Jesse purchased a full tank of gas on thursday on friday he took a road trip and use one half of a tank on sunday he did the same here and use an additional one third of the tank how much gas does jesse have left

Thursday: got full tank of gas
friday: took a road trip, used one half the tank. One half of a tank of gas left
sunday: did the same here and used an additional one third of the tank

1/2 tank of gas minus 1/3 tank of gas = how much he has left

first you need a common denominator, we're going to use 6
then you need to multiply each fraction by 1 to get it to the same denominator. 
to get the denominator of 2 to 6, you multiply by 3 so
1 x 3 = 3
2    3    6

do the same for 1/3, except multiply by 2 on both sides
1 x 2 = 2
3    2    6

now just subtract the two fractions

3 - 2 = 1
6    6   6

Jesse has 1/6 tank of gas left.