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SAT Math : Order of Operations

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Example Questions

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Example Question #51 : How To Find Order Of Operations

Solve:

6-4(2*4)+6

Possible Answers:

Correct answer:

Explanation:

In PEMDAS, we apply parentheses first, followed by multiplication and finally subtraction and addition from left to right.

Therefore,

6-4(2*4)+6

=6-4*8+6

=6-32+6

=-26+6

=-20

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Example Question #52 : How To Find Order Of Operations

Solve:

(9-7)2+4*3(2-4)^2

Possible Answers:

Correct answer:

Explanation:

In PEMDAS, parentheses from left to right, followed by exponents, multiplication from left to right, and finally addition.

Therefore,

(9-7)2+4*3(2-4)^2

=2*2+4*3(-2)^2

=4+4*3*4

=4+48

=52

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Example Question #51 : How To Find Order Of Operations

Solve:

4^2+(8-3*3)

Possible Answers:

Correct answer:

Explanation:

In PEMDAS, parentheses is applied with multiplication first followed by subtraction and finally do the exponents and addition.

Therefore,

4^2+(8-3*3)

=16+(8-9)

=16+(-1)

=16-1

=15

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Example Question #51 : Order Of Operations

Solve:

7+2^3(4-8)

Possible Answers:

Correct answer:

Explanation:

In PEMDAS, the exponent is applied first, followed by parentheses, then multiplication and lastly addition.

Therefore,

7+2^3(4-8)

=7+8*-4

=7+(-32)

=-25

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Example Question #51 : Arithmetic

If x=-2 and y=4 , then what is xy(y^2-x) ?

Possible Answers:

Correct answer:

Explanation:

xy(y^2-x) Apply substitution.

(-2*4)(4^2-(-2))

=-8*18

=-144

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Example Question #56 : How To Find Order Of Operations

If x=3 and y=-4 , then what is x^2-xy+y^2 ?

Possible Answers:

Correct answer:

Explanation:

x^2-xy+y^2 Apply substitution.

=3^2-3(-4)+4^2

=9+12+16

=37

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Example Question #51 : How To Find Order Of Operations

Consider the expression

$A \cdot (B + C) \div D^{2} - E$

If the values of all of the variables are known, which operation is carried out third?

Possible Answers:

Multiplication

Squaring

Addition

Division

Subtraction

Correct answer:

Multiplication

Explanation:

The order of operations dictates that any operations within grouping symbols, such as parentheses, be carried out first; in this expression, this is the addition.

This leaves a multiplication, a division, an exponentiation (squaring), and a subtraction. The squaring takes precedence over the others, so it is carried out second. Multiplication and division take precedence over subtraction; since the multiplication is first in left-to-right order, it is carried out third. This makes multiplication the correct response.

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Example Question #52 : How To Find Order Of Operations

Consider the expression

$A \cdot [ (B + C)^{2} \div D - E]$

If the values of all of the variables are known, which operation is carried out third?

Possible Answers:

Multiplication

Addition

Subtraction

Squaring

Division

Correct answer:

Division

Explanation:

The order of operations dictates that any operations within grouping symbols is carried out first, going from the innermost symbols to the outermost symbols. The innermost symbols - the parentheses - flank an addition, so that operation is carried out first.

The operations between the outermost symbols - the brackets - are carried out next. There is an exponentiation (squaring), a division, and a subtraction there; by order of operations, the squaring is carried out next, and the division after that. Division is therefore the correct response.

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Example Question #53 : How To Find Order Of Operations

Consider the expression

$A \cdot (B + C^{2}) \div D - E$

If the values of all of the variables are known, which operation is carried out third?

Possible Answers:

Multiplication

Squaring

Division

Addition

Subtraction

Correct answer:

Multiplication

Explanation:

The order of operations dictates that any operations within grouping symbols, such as parentheses, be carried out first; in this expression. There are two expressions - an exponentiation (squaring) and an addition - that fall between the parentheses; by the order of operations, the squaring is carried out, then the addition.

This leaves a multiplication, a division, and a subtraction. Multiplication and division have precedence over subtraction; since the multiplication appears first in left-to-right order, the multiplication is carried out next. This makes multiplication the correct response.

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Example Question #54 : How To Find Order Of Operations

Consider the expression

$A \cdot B + C ^{2} \div D - E$

If the values of all of the variables are known, which operation is carried out third?

Possible Answers:

Division

Addition

Multiplication

Subtraction

Squaring

Correct answer:

Division

Explanation:

The order of operations dictates that the exponentiation (squaring) be carried out first. The multiplication and the division come next, in left-to-right order; since the multiplication appears to the left, this is worked first, followed by the division. Division is the correct response.

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SAT Math : Order of Operations

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #51 : How To Find Order Of Operations

Example Question #52 : How To Find Order Of Operations

Example Question #51 : How To Find Order Of Operations

Example Question #51 : Order Of Operations

Example Question #51 : Arithmetic

Example Question #56 : How To Find Order Of Operations

Example Question #51 : How To Find Order Of Operations

Example Question #52 : How To Find Order Of Operations

Example Question #53 : How To Find Order Of Operations

Example Question #54 : How To Find Order Of Operations

All SAT Math Resources

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