# George is making 8 gallons of Tropical punch. He has already poured in 1 3/4 gallons of pineapple juice and 2 1/2 gallons of orange juice. The only other ingredient is 7-Up. How much 7-Up does George need in gallons?

May 5, 2018

George will have to add $3 \frac{3}{4}$ gallons of 7-Up to bring the total to $8$ gallons.

#### Explanation:

Add the gallons of juice that he has already used. Subtract that from $8$ gallons.

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

Convert both mixed fractions to improper fractions. Multiply the denominator by the whole number, add the numerator, and place the result over the denominator.

$\frac{\left(4 \times 1 + 3\right)}{4} + \frac{\left(2 \times 2 + 1\right)}{2}$

Simplify.

$\frac{7}{4} + \frac{5}{2}$

When adding or subtracting fractions, they must have the same denominator. Multiply $\frac{5}{2}$ by $\frac{2}{2}$ to get an equivalent fraction with $4$ as the denominator.

$\frac{7}{4} + \frac{5}{2} \times \frac{2}{2}$

Simplify.

$\frac{7}{4} + \frac{10}{4}$

$\frac{17}{4}$

George has already poured in $\frac{17}{4}$ gallons of juice.

To determine how much 7-Up he needs to add, subtract $\frac{17}{4}$ gallons from $8$ gallons.

$8 - \frac{17}{4}$

Any whole number is understood to have a denominator of $1$. $\left(n = \frac{n}{1}\right)$

Rewrite the expression.

$\frac{8}{1} - \frac{17}{4}$

Multiply $\frac{8}{1}$ by $\frac{4}{4}$ to get an equivalent fraction with $4$ as the denominator.

$\frac{8}{1} \times \frac{4}{4} - \frac{17}{4}$

Simplify.

$\frac{32}{4} - \frac{17}{4}$

$\frac{15}{4}$

Convert $\frac{15}{4}$ to a mixed number. Divide $15$ by $4$ to get a whole number quotient and a remainder. The whole number quotient is the whole number of the mixed number, the remainder is the numerator, and the divisor $\left(4\right)$, is the denominator.

$15 \div 4$$=$$3$ $\text{R}$ $3$

$15 \div 4 = 3 \frac{3}{4}$

George will have to add $3 \frac{3}{4}$ gallons of 7-Up.