the total amount of water a tank and how old is 14 and 1/2 gallons or all wants to find out it how many 1 and 1/4 gallons buckets

If the tank is 3/4 full, and the tank holds 14.5 gal, then we need to multiply 14.5 * 3/4

First, convert 14.5 to 14 1/2 = 29/2 as an improper fraction

Now, we have 29/2 * 3/4 = 87/8 = 10 7/8 gal

That's how much gas is in the tank now. However, we want to know how much is needed to fill the tank. That can be determined by subtracting 10 7/8 from the amount that the tank can hold when full, which is 14.5 or 14 1/2.

14 1/2 - 10 7/8 can be re-written using improper fractions

29/2 - 87/8 We need a common denominator, which is 8

116/8 - 87/8 = 29/8 = 3 5/8 gal