Question

Which is a requirement for a number to a rational number?

The number can be written as a fraction.

The denominator is an integer.

The numerator is an integer.

All of the above.

Answer 1

\[ \frac{1}{0.5} \]
is rational (equal to 2)

similarly
\[ \frac{0.5}{1}\] is rational = 1/2

Answer 2

@ImNotGoodAtMath

Answer 3

Let's go through all these choices

A) "The number can be written as a fraction."

A fraction of what? If we have a fraction of numbers like \(\large \sqrt{2}\) and \(\large \sqrt{7}\), then we don't have a rational number.

The number has to be able to be written as a fraction of INTEGERS

This all shows that choice A is false.

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B) " The denominator is an integer."

This is a slightly better clarification. So the denominator is now an integer, but what about the numerator? That could be a number like \(\large \sqrt{31}\), which makes the number not rational.

This shows B is wrong.

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C) " The numerator is an integer."

All integers are rational numbers because you can use the rule x = x/1

Examples

3 = 3/1
41 = 41/1
88 = 88/1
-23 = -23/1
etc etc

So because we can write any integer as a fraction of two integers, this means that all integers are rational numbers. It doesn't work the other way around since 1/2 is rational but not an integer.

So we have our answer here.

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D) " All of the above."

This is automatically false once you've proven A is false

Answer 4

ty i was lost and im very thankfull you took ur time to explian every answer :)