Question

the penguins at the zoo eat $4\\ 2/3$ pounds of fish each day. the zookeeper bought $9\\ 1/3$ pounds of fish. how many days will the fish last? simplify your answer and write it as a fraction or as a whole or mixed number. \boxed{} days

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert \(4\frac{2}{3}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(4\frac{2}{3}\), we have \(a = 4\), \(b = 2\), \(c = 3\). Then \(4\frac{2}{3}=\frac{4\times3 + 2}{3}=\frac{12 + 2}{3}=\frac{14}{3}\).

Next, convert \(9\frac{1}{3}\) to an improper fraction. Using the same formula, \(a = 9\), \(b = 1\), \(c = 3\). So \(9\frac{1}{3}=\frac{9\times3+1}{3}=\frac{27 + 1}{3}=\frac{28}{3}\).

Step2: Divide the total amount of fish by the daily consumption

To find the number of days the fish will last, we divide the total amount of fish (\(\frac{28}{3}\) pounds) by the daily consumption (\(\frac{14}{3}\) pounds per day). When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction. So \(\frac{28}{3}\div\frac{14}{3}=\frac{28}{3}\times\frac{3}{14}\).

The 3 in the numerator and denominator cancels out, leaving \(\frac{28}{14}\).

Step3: Simplify the result

Simplify \(\frac{28}{14}\). Since \(28\div14 = 2\), the result is 2.

Answer:

2