$1 \div \frac{1}{2} \div \frac{1}{3}$
The given expression is \(1 \div \frac{1}{2} \div \frac{1}{3}\). According to the standard order of operations, division is performed from left to right when no grouping symbols (like parentheses) are present. Therefore, we first evaluate the expression as \((1 \div \frac{1}{2}) \div \frac{1}{3}\).
To divide by a fraction, we multiply by its reciprocal. The reciprocal of \(\frac{1}{2}\) is \(2\). Thus, the first part of the expression is \(1 \div \frac{1}{2} = 1 \times 2 = 2\).
Now, we substitute the result into the original expression: \(2 \div \frac{1}{3}\). Again, to divide by a fraction, we multiply by its reciprocal. The reciprocal of \(\frac{1}{3}\) is \(3\). Thus, the operation is \(2 \times 3 = 6\).
Imagine you have a full chocolate bar and you want to share it among friends in pieces of half-size. First, you get 2 pieces. If you then want to take each of those 2 pieces and further divide them into thirds (for example, to make smaller snack-sized bites), you would end up with \(2 \times 3 = 6\) pieces in total. This demonstrates how dividing by fractions corresponds to multiplying by their reciprocals in real-life resource distribution.