Pre-Algebra : Operations and Properties

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #41 : Order Of Operations

Evaluate

\displaystyle 4+6\div2

Possible Answers:

\displaystyle 4

\displaystyle 5

\displaystyle 6

\displaystyle 8

\displaystyle 7

Correct answer:

\displaystyle 7

Explanation:

When doing multiple operations, always remember PEMDAS. There is division and addition. D comes first and is the division so we do that first followed by addition. So we have \displaystyle 4+6\div2=4+3=7

Example Question #42 : Order Of Operations

Evaluate

\displaystyle (3*4)\div(2*6)

Possible Answers:

\displaystyle 36

\displaystyle 6

\displaystyle 12

\displaystyle 1

\displaystyle 24

Correct answer:

\displaystyle 1

Explanation:

When doing multiple operations, always remember PEMDAS. There is division and multiplication but parantheses present. P is parantheses and always has priority over every operation. So let's work the math inside the parantheses. So we have \displaystyle (4*3)\div (6*2)=12\div12=1

Example Question #43 : Order Of Operations

Evaluate

\displaystyle 68\div17-9\div3

Possible Answers:

\displaystyle 2.83

\displaystyle 7

\displaystyle 3.17

\displaystyle 2.67

\displaystyle 1

Correct answer:

\displaystyle 1

Explanation:

When doing multiple operations, always remember PEMDAS. There is division and subtraction. D is division and has priority over subtraction.  So we have \displaystyle 68\div17-9\div3=4-3=1

Example Question #44 : Order Of Operations

Evaluate

\displaystyle 7^2-12

Possible Answers:

\displaystyle 49

\displaystyle 35

\displaystyle -5

\displaystyle 37

\displaystyle 2

Correct answer:

\displaystyle 37

Explanation:

When doing multiple operations, always remember PEMDAS. There is exponents and subtraction. E is exponents and has priority over subtraction.  So we have \displaystyle 7^2-12=49-12=37

Example Question #45 : Order Of Operations

Evaluate

\displaystyle 6-5(4^2+3)

Possible Answers:

\displaystyle 49

\displaystyle -69

\displaystyle 19

\displaystyle -29

\displaystyle -89

Correct answer:

\displaystyle -89

Explanation:

When doing multiple operations, always remember PEMDAS. There is parentheses, exponents, multiplication, addition, and subtraction. We will work the parentheses first, follow by exponent thenaddition, then multiplication, and finally subtraction.  So we have \displaystyle 6-5(4^2+3)=6-5(16+3)=6-5(19)=6-95=-89

Example Question #46 : Order Of Operations

Evaluate

\displaystyle 5+(3*4^2-3)

Possible Answers:

\displaystyle 24

\displaystyle 34

\displaystyle 50

\displaystyle 44

\displaystyle 125

Correct answer:

\displaystyle 50

Explanation:

When doing multiple operations, always remember PEMDAS. There are parantheses, exponents, multiplication, addition and subtraction. We will do the parantheses first, then exponents, then multiplication, addition and last subtraction.  So we have \displaystyle 5+(3*4^2-3)=5+(3*16-3)=5+(48-3)=5+45=50

Example Question #47 : Order Of Operations

Evaluate.

\displaystyle 3+4-5

Possible Answers:

\displaystyle -1

\displaystyle -2

\displaystyle 7

\displaystyle 2

\displaystyle 8

Correct answer:

\displaystyle 2

Explanation:

When doing multiple operations, always remember PEMDAS. There is addition and subtraction and they are grouped together as last priority. So we just do the operations from left to right. \displaystyle 3+4=7

\displaystyle 7-5=2. Answer is \displaystyle 2

Example Question #48 : Order Of Operations

Evaluate

\displaystyle 3*4\div2*6

Possible Answers:

\displaystyle 36

\displaystyle 1

\displaystyle 6

\displaystyle 24

\displaystyle 12

Correct answer:

\displaystyle 36

Explanation:

When doing multiple operations, always remember PEMDAS. There is division and multiplication. They are grouped together is third priority. So must work from left to right.

\displaystyle 3\ast4=12

\displaystyle 12\div2=6

\displaystyle 6\ast6=36

The answer is \displaystyle 36

Example Question #49 : Order Of Operations

Evaluate

\displaystyle (4+5)3+7

Possible Answers:

\displaystyle 90

\displaystyle 34

\displaystyle 25

\displaystyle 19

\displaystyle 26

Correct answer:

\displaystyle 34

Explanation:

When doing multiple operations, always remember PEMDAS. There is addition and multiplication but parantheses present. There is multiplication because the \displaystyle 3 connected to the parantheses represents multiplying in which the sign doesn't need to be present. It is meant to be distributed. P is parantheses and always has priority over every operation. So let's work the math inside the parantheses. So we have \displaystyle (4+5)3+7=(9)3+7=27+7=34

Example Question #50 : Order Of Operations

Evaluate

\displaystyle 4(3^2-7)\div2*17

Possible Answers:

\displaystyle 32

\displaystyle 17

\displaystyle 68

\displaystyle \frac{4}{17}

\displaystyle \frac{8}{17}

Correct answer:

\displaystyle 68

Explanation:

When doing multiple operations, always remember PEMDAS. We have parenthesis, exponents, multplication, and division. We will do the parenthesis first followed by exponents and multiply and divide from left to right. So we have \displaystyle 4(3^2-7)\div2*17=4(9-7)\div 2*17=4(2)\div 2\ast 17=8\div2*17=4*17=68

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