Question

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Answer 1

Answer:

In order to prove that these numbers are all rational, you must be able to express then as a fraction, $\frac{a}{b}$, where b ≠ 0.

Firstly, in order to turn 3 into a fraction, remember that any number divided by 1 is 0. Therefore, 3 as a fraction can be expressed as $\frac{3}{1}$.

This satisfies the criteria: A fraction in the form $\frac{a}{b}$, where b ≠ 0.

Next, -2. Same with 3, any number over itself is 1. -2 as a fraction is -$\frac{2}{1}$. This, again, satisfies the given definition for a rational number.

Now, the more challenging one, -0.75.

It is likely a commonly known fact that 0.75 is equal to three quarters, but I will show the formal way to convert decimals to fraction, just in case in the future there is some other confusing decimal that isn't that commonly seen.

For terminating decimals (ones that do not go on forever), you can simply put it over 1, then multiply it by 100:

-0.75

= -$\frac{0.75}{1}$

Multiply that by 100:

-$\frac{75}{100}$

We could simplify this fraction further, but that is enough to show that -0.75 is a rational number: it fits the given definition!

I hope this helps you out! If you still have any questions, you can reply to this answer :)