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Pre-Algebra : Operations and Properties

Study concepts, example questions & explanations for Pre-Algebra

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11 Diagnostic Tests 177 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #11 : Order Of Operations

Simplify:

2^3-[4(2+1-2+4-3)]+4(1+2-5)

Possible Answers:

Correct answer:

Explanation:

Follow the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. Work from left to right, and start with the innermost nested operations when dealing with multiple parentheses:

2^3-[4(2+1-2+4-3)]+4(1+2-5)

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

=8-[8]+(-8)

=-8

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Example Question #11 : Operations

Simplify:

3^3+2(2^3-4)+2(-1+2-3)

Possible Answers:

Correct answer:

Explanation:

3^3+2(2^3-4)+2(-1+2-3)

=3^3+2(8-4)+2(-2)

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

=27+8+(-4)

=31

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Example Question #12 : Operations

Simplify:

3^2(2^2-4+3)-[5(3+1-2+6-5)]

Possible Answers:

Correct answer:

Explanation:

3^2(2^2-4+3)-[5(3+1-2+6-5)]

=3^2(4-4+3)-[5(3)]

=3^2(3)-[15]

=9(3)-15

=27-15

=12

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Example Question #13 : Operations

Simplify:

$3^3[2-(-4)]+2^4-6+3^{(4-2)}$

Possible Answers:

181

Correct answer:

181

Explanation:

$3^3[2-(-4)]+2^4-6+3^{(4-2)}$

$=3^3[6]+2^4-6+3^{(2)}$

=27[6]+16-6+9

=162+16-6+9

=181

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Example Question #14 : Operations

Simplify:

2^4-2[4-(-5)]+7(2+1-4)

Possible Answers:

Correct answer:

Explanation:

2^4-2[4-(-5)]+7(2+1-4)

=2^4-2[9]+7(-1)

=16-[18]+(-7)

=-9

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Example Question #15 : Operations

Simplify:

$2^3(2-3)+3^{[2(1+3-2-1)]}-3[2-(-2)]$

Possible Answers:

Correct answer:

Explanation:

$2^3(2-3)+3^{[2(1+3-2-1)]}-3[2-(-2)]$

$=2^3(-1)+3^{[2(1)]}-3[4]$

$=8(-1)+3^{2}-12$

=(-8)+9-12

=-11

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Example Question #16 : Operations

$3-7\ast8+4\div2=?$

Possible Answers:

Correct answer:

Explanation:

Remember the order of operations: "PEMDAS” or "Please Excuse My Dear Aunt Sally" stands for "Parentheses, Exponents, Multiplication and Division, Addition and Subtraction".

$3-7\ast8+4\div2=?$

$3-\left (7\ast8 \right )\left +(4\div2 \right )=$

3-56+2=

-53+2=-51

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Example Question #17 : Operations

Simplify:

$6-(2+5^{2})$

Possible Answers:

Correct answer:

Explanation:

Follow the order of operations.

First take care of any exponents:

$6-(2+5^{2})$

= 6 - (2 + 25)

Then perform the operations in parentheses:

= 6 - 27

= -21

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Example Question #19 : Order Of Operations

Simplify:

$2^{^{2}}+8\div(2*4)$

Possible Answers:

$\frac{4}{3}$

Correct answer:

Explanation:

By order of operations you are supposed to simplify what is in parentheses first giving you

$2^{2}+8\div8$

then you must simplify the exponent to give you

$4+8\div8$

then you must simplify the division portion of the equation to get

4+1

then simplify this.

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Example Question #18 : Operations

$0.5(8-4)^{2}\cdot (-1+2)-9+1$

Possible Answers:

Correct answer:

Explanation:

Remember the acronym PEMDAS to help you keep track of the order of operations:

Parentheses
Exponents
Multiplication and Division (whichever comes first when reading the problem from left to right)
Addition and Subtraction (whichever comes first when reading the problem from left to right)

Step 1: Parentheses

$0.5(8-4)^{2}\cdot (-1+2)-9+1=0.5 (4)^{2}\cdot(1)-9+1$

Step 2: Exponents

$0.5(4\cdot 4)\cdot(1)-9+1=0.5(16)\cdot(1)-9+1$

Step 3: Multiplication

$8\cdot1-9+1=8-9+1$

Step 4: Addition and Subtraction

8-9+1=-1+1=0

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Pre-Algebra : Operations and Properties

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #11 : Order Of Operations

Example Question #11 : Operations

Example Question #12 : Operations

Example Question #13 : Operations

Example Question #14 : Operations

Example Question #15 : Operations

Example Question #16 : Operations

Example Question #17 : Operations

Example Question #19 : Order Of Operations

Example Question #18 : Operations

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