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

$3\frac{1}{2}+5\frac{3}{4}$

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

$\begin{gathered} 3\frac{1}{2}=\frac{2\cdot3+1}{2}=\frac{7}{2} \\ \text{and} \\ 5\frac{3}{4}=\frac{4\cdot5+3}{4}=\frac{23}{4} \end{gathered}$

so, the total amount of soda is given by

$\frac{7}{2}+\frac{23}{4}$

which gives

$\begin{gathered} \frac{7}{2}+\frac{23}{4}=\frac{14}{4}+\frac{23}{4}=\frac{14+23}{4}=\frac{37}{4} \\ \end{gathered}$

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

$2\frac{3}{8}=\frac{8\cdot2+3}{8}=\frac{19}{8}$

Then, Dan's family drank:

$\frac{37}{4}-\frac{19}{8}$

which gives

$\frac{37}{4}-\frac{19}{8}=\frac{74}{8}-\frac{19}{8}=\frac{55}{8}$

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

$\frac{55}{8}=6\frac{7}{8}$