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The way in which the binary functions, addition and multiplication, are defined on the set of rational numbers ensures that the set is closed under these two operations.

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Q: Why does a rational number plus a rational number or a rational number multiplied by a rational number equal to rational number?
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Related questions

Is an irrational number plus an irrational number equal a rational or an irrational number?

An irrational number is a number that has no definite end. So it can't be multiplied or divided by anything to make a rational number that does have a definite end.


Can a rational number plus an irrational number equal a rational number?

No, never.


Does an irrational number plus a rational number equal an irrational number?

Yes


Does an irrational plus a rational number equal an irrational number?

Yes, always.


If x is a rational number and y is a rational number than is x plus y rational?

If both numbers are rational then x plus y is a rational number


Why does a negative number plus a negative number equal a positive number?

It does not. A negative number multiplied by a negative number equals a positive number.


Is a rational number plus a rational number always a rational number?

Yes, it is.


Why does a rational number plus an irrational number equal an irrational number?

from another wikianswers page: say that 'a' is rational, and that 'b' is irrational. assume that a + b equals a rational number, called c. so a + b = c subtract a from both sides. you get b = c - a. but c - a is a rational number subtracted from a rational number, which should equal another rational number. However, b is an irrational number in our equation, so our assumption that a + b equals a rational number must be wrong.


Why an irrational number plus an irrational number equal a rational?

That simply isn't true. The sum of two irrational numbers CAN BE rational, but it can also be irrational. As an example, the square root of 2 plus the square root of 2 is irrational.


Is a Rational number plus rational number equals rational number?

Yes, the sum is always rational.


What does 1.5 multiplied by 180 plus -30a plus 30 equal?

That depends what the value of a is.


Is 17 plus 0.02 rational or irrational?

They add up to 17.02 which is rational number