Question

unit: fractions and mixed numbers
progress:
question id: 97266
the movement of the progress bar may be uneven because questions can be worth more or less (including zero) depending on your answer.
peter mixes $4\frac{1}{4}$ cups of orange juice, $2\frac{1}{4}$ cups of ginger ale, and $6\frac{1}{3}$ cups of strawberry lemonade to make some punch. what is the total number of cups of punch that peter makes?
\\(\circ\\) $12\frac{3}{11}$
\\(\circ\\) $12\frac{2}{5}$
\\(\circ\\) $12\frac{5}{6}$
\\(\circ\\) $12\frac{1}{4}$

Explanation:

Step1: Add the whole numbers

First, we add the whole number parts of the mixed numbers: \(4 + 2 + 6 = 12\).

Step2: Add the fractional parts

Next, we add the fractional parts. For the first two fractions, \(\frac{1}{4} + \frac{1}{4} = \frac{2}{4} = \frac{1}{2}\). Now we need to add \(\frac{1}{2}\) and \(\frac{1}{3}\). To add these, we find a common denominator, which is 6. So \(\frac{1}{2} = \frac{3}{6}\) and \(\frac{1}{3} = \frac{2}{6}\). Then \(\frac{3}{6} + \frac{2}{6} = \frac{5}{6}\).

Step3: Combine whole and fractional parts

Now we combine the whole number part (12) and the fractional part (\(\frac{5}{6}\)) to get \(12\frac{5}{6}\).

Answer:

\(12\frac{5}{6}\) (corresponding to the option with this value, e.g., if it's option C: \(12\frac{5}{6}\), then the answer is C. \(12\frac{5}{6}\))