Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Sep 19, 2023

Which equation shows the multiplicative identity element? $x \cdot 1=x$

STEP 1

Assumptions1. We are looking for the equation that represents the multiplicative identity element. . The multiplicative identity element is a number that, when multiplied by any number, leaves the number unchanged.

STEP 2

Let's consider each equation one by one.
The first equation is $x+0=x$ . This equation represents the additive identity element, not the multiplicative identity element. The additive identity is a number that, when added to any number, leaves the number unchanged. Here, adding0 to any number x does not change the value of x.

STEP 3

The second equation is $x-x=0$ . This equation represents the result of subtracting a number from itself, which always equals zero. This is not related to the multiplicative identity element.

STEP 4

The third equation is $x \cdot \frac{1}{x}=1$ . This equation represents the multiplicative inverse property, which states that any number multiplied by its reciprocal equals1. This is not the multiplicative identity element.

STEP 5

The fourth equation is $x \cdot1=x$ . This equation represents the multiplicative identity element. The multiplicative identity is a number that, when multiplied by any number, leaves the number unchanged. Here, multiplying any number x by1 does not change the value of x.
So, the equation that illustrates the multiplicative identity element is $x \cdot1=x$ .

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