To determine which scenario matches the expression \( \frac{2}{3} \div \frac{1}{3} \), we need to interpret the expression in the context of the options given.
The expression \( \frac{2}{3} \div \frac{1}{3} \) simplifies to \( 2 \) because dividing by a fraction is equivalent to multiplying by its reciprocal:
\[ \frac{2}{3} \div \frac{1}{3} = \frac{2}{3} \times \frac{3}{1} = 2 \]
Now, let's analyze each option:
A. This scenario asks how many times greater the gravity on planet A (which is \( \frac{2}{3} \) of Earth's gravity) is than the gravity on planet B (which is \( \frac{1}{3} \) of Earth's gravity). This does match \( \frac{2}{3} \div \frac{1}{3} \), which indicates that planet A's gravity is 2 times greater than that of planet B.
B. This scenario compares the distances Jess and Beth walk home. It does not ask how many times more Jess walks than Beth; rather, it finds the difference in their distances, so this does not match our expression.
C. This scenario asks how much more soup Mrs. Roth ate than her daughter. It does not correspond to the concept of "how many times more" one amount is than another.
D. This scenario compares the amounts of chemical A and B used in a science experiment, but it does not address how many times more one is than the other in the context of \( \frac{2}{3} \div \frac{1}{3} \).
Based on the analysis, 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?
7 answers