To determine the correct division problem represented by the number line you described, we need to analyze the increments and the positioning of the numbers.
The number line goes from \(0\) to \(\frac{10}{3}\) in increments of one-third. You mention that there is an arrow from \(0\) to \(\frac{5}{3}\) and from \(\frac{5}{3}\) to \(\frac{10}{3}\).
- The distance from \(0\) to \(\frac{5}{3}\) represents the first part of the arrow.
- The distance from \(\frac{5}{3}\) to \(\frac{10}{3}\) represents the second part of the arrow.
To find out what type of division problem might fit, we can express the lengths of each segment.
- The length from \(0\) to \(\frac{5}{3}\) is simply \(\frac{5}{3} - 0 = \frac{5}{3}\).
- The length from \(\frac{5}{3}\) to \(\frac{10}{3}\) is \(\frac{10}{3} - \frac{5}{3} = \frac{5}{3}\).
Thus, if you are taking \(\frac{10}{3}\) as the whole and dividing it into parts (where each part is \(\frac{5}{3}\)), the expression for this division problem would be:
\[ \frac{10}{3} \div \frac{5}{3} \]
So, the correct choice from your options is:
\(\frac{10}{3} \div \frac{5}{3}\).
The other division problems do not logically fit the scenario of how the parts divide into the whole on the number line described.
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