Question

3 4. Dan bought soda for his family's party. He bought 3 1/2 liters of Pepsi and 5 3/4 liters of Sprite. They drank all but 2 3/8 liters of soda. How much soda did Dan-and his family drink?

Answer 1

The total amount of soda is

`3(1)/(2)+5(3)/(4)`

In order to make this addition, we must convert these fractions into a simple fraction form. That is,

`\begin{gathered} 3(1)/(2)=(2\cdot3+1)/(2)=(7)/(2) \\ \text{and} \\ 5(3)/(4)=(4\cdot5+3)/(4)=(23)/(4) \end{gathered}`

so, the total amount of soda is given by

`(7)/(2)+(23)/(4)`

which gives

`\begin{gathered} (7)/(2)+(23)/(4)=(14)/(4)+(23)/(4)=(14+23)/(4)=(37)/(4) \\ \end{gathered}`

Now, we must subtact 2 3/8 of soda and we must convert it into a simple fraction form:

`2(3)/(8)=(8\cdot2+3)/(8)=(19)/(8)`

Then, Dan's family drank:

`(37)/(4)-(19)/(8)`

which gives

`(37)/(4)-(19)/(8)=(74)/(8)-(19)/(8)=(55)/(8)`

that is, they drank 55/8 of soda. In mixed fraction form, this result is equivalent to

`(55)/(8)=6(7)/(8)`