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== == The set of natural numbers is {1, 2, 3, ...} The set of integers is {..., -3, -2, -1, 0, 1, 2, 3, ...} All natural numbers are integers.

A rational number is an integer 'A' divided by a natural number 'B'; i.e. A / B. Suppose we add two rational numbers: A / B + C / D This is algebraically equal to (AD + BC) / BD Since A and C are integers and B and D are natural numbers, then AD and BC are integers because two integers multiplied yields an integer. If you add these together, you get an integer. So we have an integer (AD + BC) on the top.

B and D are natural numbers. Multiply them and you get a natural number. So we have a natural number BD on the bottom.

Since (AD + BC) / BD is a rational number, A / B + C / D is a rational number.

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Since a rational number is, by definition, one that can be written a a ratio of 2 integers, adding 2 rationals is tantamount to adding 2 fractions, which always produces a fraction (ratio of 2 integers) for the answer, so the answer is, by definition, rational. llllaaaaaaaaaaaaaalllllllllaaaaaaaaaalllllllllllaaaaaaaaaaaalaaaaaaaa

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โˆ™ 2009-09-05 08:58:22
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Q: Why is the sum of any two rational numbers a rational number?
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What is the sum of the rational numbers?

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


Is the sum of a rational number irrational?

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Can you add two irrational numbers to get a rational number?

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Every time. The sum of two rational numbers MUST be a rational number.


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Is sum of any 2 rational number is a rational number?

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