First, let's restate the problem: We need to find the ratio of 30 minutes to 2 hours in its simplest form.
To do this, we need to ensure that both quantities are in the same unit. Let's convert the 2 hours into minutes because the other quantity is already given in minutes.
There are 60 minutes in an hour, so:
[tex]\[
2 \text{ hours} = 2 \times 60 = 120 \text{ minutes}
\][/tex]
Now, we need to find the ratio of 30 minutes to 120 minutes. That is:
[tex]\[
\text{Ratio} = \frac{30 \text{ minutes}}{120 \text{ minutes}}
\][/tex]
To simplify this ratio, we divide both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 30 and 120 is 30. Dividing both the numerator and the denominator by 30, we get:
[tex]\[
\frac{30 \div 30}{120 \div 30} = \frac{1}{4}
\][/tex]
So, the ratio of 30 minutes to 2 hours in its simplest form is [tex]\(\frac{1}{4}\)[/tex].
The correct answer is [tex]\(\frac{1}{4}\)[/tex].
