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Pre-Algebra : Pre-Algebra

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 #51 : Absolute Value

$\left | -15 | + \left | 24 | = ?$

Possible Answers:

Correct answer:

Explanation:

The symbol | | around each real number signifies absolute value. Absolute value is the true magnitude of a real number, without looking at the positive or negative sign attached to it. To rewrite this problem when solving, remove all absolute value symbols as well as signs.

15 + 24 = 39

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Example Question #52 : Absolute Value

Solve the following:

$\left | -12 \right | + \left | -4\right |$

Possible Answers:

Correct answer:

Explanation:

The absolute value of a number is defined as the position or distance of the number from zero on the number. Because it is a distance, the value cannot be negative. So,

$\left | -12\right | = 12$

and

$\left | -4\right | = 4$

$\left | -12\right | + \left | -4\right | = 12 + 4 = 16$

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Example Question #363 : Operations And Properties

If x = 5 , what is the value of |-18 - |x + 18 || ?

Possible Answers:

Correct answer:

Explanation:

Substitute 5 for in the given equation and evaluate.

|-18 - |5+ 18 ||= |-18 - |23 ||

Remember that the absolute value of a number is its distance from zero on a number line. Distance is always positive; therefore, you can rewrite the expression.

|-18 - |23 ||= |-18 - 23|

Subtracting a positive number from a negative number is the same as adding a negative number.

$|-18 - 23|= |-18 +\left ( - 23 \right )|$

$|-18 +\left ( - 23 \right )|= |-\left (18 + 23 \right )|$

$|-\left (18 + 23 \right )|= |- 41|$

Solve.

|- 41|= 41

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Example Question #1 : Identities And Properties

What property can be applied to the following expression?

$2 + \sqrt{x} = \sqrt{x} + 2$

Possible Answers:

Associative of Addition

Commutative of Multiplication

Commutative of Addition

Additive Identity

Additive Inverse

Correct answer:

Commutative of Addition

Explanation:

The rule for Commutative Property of Addition is a + b = b + a

Expression given in the question is: $2 + \sqrt{x} = \sqrt{x} + 2$

Hence the property is Commutative of Addition.

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Example Question #1 : Identities And Properties

Identify the property being applied.

10.5+6.2+3.7=6.2+3.7+10.5

Possible Answers:

Associative Property of Addition

Order of Operations

Associative Inverse Property

Additive Property of Addition

Communitive Property of Addition

Correct answer:

Communitive Property of Addition

Explanation:

Correct Answer: Communitive Property of Addition

This property states that any set of terms can be added together in any order to achieve the same solution.

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Example Question #1 : How To Add Fractions

Which of the following statements demonstrates the commutative property of addition?

Possible Answers:

None of the examples in the other responses demonstrates the commutative property of addition.

$\frac{3}{4} +0 = \frac{3}{4}$

$\frac{3}{4} +\left ( \frac{7}{8} + \frac{1}{6} \right )= \left (\frac{3}{4} + \frac{7}{8} \right ) + \frac{1}{6}$

$\frac{7}{8} + \left (- \frac{7}{8} \right ) = 0$

$\frac{3}{4} + \frac{7}{8} = \frac{7}{8} + \frac{3}{4}$

Correct answer:

$\frac{3}{4} + \frac{7}{8} = \frac{7}{8} + \frac{3}{4}$

Explanation:

The commutative property of addition states that two numbers can be added in either order to obtain the same sum. Of the given responses, only

$\frac{3}{4} + \frac{7}{8} = \frac{7}{8} + \frac{3}{4}$

demonstrates this property, so it is the correct choice.

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Example Question #2 : Identities And Properties

Which of the following best represents the commutative property of addition?

Possible Answers:

$5\times 2+3 = 3+2\times 5$

1+3+5 = 9

30+1 = 1+30

1+3 = 5-1

1+3+5 = 1+(3+5)

Correct answer:

30+1 = 1+30

Explanation:

The property is defined as:

X+Y=Y+X

Switching the order of the numbers and adding the numbers will yield the same result.

The only answer is: 30+1 = 1+30

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Example Question #3 : Identities And Properties

Which of the following choices best represent the commutative property of addition?

Possible Answers:

A+B+C = A +(B+C)

1+3+5+7 = 16

(2+3) +4 = 2+(3+4)

20+1 = 1+20

5(x+y) = 5x+5y

Correct answer:

20+1 = 1+20

Explanation:

Write the rule for the commutative property of addition, letting and be any number.

x+y = y+x

Changing the order of these two numbers will not affect the final answer.

The best choice is: 20+1 = 1+20

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Example Question #2 : Identities And Properties

Which property is illustrated by the example:

$4\times 3=3\times 4$

Possible Answers:

Multiplicative identity property

Associative property of multiplication

Commutative property of multiplication

Distributive property

Correct answer:

Commutative property of multiplication

Explanation:

The commutative property of mulitplication states that the order in which 2 numbers are multiplied does not affect the result:

$a\times b=b\times a$

Or in this case,

$4\times 3=3\times 4$

$4\times3=12$

$3\times 4=12$

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Example Question #2 : Commutative Property Of Multiplication

Use the Commutative Property of Multiplication to write the below expression in a different way.

$6 \times x^{1/2}$

Possible Answers:

$6 / x^{1/2}$

$x \times 6^{1/2}$

$1 / 6x^{1/2}$

$x^{2} \times 6$

$x^{1/2}\times 6$

Correct answer:

$x^{1/2}\times 6$

Explanation:

The rule for Commutative Property of Multiplication is $a \times b = b \times a$

Using this rule, the expression $6 \times x^{1/2}$ can be written as $x^{1/2} \times 6$

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Pre-Algebra : Pre-Algebra

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #51 : Absolute Value

Example Question #52 : Absolute Value

Example Question #363 : Operations And Properties

Example Question #1 : Identities And Properties

Example Question #1 : Identities And Properties

Example Question #1 : How To Add Fractions

Example Question #2 : Identities And Properties

Example Question #3 : Identities And Properties

Example Question #2 : Identities And Properties

Example Question #2 : Commutative Property Of Multiplication

All Pre-Algebra Resources

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