To determine how much gas Jan added to her tank, we start with the initial and final amounts of gas in the tank.
1. Initial amount of gas: [tex]\(\frac{1}{12}\)[/tex] of the tank
2. Final amount of gas: [tex]\(\frac{2}{3}\)[/tex] of the tank
We need to find the difference between the final amount and the initial amount to determine how much gas Jan added. This difference can be calculated as follows:
[tex]\[
\text{Gas added} = \text{Final amount} - \text{Initial amount}
\][/tex]
Let’s plug in the given values:
[tex]\[
\text{Gas added} = \frac{2}{3} - \frac{1}{12}
\][/tex]
To perform this subtraction, we need to have a common denominator. The least common denominator (LCD) of 3 and 12 is 12. We will convert [tex]\(\frac{2}{3}\)[/tex] to a fraction with a denominator of 12:
[tex]\[
\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}
\][/tex]
Now we can directly subtract [tex]\(\frac{1}{12}\)[/tex] from [tex]\(\frac{8}{12}\)[/tex]:
[tex]\[
\frac{8}{12} - \frac{1}{12} = \frac{8 - 1}{12} = \frac{7}{12}
\][/tex]
Therefore, the amount of gas Jan added to her tank is:
[tex]\[
\frac{7}{12}
\][/tex]
So, the correct answer is [tex]\(\frac{7}{12}\)[/tex].
