Pre-Algebra : Operations and Properties

Study concepts, example questions & explanations for Pre-Algebra

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Example Questions

Example Question #1121 : Pre Algebra

Solve:

\displaystyle 4\cdot2+6-3+3\cdot2

Possible Answers:

\displaystyle 20

\displaystyle 16

\displaystyle 4

\displaystyle 28

Correct answer:

\displaystyle 20

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:

\displaystyle 4\cdot2+6-3+3\cdot2

\displaystyle 8+6-3+3\cdot2

\displaystyle 8+6-3+9

\displaystyle 14-3+9

\displaystyle 11+9=20

Example Question #1122 : Pre Algebra

Solve:

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

Possible Answers:

\displaystyle 14

\displaystyle 25

\displaystyle 36

\displaystyle 24

Correct answer:

\displaystyle 24

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:

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

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

\displaystyle 32-24+8-9+17

\displaystyle 8+8-9+17

\displaystyle 16-9+17

\displaystyle 7+17=24

Example Question #111 : Operations

Solve:

\displaystyle 2^{2}+6^{2}-5^{2}+3^{2}

Possible Answers:

\displaystyle 34

\displaystyle 36

\displaystyle 19

\displaystyle 26

Correct answer:

\displaystyle 34

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:

\displaystyle 2^{2}+6^{2}-5^{2}+3^{2}

\displaystyle 4+6^{2}-5^{2}+3^{2}

\displaystyle 4+36-5^{2}+3^{2}

\displaystyle 4+36-25+3^{2}

\displaystyle 4+36-25+9

\displaystyle 40-25+9

\displaystyle 15+9=34

Example Question #1123 : Pre Algebra

Solve:

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

Possible Answers:

\displaystyle 25

\displaystyle 13

\displaystyle 12

\displaystyle 33

Correct answer:

\displaystyle 13

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:

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

\displaystyle 16-6+2\cdot5-7

\displaystyle 16-6+10-7

\displaystyle 10+10-7

\displaystyle 20-7=13

Example Question #1124 : Pre Algebra

Solve:

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

Possible Answers:

\displaystyle 19

\displaystyle 42

\displaystyle 35

\displaystyle 21

Correct answer:

\displaystyle 19

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:

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

\displaystyle 49-14+2-6\cdot3

\displaystyle 49-14+2-18

\displaystyle 35+2-18

\displaystyle 37-18=19

Example Question #1125 : Pre Algebra

Solve:

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

Possible Answers:

\displaystyle 54

\displaystyle 27

\displaystyle 30

\displaystyle 34

Correct answer:

\displaystyle 54

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:

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

\displaystyle 9\cdot4-9+27

\displaystyle 36-9+27

\displaystyle 27+27=54

Example Question #1131 : Pre Algebra

Solve:

\displaystyle 15^{2}-12^{2}+7

Possible Answers:

\displaystyle 88

\displaystyle 81

\displaystyle 75

\displaystyle 112

Correct answer:

\displaystyle 88

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:

\displaystyle 15^{2}-12^{2}+7

\displaystyle 225-12^{2}+7

\displaystyle 225-144+7

\displaystyle 81+7=88

Example Question #1132 : Pre Algebra

Solve:

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

Possible Answers:

\displaystyle 12

\displaystyle 38

\displaystyle 34

\displaystyle 24

Correct answer:

\displaystyle 24

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:

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

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

\displaystyle 6\cdot2+(1+11)

\displaystyle 6\cdot2+12

\displaystyle 12+12=24

Example Question #1133 : Pre Algebra

Solve:

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

Possible Answers:

\displaystyle 99

\displaystyle 2

\displaystyle 20

\displaystyle 11

Correct answer:

\displaystyle 99

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:

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

\displaystyle 9\cdot (5+6)

\displaystyle 9\cdot11=99

Example Question #111 : Operations And Properties

Solve the following using the order of operations.

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

Possible Answers:

\displaystyle 2

\displaystyle 39

\displaystyle 44

\displaystyle 25

\displaystyle 29

Correct answer:

\displaystyle 29

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

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

Parentheses

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

Multiplication

\displaystyle 32 + 12 \div 6-5

Division

\displaystyle 32 + 2-5

Addition

\displaystyle 34-5

Subtraction

\displaystyle 29

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