Question

gemlia filled a bucket with 5 2/3 gallons of the water. later,she poured out 2 4/9 gallons of the water. how much water is left in the bucket?

Answer 1

The water in the bucket =
`5(2)/(3)` gallons.

Gemlia poured out water from the bucket =
`2(4)/(9)` gallons

First we will have to convert the mixed fraction to improper fraction.

`5(2)/(3) = ((5)(3)+2)/(3)` =
`((15+2))/(3) = (17)/(3)`

`2(4)/(9)= ((2)(9)+4)/(9)=((18+4))/(9)=(22)/(9)`

To find the left over water we have to subtract poured out water from total amount of water.

So we will get,

`(17)/(3) - (22)/(9)`

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.

`((17)(3))/((3)(3)) - (22)/(9)`

`(51)/(9) - (22)/(9)`

Now as the denominator is same , we will subtract the numerator.

`((51-22))/(9)`

`(29)/(9)`

So we have got there is
`(29)/(9)` gallons of water left in the bucket.

We will convert that improper fraction to mixed fraction now.

`(29)/(9) = 3(2)/(9)`

So the required answer is
`3(2)/(9)` gallons of water left over in the bucket.