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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 #351 : Operations

Solve the expression: $-\left | 3\cdot2\right |-3\left | -2\right |$

Possible Answers:

Correct answer:

Explanation:

To solve this, first evaluate the terms inside the absolute values.

Recall that any value inside an absolute value sign will become positive and the absolute value bars will go away.

$-\left | 3\cdot2\right |-3\left | -2\right | = -(6)-3(2)$

Simplify.

-(6)-3(2) = -6-6 =-12

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Example Question #352 : Operations

Solve:

$-\left | -3^2\right |^3$

Possible Answers:

243

Correct answer:

Explanation:

Solve by evaluating the quantity inside the absolute value.

-3^2 = -9

Remember that the absolute value bars will turn any value inside of them to a positive value.

Now simplify the absolute value, and apply order of operations.

$\\ -\left | -3^2\right |^3 = -\left | -9 |^3 \\ = -(9)^3 = -(9\times 9\times 9) \\= -729$

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Example Question #353 : Operations

Solve: $\left | -9(-9)\right |-\left | -18\right |$

Possible Answers:

Correct answer:

Explanation:

Simplify the terms inside the absolute value.

Negative and positive values inside the absolute value will become positive.

$\left | 81\right |-\left | 18\right | = 81-18 = 63$

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Example Question #354 : Operations

Solve: $\left | -2\right |^3 -2^4$

Possible Answers:

Correct answer:

Explanation:

Evaluate by first eliminating the absolute value. Any positive or negative value inside the absolute value will be converted to a positive value.

$\left | -2\right |^3 -2^4 = (2)^3 -2^4$

The exponents can be expanded.

$(2)^3 -2^4 = 2\cdot2\cdot2 - 2\cdot2\cdot2\cdot2$

Multiply the terms and subtract.

=8-16

The answer is .

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Example Question #355 : Operations

Possible Answers:

Correct answer:

Explanation:

Simplify the numbers inside the absolute value first. Do not distribute the negative signs into the absolute value. Values inside the absolute value sign are converted to positive values.

Simplify the above expression.

-(3)-(4)(4) = -3-16

Subtract the values.

-3-16 = -19

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Example Question #356 : Operations

Determine the value of: $-\left |(10)^2 \right |$

Possible Answers:

100

200

Correct answer:

Explanation:

Evaluate the quantity that is squared.

Any value inside the absolute value sign will be converted to a positive number.

$-\left |100 \right | = -100$

The answer is:

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Example Question #357 : Operations

Solve the absolute value: $\left |-6-6 \right |^{-2}$

Possible Answers:

$\frac{1}{24}$

$\frac{1}{144}$

$-\frac{1}{144}$

Correct answer:

$\frac{1}{144}$

Explanation:

Solve the terms inside the absolute value first.

$\left |-6-6 \right |^{-2} = \left | -12\right |^{-2}$

Simplify the absolute value. Any term inside the absolute value is converted to a positive value.

$(12)^{-2}$

Convert the negative exponent to a positive exponent by taking the reciprocal of the inner term. Simplify.

$(12)^{-2} = \frac{1}{12^2} = \frac{1}{144}$

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Example Question #358 : Operations

Solve the equation below.

$\left | 3 * -5\right | + -2 =$

Possible Answers:

Correct answer:

Explanation:

The straight brackets indicate absolute value.

Absolute value means the distance from zero.

Example: Even a -16 is still 16 away from zero.

Therefore, $\left | 3 * -5\right | + - 2 =$

$\left | - 15\right | + - 2 =$

The absolute value of -15 is 15.

15 + -2 = 13

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Example Question #359 : Operations

Solve the following equation.

$\left | -7 \right | \cdot \left | 6\right |$

Possible Answers:

Correct answer:

Explanation:

The absolute value of a number is its distance from zero on a number line. Because of that, the absolute value of a number can never be negative.

So,

$\left | -7\right | = 7$

because the distance from zero to -7 on a number line is 7.

So,

$\left | -7 \right | \cdot \left | 6\right | = 7 \cdot 6 = 42$

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Example Question #360 : Operations

Solve:

$\left | 8-15\right |\div -8$

Possible Answers:

$\frac{23}{8}$

$-\frac{23}{8}$

$\frac{7}{8}$

$-\frac{7}{8}$

None of the other answers

Correct answer:

$-\frac{7}{8}$

Explanation:

First, we solve the absolute value portion:

$\left | 8-15\right |\div -8$

$\left | -7\right |\div -8$

$7\div -8$

$\frac{7}{-8}$

$-\frac{7}{8}$

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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 #351 : Operations

Example Question #352 : Operations

Example Question #353 : Operations

Example Question #354 : Operations

Example Question #355 : Operations

Example Question #356 : Operations

Example Question #357 : Operations

Example Question #358 : Operations

Example Question #359 : Operations

Example Question #360 : Operations

All Pre-Algebra Resources

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