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If x and y are additive opposites, then y = -x.If x >= 0 then abs(x) = x

also y <=0 so that abs(y) = -y = x


and

if x < 0 then abs(x) = -x = y

also y > 0 so that abs(y) = y.

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Q: Why do x and y have the same absolute value if x is a rational number and y is the opposite?
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Related questions

How do you identify opposite and absolute value of a rational number?

how do you identify opposite and absolute value of a rational number


How do you identify opposites and absolute value of rational numbers?

how do you identify opposite and absolute value of a rational number


What is absolute value of the opposite of a nonzero rational number?

The absolute value is always positive.


How do you identify the opposite of the absolute value of a rational number?

The opposite of the absolute value of x is always -abs(x).


How do you identity the opposite and the absolute value of a rational number?

The additive opposite of the rational number q is -q. One of q and -q must be non-negative and that is its absolute value.


When are the absolute value and the opposite of rational number equal?

When the number is 0.


What is a rational number whose opposite and absolute value are the same?

They are all non-positive rational numbers.


What is the additive inverse of a rational number?

It is the number with the same magnitude (absolute value) and the opposite sign.


When it went off absolute value and the opposite of a rational number equal?

When the number is non-positive.


How do you identify the opposite and the absolute values of a rational numbers?

An "opposite" is not a well defined term since there are additive opposites and multiplicative opposites and you have not specified which one.The absolute value of a rational number is the value of the number with a positive sign.Thus (abs(5/7) = 5/7and abs(-5/7) = 5/7


If x is a rational number a y is the opposite of x why do x and y have the same absolute value?

That is how absolute values are defined.


How do you Use absolute value to write definition of the opposite of a nonzero rational number?

I would do it that way.