Question

during a biology experiment,
\\( \frac { 2 } { 3 } \\) of a liter of saline solution
is used to prepare \\( \frac { 1 } { 2 } \\) dozen
petri dishes.
how many liters of solution
are required per petri dish?

Explanation:

Step1: Calculate the number of petri dishes

Since \(1\) dozen \( = 12\) units, then \(\frac{1}{2}\) dozen petri dishes \(n=\frac{1}{2}\times12 = 6\) petri dishes.

Step2: Calculate the amount of solution per petri dish

We know the total amount of solution is \(\frac{2}{3}\) liters and the number of petri dishes is \(n = 6\). Using the formula for unit - rate \(r=\frac{\text{total amount}}{\text{number of units}}\), we have \(r=\frac{\frac{2}{3}}{6}\).
According to the rule of dividing by a number is the same as multiplying by its reciprocal, \(\frac{\frac{2}{3}}{6}=\frac{2}{3}\times\frac{1}{6}\).
Multiply the numerators (\(2\times1 = 2\)) and the denominators (\(3\times6=18\)), so \(\frac{2}{3}\times\frac{1}{6}=\frac{2}{18}\).
Simplify the fraction \(\frac{2}{18}=\frac{1}{9}\) liters per petri dish.

Answer:

\(\frac{1}{9}\) liters per petri dish.