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Q: Is 9 over 5 rational

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Yes. Any rational number divided by another rational number is also rational.

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is 5 over 7 a rational number

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Yes. In fact, most factions are rational. For example, 4/5 is rational, 9/234 is rational, 1/998001 is rational, any whole number over a whole number is rational.

41/9 is a rational number because all fractions are rational numbers

It is rational

-1/9 is rational because it can be expressed as a fraction (ratio).

Any addition, subtraction, multiplication, or division of rational numbers gives you a rational result. You can consider 8 over 9 as the division of 8 by 9, so the result is rational.

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No, it is rational.

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2/9 is rational by definition- it is a ratio of two integers.

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Yes, it is.

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