Identities and Properties - Pre-Algebra

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Question

Which of the following demonstrates the multiplicative inverse property?

Answer

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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Question

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

Answer

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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Question

What property can be applied to the following expression?

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

Answer

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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Question

Which equation shows an example of the multiplicative identity property?

Answer

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

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Question

Which property does the equation below represent?

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

Answer

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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Question

Which of the following displays the multiplicative identity property?

Answer

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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Question

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

Answer

The inverse property of multiplication states that for every real number, a number exists, called the multiplicative inverse, such that the number and its inverse have product 1. Of the statements given, only

$\frac{6}{7} \times \frac{7}{6} = 1$

demonstrates this property.

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Question

Simplify.

$\frac{\frac{12}{c}}{\frac{3}{c^2}}$

Answer

To simplify a compound fraction, multiply the numerator by the reciprocal of the denominator. Remember that a compound fraction can easily be rewritten as a division problem!

$\frac{\frac{12}{c}}{\frac{3}{c^2}}=\frac{12}{c}\div\frac{3}{c^2}=\frac{12}{c}\times\frac{c^2}{3}$

Solve the multiplication.

$\frac{12}{c}\times\frac{c^2}{3}=\frac{12\times c^2}{c\times3}=\frac{12c^2}{3c}$

Now we need to reduce the fraction to find our final answer.

$\frac{12c^2}{3c}=\frac{3c(4c)}{3c}=4c$

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Question

What is the multiplicative inverse of $\frac{x^{2}}{x +\sqrt{3}}$ where $\left ( \frac{x^{2}}{x + \sqrt{3}} \neq 0\right )$

Answer

The rule for Multiplicative Inverse Property is $a \times \frac{1}{a} = 1$ where $\left ( a \neq 0\right )$ .

Using this rule, if

$a = \frac{x^{2}}{x + \sqrt{3}}$ ,

then $\frac{1}{a}$ is the Mulitplicative inverse, which is $\frac{1}{\frac{x^{2}}{x +\sqrt{3}}}$ .

After you simplify you get $\frac{x + \sqrt{3}}{x^{2}}$ which is the Multiplicative Inverse.

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Question

What is the multiplicative inverse of $-\frac{1}{\sqrt{x^{3}}}$ where $\left ( x > 0\right )$ ?

Answer

The rule for Multiplicative Inverse Property is

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

where $\left ( a \neq 0\right )$ .

Using this rule, if

$a = -\frac{1}{\sqrt{x^{3}}}$ ,

then $\frac{1}{a}$ is the mulitplicative inverse, which is $\frac{1}{-\frac{1}{\sqrt{x^{3}}}}$ .

After you simplify you get $-\sqrt{x^{3}}$ which is the multiplicative inverse.

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Question

Which of the following displays the multiplicative inverse property?

Answer

The mulitplicative inverse property deals with reciprocals. For example, the multiplicative inverse, or reciprocal, of the number 7 is $\frac{1}{7}$ .

The multiplicative inverse property states that a number times its multiplicative inverse equals 1.

Therefore,

$a \cdot \frac{1}{a} = 1$

displays the multiplicative inverse property.

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Question

Which property does the equation below represent?

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

Answer

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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Question

Which of the following displays the multiplicative identity property?

Answer

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.

Compare your answer with the correct one above

Question

Which of the following demonstrates the multiplicative inverse property?

Answer

The multiplicative inverse property states that for some value ,

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

Therefore, the statement demonstrating the multiplicative inverse property is

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

Compare your answer with the correct one above

Question

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

Answer

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.

Compare your answer with the correct one above

Question

What property can be applied to the following expression?

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

Answer

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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Question

Which equation shows an example of the multiplicative identity property?

Answer

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

Compare your answer with the correct one above

Question

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

Answer

The inverse property of multiplication states that for every real number, a number exists, called the multiplicative inverse, such that the number and its inverse have product 1. Of the statements given, only

$\frac{6}{7} \times \frac{7}{6} = 1$

demonstrates this property.

Compare your answer with the correct one above

Question

Simplify.

$\frac{\frac{12}{c}}{\frac{3}{c^2}}$

Answer

To simplify a compound fraction, multiply the numerator by the reciprocal of the denominator. Remember that a compound fraction can easily be rewritten as a division problem!

$\frac{\frac{12}{c}}{\frac{3}{c^2}}=\frac{12}{c}\div\frac{3}{c^2}=\frac{12}{c}\times\frac{c^2}{3}$

Solve the multiplication.

$\frac{12}{c}\times\frac{c^2}{3}=\frac{12\times c^2}{c\times3}=\frac{12c^2}{3c}$

Now we need to reduce the fraction to find our final answer.

$\frac{12c^2}{3c}=\frac{3c(4c)}{3c}=4c$

Compare your answer with the correct one above

Question

What is the multiplicative inverse of $\frac{x^{2}}{x +\sqrt{3}}$ where $\left ( \frac{x^{2}}{x + \sqrt{3}} \neq 0\right )$

Answer

The rule for Multiplicative Inverse Property is $a \times \frac{1}{a} = 1$ where $\left ( a \neq 0\right )$ .

Using this rule, if

$a = \frac{x^{2}}{x + \sqrt{3}}$ ,

then $\frac{1}{a}$ is the Mulitplicative inverse, which is $\frac{1}{\frac{x^{2}}{x +\sqrt{3}}}$ .

After you simplify you get $\frac{x + \sqrt{3}}{x^{2}}$ which is the Multiplicative Inverse.

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