Jan's gas tank is nearly empty, at [tex]\frac{1}{12}[/tex] full. She doesn't have enough cash to fill the tank, but she adds enough gas to reach [tex]\frac{2}{3}[/tex] full.

How much gas did she add, as a fraction of the tank?

A. [tex]\frac{5}{12}[/tex]
B. [tex]\frac{7}{12}[/tex]
C. [tex]\frac{1}{3}[/tex]
D. [tex]\frac{2}{9}[/tex]



Answer :

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].