Respuesta :
The water in the bucket = [tex] 5\frac{2}{3} [/tex] gallons.
Gemlia poured out water from the bucket = [tex] 2\frac{4}{9} [/tex] gallons
First we will have to convert the mixed fraction to improper fraction.
[tex] 5\frac{2}{3} = \frac{(5)(3)+2}{3} [/tex] = [tex] \frac{(15+2)}{3} = \frac{17}{3} [/tex]
[tex] 2\frac{4}{9}= \frac{(2)(9)+4}{9}=\frac{(18+4)}{9}=\frac{22}{9} [/tex]
To find the left over water we have to subtract poured out water from total amount of water.
So we will get,
[tex] \frac{17}{3} - \frac{22}{9} [/tex]
To subtract them first we have to make the denominatior same. As 9 is multiple of 3, so we can make the common denominator as 3.
To make the denominator of the first fraction as 3, we know that 3 times 3 is 9, So we will multiply the numerator and denominator of the first fraction by 3.
[tex] \frac{(17)(3)}{(3)(3)} - \frac{22}{9} [/tex]
[tex] \frac{51}{9} - \frac{22}{9} [/tex]
Now as the denominator is same , we will subtract the numerator.
[tex] \frac{(51-22)}{9} [/tex]
[tex] \frac{29}{9} [/tex]
So we have got there is [tex] \frac{29}{9} [/tex] gallons of water left in the bucket.
We will convert that improper fraction to mixed fraction now.
[tex] \frac{29}{9} = 3\frac{2}{9} [/tex]
So the required answer is [tex] 3\frac{2}{9} [/tex] gallons of water left over in the bucket.
