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ACT Math : Order of Operations

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Example Question #21 : Arithmetic

Simplify: $2-5(7-3^2)^3 \div 2$

Possible Answers:

Correct answer:

Explanation:

Using PEMDAS helps us solve our equation step-by-step:

$2-5(7-3^2)^3 \div 2$ State the equation.

$2-5(7-9)^3 \div 2$ Solve inside the parenthesis first.

$2-5(-2)^3 \div 2$ Simplify inside the parenthesis.

$2-5(-8) \div 2$ Solve the exponent.

$2+ 40 \div 2$ Multiply.

2+ 20 Divide.

Add.

Thus, our answer is .

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Example Question #21 : How To Find Order Of Operations

Three less than half of a certain number is more than twice the sum of another number and the cube of the first number.

Which of the expressions below represents this?

Possible Answers:

$\frac{x}{2}-3 < 2yx^3$

$-\frac{3}{2x} > 2y+ x^3$

$\frac{x}{2}-3 > 2y+ 2x^3$

$\frac{x}{2}-3 < 2(y+ x^3)$

$\frac{3x}{2} > 2(y+ x^3)$

Correct answer:

$\frac{x}{2}-3 > 2y+ 2x^3$

Explanation:

We know that the first half of this equation is three less than half of a number. So, we look for those equations which divide a variable by two, showing $\frac{x}{2}$ . Next, we know to subtract , so $\frac{x}{2} -3$ must be the first half. Lastly, we know that this amount is more than the other half of our equation, so we eliminate the answers with .

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Example Question #23 : Arithmetic

Which equation represents a quantity which, when squared, equals twice its own square root?

Possible Answers:

$\textup{None of these}$

$x^2 = 2\sqrt{x}$

$x^2 = \sqrt{x^2}$

$2x^2 = \sqrt{x}$

$x^2 = \sqrt{2x}$

Correct answer:

$x^2 = 2\sqrt{x}$

Explanation:

"Which equation represents a quantity which, when squared, equals twice its own square root?" To answer, square a variable on one side of an equation.

x^ 2 =

Now, square root the variable on the other side.

$x^2 = \sqrt{x}$

Lastly, multiply the square root by :

$x^2 = 2\sqrt{x}$

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Example Question #1091 : Act Math

Simplify:

6+7*2-5+3*2

Possible Answers:

Correct answer:

Explanation:

To solve, simply use PEMDAS to do the correct order of operations.

PEMDAS stands for,

Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.

Thus,

$6+7*2-5+3*2\rightarrow 6+14-5+6=20+1=21$

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Example Question #22 : Arithmetic

By how much does the value of 2x^2-2y exceed the value of 2x^2-2y^2 when x=4 and y=3?

Possible Answers:

Correct answer:

Explanation:

This problem requires proper order of operations. Remember the acronym for the order of operations: PEMDAS. This acronym will help you to remember the proper order for solving problems:

Parentheses
Exponents
Multiplication and Division (whichever comes first as you read the problem from left to right)
Addition and Subtraction (whichever comes first as you read the problem from left to right)

Let's start with the first expression:

2x^2 - 2y

Substitute in our values for the x- and y-variables.

$2(4^2) - 2\times3$

Step 1: Since there are no parentheses we will start with exponents.

$2(16) - 2\times3$

Step 2: Multiplication

$2\times16 - 2\times3$

32 - 6

Step 3: Subtraction

32-6=26

For the second expression, we will proceed in a similar fashion. Let's start with the first expression:

2x^2-2y^2

Substitute in our values for the x- and y-variables.

2(4^2)-2(3^2)

Step 1: Since there are no parentheses we will start with exponents.

2(16)-2(9)

Step 2: Multiplication

$2\times 16-2\times9$

32-18

Step 3: Subtraction

32-18=14

Last, the difference between the first expression and the second is as follows:

26 -14 = 12

The correct choice is

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ACT Math : Order of Operations

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #21 : Arithmetic

Example Question #21 : How To Find Order Of Operations

Example Question #23 : Arithmetic

Example Question #1091 : Act Math

Example Question #22 : Arithmetic

All ACT Math Resources

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