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Pre-Algebra : Order of Operations

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Example Questions

Example Question #91 : Operations

Evaluate:

$2-2\times 3+5$

Possible Answers:

Correct answer:

Explanation:

Recall the order of operations, PEMDAS, which stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.

From the concept of order of operations, we would evaluate terms in multiplication first since there are no parentheses or exponents.

$2-2\times 3+5 = 2-(2\times 3)+5$

Once we multiply two and three together, add and subtract values starting from the left, working your way to the right.

2-6+5 = 1

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Example Question #92 : Operations

Solve: $10-10\times 2-2$

Possible Answers:

Correct answer:

Explanation:

Recall the order of operations to solve this problem.

PEMDAS stands for the order in which to solve an expression. First do whatever is inside of parentheses, then apply the exponents. Next, perform the multiplication and division and lastly do any addition and subtraction from left to right.

Evalute this by first applying the order of operations.

Multiply the second and the third terms first.

$10-(10\times 2)-2 = 10-20-2$

Subtract.

10-20-2=-12

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Example Question #93 : Operations

Solve:

$4-4\times7+12\div4$

Possible Answers:

$-\frac{16}{3}$

Correct answer:

Explanation:

Use the order of operations to solve. Evaluate the parentheses, exponents, multiplication, division, addition, and subtraction in chronological order.

This is known as PEMDAS.

$\\4-(4\times7)+(12\div4) \\= 4-28+3$

Solve by adding and subtracting the values from left to right.

4-28+3 = -21

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Example Question #94 : Operations

Solve: $\frac{3}{2}-\frac{3}{2}(2-3)$

Possible Answers:

$-\frac{3}{2}$

$\frac{3}{2}$

Correct answer:

Explanation:

Evaluate this by order of operations. Solve the parentheses first.

$\frac{3}{2}-\frac{3}{2}(2-3) = \frac{3}{2}-\frac{3}{2}(-1)$

Eliminate the parentheses by multiplying the fraction and the whole number. Remember that multiplying two negative numbers will result in a positive number.

$\frac{3}{2}-\frac{3}{2}(-1) = \frac{3}{2}+\frac{3}{2}$

Add the two fractions.

$\frac{3}{2}+\frac{3}{2}$

The numerators can be added since the denominators are common. The denominators will stay the same.

$\frac{3}{2}+\frac{3}{2} = \frac{6}{2}$

Divide six and two.

$\frac{6}{2}=3$

The answer is .

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Example Question #95 : Operations

Solve:

$26+3\cdot4\div2+7\cdot5-19$

Possible Answers:

116

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/division before addition/subtraction to get our final answer of 48:

$26+3\cdot4\div2+7\cdot5-19$

$26+12\div2+35-19$

26+6+35-19

32+35-19

67-19=48

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Example Question #96 : Operations

Solve:

$6\cdot4+3-6+13$

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 multiplication before addition to get our final answer of 34:

$6\cdot4+3-6+13$

24+3-6+13

27-6+13

21+13=34

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Example Question #97 : Operations

Using the order of operations, solve the following.

2(4+3) + 3^2 *7

Possible Answers:

140

161

Correct answer:

Explanation:

To solve this, we use the order of operations. The order of operations is

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

We must solve the problem in the proper order, starting first with parentheses and ending with subtraction. Using the order of operations, we get

Initial Problem:

2(4+3) + 3^2 *7

Solve parentheses:

2(7) + 3^2 *7

Solve exponents:

2(7) + 9 *7

Mulitply:

14 + 63

Add:

So the final solution is 77.

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Example Question #91 : Order Of Operations

Solve:

$2^{2}-3+15-6\div2$

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 complete the division before doing the addition/subtraction to get our final answer of 13:

$2^{2}-3+15-6\div2$

$4-3+15-6\div2$

4-3+15-3

1+15-3

16-3=13

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Example Question #99 : Operations

Solve:

$15-6+3\cdot4-7$

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 do the multiplication before the addition/subtraction to get our final answer of 14:

$15-6+3\cdot4-7$

15-6+12-7

9+12-7

21-7=14

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Example Question #100 : Operations

Solve:

$4+6\div (3^{2}+4-7)$

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 do the parentheses first. Inside the parentheses solve the exponent before doing addition and subtraction. Once the parentheses are solved complete the division before addition to get a final answer of 5:

$4+6\div (3^{2}+4-7)$

$4+6\div (9+4-7)$

$4+6\div (13-7)$

$4+6\div6$

4+1=5

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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 #91 : Operations

Example Question #92 : Operations

Example Question #93 : Operations

Example Question #94 : Operations

Example Question #95 : Operations

Example Question #96 : Operations

Example Question #97 : Operations

Example Question #91 : Order Of Operations

Example Question #99 : Operations

Example Question #100 : Operations

All Pre-Algebra Resources

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