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Pre-Algebra : Order of Operations

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Example Questions

Example Question #101 : Operations And Properties

Solve:

$6-4+4\cdot7\div2$ $\displaystyle 6-4+4\cdot7\div2$

Possible Answers:

$\displaystyle 12$

$\displaystyle 8$

$\displaystyle 0$

$\displaystyle 16$

Correct answer:

$\displaystyle 16$

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/division before addition/subtraction to get our final answer of 16:

$6-4+4\cdot7\div2$ $\displaystyle 6-4+4\cdot7\div2$

$6-4+28\div2$ $\displaystyle 6-4+28\div2$

6-4+14 $\displaystyle 6-4+14$

2+14=16 $\displaystyle 2+14=16$

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Example Question #101 : Order Of Operations

Solve:

$26-14+(2^{3}+6-12)$ $\displaystyle 26-14+(2^{3}+6-12)$

Possible Answers:

$\displaystyle 12$

$\displaystyle 26$

$\displaystyle 49$

$\displaystyle 14$

Correct answer:

$\displaystyle 14$

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 parentheses first. Inside the parentheses solve the exponent before doing addition and subtraction. Once the parentheses are solved complete the addition and subtraction to get a final answer of 14:

$26-14+(2^{3}+6-12)$ $\displaystyle 26-14+(2^{3}+6-12)$

$\displaystyle 26-14+(8+6-12)$

$\displaystyle 26-14+(14-12)$

26-14+2 $\displaystyle 26-14+2$

12+2=14 $\displaystyle 12+2=14$

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Example Question #103 : Order Of Operations

Solve:

$3^{2}-4+5^{2}+2-15$ $\displaystyle 3^{2}-4+5^{2}+2-15$

Possible Answers:

$\displaystyle 37$

$\displaystyle 17$

$\displaystyle 42$

$\displaystyle 15$

Correct answer:

$\displaystyle 17$

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 doing addition and subtraction to get a final answer of 17:

$3^{2}-4+5^{2}+2-15$ $\displaystyle 3^{2}-4+5^{2}+2-15$

$\displaystyle 9-4+25+2-15$

$\displaystyle 5+25+2-15$

30+2-15 $\displaystyle 30+2-15$

$\displaystyle 32-15=17$

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Example Question #101 : Operations And Properties

Solve:

$12-5+6\cdot4$ $\displaystyle 12-5+6\cdot4$

Possible Answers:

$\displaystyle 31$

$\displaystyle 34$

$\displaystyle 27$

$\displaystyle 41$

Correct answer:

$\displaystyle 31$

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 addition/subtraction to get our final answer of 31:

$12-5+6\cdot4$ $\displaystyle 12-5+6\cdot4$

12-5+24 $\displaystyle 12-5+24$

7+24=31 $\displaystyle 7+24=31$

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Example Question #105 : Order Of Operations

Solve:

$3\cdot2+7-4+4\cdot9$ $\displaystyle 3\cdot2+7-4+4\cdot9$

Possible Answers:

$\displaystyle 35$

$\displaystyle 74$

$\displaystyle 41$

$\displaystyle 45$

Correct answer:

$\displaystyle 45$

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 multiplicationbefore addition/subtraction to get our final answer of 45:

$3\cdot2+7-4+4\cdot9$ $\displaystyle 3\cdot2+7-4+4\cdot9$

$6+7-4+4\cdot9$ $\displaystyle 6+7-4+4\cdot9$

$\displaystyle 6+7-4+36$

13-4+36 $\displaystyle 13-4+36$

9+36=45 $\displaystyle 9+36=45$

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Example Question #106 : Order Of Operations

Solve:

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

Possible Answers:

$\displaystyle 35$

$\displaystyle 15$

$\displaystyle 3$

$\displaystyle 5$

Correct answer:

$\displaystyle 3$

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/subtraction to get our final answer of 3:

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

$\displaystyle 16+9-25+3$

25-25+3 $\displaystyle 25-25+3$

0+3=3 $\displaystyle 0+3=3$

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Example Question #107 : Order Of Operations

Solve:

$12-2\cdot6+4\cdot5-6$ $\displaystyle 12-2\cdot6+4\cdot5-6$

Possible Answers:

$\displaystyle 14$

$\displaystyle 24$

$\displaystyle 56$

$\displaystyle 74$

Correct answer:

$\displaystyle 14$

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 addition/subtraction to get our final answer of 48:

$12-2\cdot6+4\cdot5-6$ $\displaystyle 12-2\cdot6+4\cdot5-6$

$12-12+4\cdot5-6$ $\displaystyle 12-12+4\cdot5-6$

$\displaystyle 12-12+20-6$

0+20-6 $\displaystyle 0+20-6$

20-6=14 $\displaystyle 20-6=14$

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Example Question #108 : Order Of Operations

Solve:

$2\cdot6-4\div2+5$ $\displaystyle 2\cdot6-4\div2+5$

Possible Answers:

$\displaystyle 15$

$\displaystyle 9$

$\displaystyle 17$

$\displaystyle 25$

Correct answer:

$\displaystyle 15$

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 and division before addition and subtraction to get our final answer of 15:

$2\cdot6-4\div2+5$ $\displaystyle 2\cdot6-4\div2+5$

$12-4\div2+5$ $\displaystyle 12-4\div2+5$

12-2+5 $\displaystyle 12-2+5$

10+5=15 $\displaystyle 10+5=15$

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Example Question #109 : Order Of Operations

Solve:

$25+2\cdot6+(7-2\cdot 3)$ $\displaystyle 25+2\cdot6+(7-2\cdot 3)$

Possible Answers:

$\displaystyle 52$

$\displaystyle 57$

$\displaystyle 38$

$\displaystyle 46$

Correct answer:

$\displaystyle 38$

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 math inside the parentheses, then multiplication before addition to get our final answer of 38:

$25+2\cdot6+(7-2\cdot 3)$ $\displaystyle 25+2\cdot6+(7-2\cdot 3)$

$25+2\cdot6+(7-6)$ $\displaystyle 25+2\cdot6+(7-6)$

$25+2\cdot6+1$ $\displaystyle 25+2\cdot6+1$

$\displaystyle 25+12+1=38$

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Example Question #110 : Order Of Operations

Solve:

$17-2+(6\cdot (2+3))-4^{2}$ $\displaystyle 17-2+(6\cdot (2+3))-4^{2}$

Possible Answers:

$\displaystyle 46$

$\displaystyle 27$

$\displaystyle 35$

$\displaystyle 29$

Correct answer:

$\displaystyle 29$

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 parentheses before anything else. Since there are two sets of them, solve the innermost set of parentheses first. After completing the parentheses, solve the exponents before doing the addition and subtraction to get our final answer of 29:

$17-2+(6\cdot (2+3))-4^{2}$ $\displaystyle 17-2+(6\cdot (2+3))-4^{2}$

$17-2+(6\cdot 5)-4^{2}$ $\displaystyle 17-2+(6\cdot 5)-4^{2}$

$17-2+30-4^{2}$ $\displaystyle 17-2+30-4^{2}$

$\displaystyle 17-2+30-16$

$\displaystyle 15+30-16$

$\displaystyle 45-16=29$

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Pre-Algebra : Order of Operations

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #101 : Operations And Properties

Example Question #101 : Order Of Operations

Example Question #103 : Order Of Operations

Example Question #101 : Operations And Properties

Example Question #105 : Order Of Operations

Example Question #106 : Order Of Operations

Example Question #107 : Order Of Operations

Example Question #108 : Order Of Operations

Example Question #109 : Order Of Operations

Example Question #110 : Order Of Operations

All Pre-Algebra Resources

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