

Explanation:

Any operation within parentheses is always done first - here, this is the addition.

Outside of this, the order of operations is as follows:

Exponents

Multiplication and division (left to right)

Addition and subtraction (left to right)

The expression has an exponentiation - a squaring - so this is done second. It also has a multiplication and a division - the multiplication is to the left, so it is done third, followed, finally, by the division. 

Example Question #32 : How To Find Order Of Operations

Consider the expression:

.

Suppose you know the value of each of the four variables. In which order do you work the operations in the expression?

Possible Answers:

Divide, add, square, multiply

Multiply, divide, add, square

Multiply, add, divide, square

Square, divide, multiply, add

Add, divide, square, multiply

Correct answer:

Divide, add, square, multiply

Explanation:

Any operation within parentheses is always done first. However, here, there are two operations within the parentheses, addition and division.

The order of operations is:

Exponents

Multiplication and division (left to right)

Addition and subtraction (left to right)

Therefore, the division is worked first, then the addition.

This leaves the exponentiation - here, a squaring - and a multiplication. By the above order, the squaring is worked third, then, finally, the multiplication.

Example Question #32 : Arithmetic

When evaluating the expression

what is the last operation that should be performed?

Possible Answers:

Addition

Cubing

Subtraction

Multiplication

Division

Correct answer:

Addition

Explanation:

The order of operations is:

Exponents

Multiplication and division (left to right)

Addition and subtraction (left to right)

Since there are no grouping symbols, and one of each operation, the addition and the subtraction will be the last two operations performed. When read left to right, the subtraction comes first, so the addition will be the last operation performed.

Example Question #33 : How To Find Order Of Operations

When evaluating the expression

what is the third operation that should be performed?

Possible Answers:

Division

Cubing

Multiplication

Addition

Subtraction

Correct answer:

Cubing

Explanation:

The order of operations states that the expressions in the parentheses must be evaluated first. the first two operations performed will be the division and the addition. This leaves the cubing - an exponentiation - the subtraction, and the multiplication. 

After grouping symbols, the order of operations is:

Exponents

Multiplication and division (left to right)

Addition and subtraction (left to right)

The cubing will be performed next - and third overall.

Example Question #33 : Order Of Operations

Solve:  

Possible Answers:

Correct answer:

Explanation:

To evaluate this expression, first simplify the quantity inside the parentheses and the exponent by order of operations.

Rewrite the expression.

Simplify the double negative.  It will turn into a positive sign.

The answer is:  

Example Question #33 : Arithmetic

Solve: 

Possible Answers:

Correct answer:

Explanation:

Following the order of operations, we can simplify this expression.

Recall the order of operations:

PEMDAS

Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. Perform these operations from left to right.

Example Question #35 : Order Of Operations

Evaluate the expression and solve for x:

Possible Answers:

Correct answer:

Explanation:

In order to find the solutions for x, you first need to simplify the equation and properly use the order of operations. The order of operations is PEMDAS- Parentheses, Exponents, Multiplication/Division, Addition/Subtraction. 

In this equation: 

you have to do first which equals 

Secondly, 

You are left with , this simplifies to 

 

After you have simplified the equation, you can factor the equation.

Therefore the solutions are  

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