To find the scenario that matches the expression \(\frac{2}{3} \div \frac{1}{3}\), we need to recognize that this expression represents "how many times larger \( \frac{2}{3} \) is compared to \( \frac{1}{3} \)."
Now let's analyze the options:
A: This scenario asks how many times greater the gravity on planet A (which is \( \frac{2}{3} \) of Earth's gravity) is than planet B (which is \( \frac{1}{3} \) of Earth's gravity). This matches our expression because it compares the values directly.
B: This scenario asks how many times more of chemical B (which is \( \frac{1}{3} \) of a liter) was used than chemical A (which is \( \frac{2}{3} \) of a liter). This does not fit our expression since it's about comparing chemical B to chemical A.
C: This scenario looks at how much more soup Mrs. Roth (who ate \( \frac{2}{3} \)) ate compared to her daughter (who ate \( \frac{1}{3} \)). This also does not fit our expression directly.
D: This scenario describes distances walked by Jess and Beth (with \( \frac{2}{3} \) miles and \( \frac{1}{3} \) miles, respectively), but it doesn’t provide a clear division concept regarding how many times larger one distance is than the other.
Given all the analyses, the correct answer is:
A: "Astronomers recently discovered two planets, planet A and planet B. The gravity on planet A is \( \frac{2}{3} \) of the gravity on Earth. The gravity on planet B is \( \frac{1}{3} \) of the gravity on Earth. How many times greater than the gravity on Earth is the gravity on planet A than planet B?"