Question

Which of the following stanements shows the inverse property of addition?

1 y=y
Oy+y= 2 y
Oy+ (-) = 0
Oy+ 0 = y

Answer 1

`0\cdot \:y+\left(-0\cdot \:y\right)=0` the statement shows the inverse property of addition as the sum of a number and its inverse is zero.

Explanation:

As we know that Inverse Property of Addition states if you add any number to its opposite, the result will be zero.

For example, 13 + (-13) = 0 shows that -13 is the additive inverse of 13.

In other words, the sum of a number and its inverse is zero.

Now checking from the available options,

`0y+\left(-0y\right)`

`\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a`

`=0\cdot \:y-0\cdot \:y`

`\mathrm{Add\:similar\:elements:}\:0\cdot \:y-0\cdot \:y=0`

`=0`

Thus,

`0\cdot \:y+\left(-0\cdot \:y\right)=0`

Therefore,
`0\cdot \:y+\left(-0\cdot \:y\right)=0` the statement shows the inverse property of addition as the sum of a number and its inverse is zero.