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Subjects>Math>Other Math

What is the sum of any rational number and its opposite?

Anonymous

∙ 7y ago

Updated: 4/28/2022

If we define "opposite" as the additive inverse, the sum is zero.

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∙ 7y ago

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More answers

When x is not zero, it can be (x + 1/x).

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∙ 8y ago

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Continue Learning about Other Math

What is the sum of the rational numbers?

The sum of any finite set of rational numbers is a rational number.

If you add a rational and irrational number what is the sum?

an irrational number PROOF : Let x be any rational number and y be any irrational number. let us assume that their sum is rational which is ( z ) x + y = z if x is a rational number then ( -x ) will also be a rational number. Therefore, x + y + (-x) = a rational number this implies that y is also rational BUT HERE IS THE CONTRADICTION as we assumed y an irrational number. Hence, our assumption is wrong. This states that x + y is not rational. HENCE PROVEDit will always be irrational.

Is an irrational number plus an irrational number rational?

No. The sum of an irrational number and any other [real] number is irrational.

Is it true that sum of a rational number and irrational number is irrational?

Yes

Explain why the sum of a rational number and an irrational number is an irrational number?

Let R1 = rational number Let X = irrational number Assume R1 + X = (some rational number) We add -R1 to both sides, and we get: -R1 + x = (some irrational number) + (-R1), thus X = (SIR) + (-R1), which implies that X, an irrational number, is the sum of two rational numbers, which is a contradiction. Thus, the sum of a rational number and an irrational number is always irrational. (Proof by contradiction)

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