Step-by-step explanation:
We have been given that the total amount of water a tank can hold is [tex]14\frac{1}{2}[/tex] gallons.
To find the number of [tex]1\frac{1}{4}[/tex] gallon buckets of water can be used to fill the tank we will divide the total amount of water in the tank by amount of water in one bucket.
[tex]\text{Number of water buckets used}=\frac{\text{Total amount of water in the tank}}{\text{Amount of water in one bucket}}[/tex]
Upon substituting our given values we will get,
[tex]\text{Number of water buckets used}=\frac{14\frac{1}{2} }{1\frac{1}{4}}[/tex]
[tex]\text{Number of water buckets used}=\frac{\frac{29}{2} }{\frac{5}{4}}[/tex]
Dividing a fraction with another fraction is same as multiplying the reciprocal of second fraction with the first fraction.
[tex]\text{Number of water buckets used}={\frac{29}{2}}\times {\frac{4}{5}}[/tex]
Therefore, all the above expressions can be used to find the number of [tex]1\frac{1}{4}[/tex] gallon buckets of water will be needed to fill the tank.
