Multiplicative Identity Property

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Which of the following displays the multiplicative identity property?

$a \cdot 1 = a$

CORRECT

$a \cdot 0 = 0$

$a \cdot b = b \cdot a$

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

$a \cdot b = ab$

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.

Which of the following demonstrates the multiplicative inverse property?

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

CORRECT

$3\times2=2\times3$

$7\times1=7$

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

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

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

Which equation shows an example of the multiplicative identity property?

CORRECT

Explanation

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

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

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

CORRECT

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

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

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

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

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.

Which property does the equation below represent?

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

Multiplicative Identity Property

CORRECT

Associative Property of Multiplication

Communitive Property of Multiplication

Zero Property of Multiplication

Distributive 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

What property can be applied to the following expression?

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

Multiplicative Identity

CORRECT

Multiplicative Inverse

Distributive Law

Commutative of Addition

Associative of Multiplication

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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