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Pre-Algebra : Identities and Properties

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Example Questions

Example Question #2 : Additive Inverse Property

What is the additive inverse of $3x^{2}$ ?

Possible Answers:

$-3x^{2}$

$3x^{2}$

$3x^{-2}$

$1/3x^{2}$

Correct answer:

$-3x^{2}$

Explanation:

The rule for Additive Inverse Property is $a + \left ( -a\right ) = 0$ .

Using this rule if $a = 3x^{2}$ ,

$3x^{2} + \left ( -3x^{2}\right ) = 0$

So the additive inverse is $-3x^{2}$ .

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Example Question #1 : Additive Inverse Property

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

Possible Answers:

2.5+5= 5+2.5

(2.5 + 5) + 7.5 = 2.5 + (5+7.5)

2.5+ (-2.5) = 0

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

2.5 + 0 = 2.5

Correct answer:

2.5+ (-2.5) = 0

Explanation:

The inverse property of addition states that for every real number, a number exists, called the additive inverse, such that the number and its inverse have sum 0. Of the statements given, only

2.5+ (-2.5) = 0

demonstrates this property, so it is the correct choice.

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Example Question #2 : Additive Inverse Property

What is the additive inverse of 30?

Possible Answers:

$\frac{1}{30}$

$-\frac{1}{30}$

Correct answer:

Explanation:

The question asks us what number added with 30 will equal zero. Write the mathematical equation that represents this scenario.

30+x = 0

Subtract 30 from both sides.

x=-30

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Example Question #3 : Additive Inverse Property

Which of the following displays the additive inverse property?

Possible Answers:

a(b + c) = ab + ac

a + b = 0

a + b = b + a

(a + b) + c = a + (b + c)

a + 0 = a

Correct answer:

a + b = 0

Explanation:

The additive inverse property is when two numbers added together equal zero. So,

a + b = 0

displays that property.

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Example Question #1 : Multiplicative Identity Property

What property can be applied to the following expression?

$\frac{x}{\sqrt{5}} \times 1 = \frac{x}{\sqrt{5}}$

Possible Answers:

Multiplicative Inverse

Commutative of Addition

Associative of Multiplication

Distributive Law

Multiplicative Identity

Correct answer:

Multiplicative Identity

Explanation:

The rule for Multiplicative Identity Property is $a \times 1 = a$

Expression given in the question is: $\frac{x}{\sqrt{5}} \times 1 = \frac{x}{\sqrt{5}}$

Hence the property is Multiplicative Identity.

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Example Question #2 : Multiplicative Identity Property

Which of the following demonstrates the multiplicative inverse property?

Possible Answers:

$\frac{1}{4}\times 4=1$

$(4\times2)\times3=4\times(2\times3)$

$3\times2=2\times3$

$7\times1=7$

Correct answer:

$\frac{1}{4}\times 4=1$

Explanation:

The multiplicative inverse property states that for some value ,

$n\times \frac{1}{n}=1$ .

Therefore, the statement demonstrating the multiplicative inverse property is

$\frac{1}{4}\times4=1$ .

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Example Question #3 : Multiplicative Identity Property

Which of the following statements demonstrates the identity property of multiplication?

Possible Answers:

None of the examples in the other responses demonstrates the identity property of multiplication.

$\frac{2}{3} \times \frac{5}{7} = \frac{5}{7} \times \frac{2}{3}$

$\frac{2}{3} \times 1 = \frac{2}{3}$

$\frac{2}{3} \times \frac{3}{2} = 1$

$\left (\frac{2}{3} \times \frac{5}{7} \right ) \times \frac{6}{11} = \frac{2}{3} \times\left ( \frac{5}{7} \times \frac{6}{11} \right )$

Correct answer:

$\frac{2}{3} \times 1 = \frac{2}{3}$

Explanation:

The identity property of multiplication states that there is a number 1, called the multiplicative identity, that can be multiplied by any number to obtain that number. Of the four statements,

$\frac{2}{3} \times 1 = \frac{2}{3}$

demonstrates this property.

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Example Question #2 : Multiplicative Identity Property

Which property does the equation below represent?

$\frac{8}{21} * 1 = \frac{8}{21}$

Possible Answers:

Multiplicative Identity Property

Distributive Property

Communitive Property of Multiplication

Associative Property of Multiplication

Zero Property of Multiplication

Correct answer:

Multiplicative Identity Property

Explanation:

When something is multiplied by the number one it remains the same number. Therefore when multiplying by one it creates its own identity.

Multiplicative Identity Property

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Example Question #3 : Multiplicative Identity Property

Which equation shows an example of the multiplicative identity property?

Possible Answers:

2 * 4 * 6 =

32 * 0 =

(7 * 5) * 2 =

64r * 1 =

8 + (6 + 12) =

Correct answer:

64r * 1 =

Explanation:

The multiplicative identity property means that when something is multiplied by 1 then it will remain the same as the other number.

64r * 1 = 64r

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Example Question #4 : Multiplicative Identity Property

Which of the following displays the multiplicative identity property?

Possible Answers:

$a \cdot 0 = 0$

$a \cdot b = ab$

$a \cdot 1 = a$

$a \cdot b = b \cdot a$

$a (b \cdot c) = (a \cdot b) \cdot (a \cdot c)$

Correct answer:

$a \cdot 1 = a$

Explanation:

The multiplicative identity property states that when you multiply a number by 1, the answer is the original number.

Therefore,

$a \cdot 1 = a$

displays the multiplicative identity property.

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Pre-Algebra : Identities and Properties

Study concepts, example questions & explanations for Pre-Algebra

All Pre-Algebra Resources

Example Questions

Example Question #2 : Additive Inverse Property

Example Question #1 : Additive Inverse Property

Example Question #2 : Additive Inverse Property

Example Question #3 : Additive Inverse Property

Example Question #1 : Multiplicative Identity Property

Example Question #2 : Multiplicative Identity Property

Example Question #3 : Multiplicative Identity Property

Example Question #2 : Multiplicative Identity Property

Example Question #3 : Multiplicative Identity Property

Example Question #4 : Multiplicative Identity Property

All Pre-Algebra Resources

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