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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 #111 : Operations

Solve:

$4\cdot2+6-3+3\cdot2$

Possible Answers:

Correct answer:

Explanation:

To complete a problem with order of operations, follow the acronym PEMDAS to remember the order of completion. PEMDAS stands for:

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

For this problem, we do the multiplication before solving the addition and subtraction to get our final answer of 20:

$4\cdot2+6-3+3\cdot2$

$8+6-3+3\cdot2$

8+6-3+9

14-3+9

11+9=20

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Example Question #112 : Operations

Solve:

$32-6\cdot4+8-3\cdot3+17$

Possible Answers:

Correct answer:

Explanation:

To complete a problem with order of operations, follow the acronym PEMDAS to remember the order of completion. PEMDAS stands for:

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

For this problem, we do the multiplication before completing the addition and subtraction to get our final answer of 24:

$32-6\cdot4+8-3\cdot3+17$

$32-24+8-3\cdot3+17$

32-24+8-9+17

8+8-9+17

16-9+17

7+17=24

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Example Question #113 : Operations

Solve:

$2^{2}+6^{2}-5^{2}+3^{2}$

Possible Answers:

Correct answer:

Explanation:

To complete a problem with order of operations, follow the acronym PEMDAS to remember the order of completion. PEMDAS stands for:

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

For this problem, we solve each of the exponents before completing addition and subtraction to get our final answer of 34:

$2^{2}+6^{2}-5^{2}+3^{2}$

$4+6^{2}-5^{2}+3^{2}$

$4+36-5^{2}+3^{2}$

$4+36-25+3^{2}$

4+36-25+9

40-25+9

15+9=34

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Example Question #114 : Operations

Solve:

$4^{2}-6+2\cdot5-7$

Possible Answers:

Correct answer:

Explanation:

To complete a problem with order of operations, follow the acronym PEMDAS to remember the order of completion. PEMDAS stands for:

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

For this problem, we solve the exponent, the do the multiplication before completing addition and subtraction to get our final answer of 13:

$4^{2}-6+2\cdot5-7$

$16-6+2\cdot5-7$

16-6+10-7

10+10-7

20-7=13

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Example Question #115 : Operations

Solve:

$7^{2}-14+2-6\cdot3$

Possible Answers:

Correct answer:

Explanation:

To complete a problem with order of operations, follow the acronym PEMDAS to remember the order of completion. PEMDAS stands for:

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

For this problem, we solve the exponent then do the multiplication before completing addition and subtraction to get our final answer of 48:

$7^{2}-14+2-6\cdot3$

$49-14+2-6\cdot3$

49-14+2-18

35+2-18

37-18=19

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Example Question #116 : Operations

Solve:

$3^{2}\cdot4-9+27$

Possible Answers:

Correct answer:

Explanation:

To complete a problem with order of operations, follow the acronym PEMDAS to remember the order of completion. PEMDAS stands for:

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

For this problem, we solve the exponent then do the multiplication before completing addition and subtraction to get our final answer of 54:

$3^{2}\cdot4-9+27$

$9\cdot4-9+27$

36-9+27

27+27=54

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Example Question #117 : Operations

Solve:

$15^{2}-12^{2}+7$

Possible Answers:

112

Correct answer:

Explanation:

To complete a problem with order of operations, follow the acronym PEMDAS to remember the order of completion. PEMDAS stands for:

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

For this problem, we solve the exponents before completing addition and subtraction to get our final answer of 88:

$15^{2}-12^{2}+7$

$225-12^{2}+7$

225-144+7

81+7=88

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Example Question #118 : Operations

Solve:

$6\cdot2+(7-2\cdot 3+11)$

Possible Answers:

Correct answer:

Explanation:

To complete a problem with order of operations, follow the acronym PEMDAS to remember the order of completion. PEMDAS stands for:

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

For this problem, we need to solve what is inside the parentheses first. In order to do this, solve the multiplication before the addition and subtraction. Complete the multiplication outside the parentheses, then solve the addition between that answer and the answer from the parentheses to get a final answer of 24:

$6\cdot2+(7-2\cdot 3+11)$

$6\cdot2+(7-6+11)$

$6\cdot2+(1+11)$

$6\cdot2+12$

12+12=24

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Example Question #119 : Operations

Solve:

$(12-3)\cdot (5+6)$

Possible Answers:

Correct answer:

Explanation:

To complete a problem with order of operations, follow the acronym PEMDAS to remember the order of completion. PEMDAS stands for:

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

For this problem, we need to solve the inside of each set of parentheses first. Once we get these answers, multiply them together to get the final answer of 99:

$(12-3)\cdot (5+6)$

$9\cdot (5+6)$

$9\cdot11=99$

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Example Question #120 : Operations

Solve the following using the order of operations.

$8 \cdot 4 + 12 \div 6-(9-4)$

Possible Answers:

Correct answer:

Explanation:

The order of operations is the order in which you must solve problems. The order is

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

where you start with parentheses and follow the order until you reach subtraction. So we will follow the order for this problem

$8 \cdot 4 + 12 \div 6-(9-4)$

Parentheses

$8 \cdot 4 + 12 \div 6-5$

Multiplication

$32 + 12 \div 6-5$

Division

32 + 2-5

Addition

34-5

Subtraction

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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 #111 : Operations

Example Question #112 : Operations

Example Question #113 : Operations

Example Question #114 : Operations

Example Question #115 : Operations

Example Question #116 : Operations

Example Question #117 : Operations

Example Question #118 : Operations

Example Question #119 : Operations

Example Question #120 : Operations

All Pre-Algebra Resources

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