Question

1. which problem is best represented by the expression $\frac{2}{3} div \frac{1}{6}$?

a. leena has $\frac{2}{3}$ of a glass of apple juice with her. she adds another $\frac{1}{6}$ glass of apple juice to it. how much apple juice does she now have?
b. leena has $\frac{2}{3}$ of a glass of milk with her. she gives $\frac{1}{6}$ of it to her cat. how much of milk is left with her now?
c. ryans mom gave ryan $\frac{2}{3}$ of a pizza to eat. ryan eats a portion that is $\frac{1}{6}$ of the whole pizza. how much pizza is left?
d. how many portions that are $\frac{1}{6}$ of a whole pizza can be made with $\frac{2}{3}$ of a pizza?

Explanation:

To determine which problem matches the expression $\frac{2}{3} \div \frac{1}{6}$, we analyze each option:

• Option A: Leena adds $\frac{1}{6}$ to $\frac{2}{3}$, so the operation is addition ($\frac{2}{3}+\frac{1}{6}$), not division. Eliminate A.
• Option B: Leena gives away $\frac{1}{6}$ of her milk, so the operation is subtraction (or multiplication for "of"), not division. Eliminate B.
• Option C: Ryan eats a portion of $\frac{1}{6}$ of the whole pizza from the $\frac{2}{3}$ he has, so the operation is subtraction (or multiplication for "of"), not division. Eliminate C.
• Option D: We need to find how many portions of $\frac{1}{6}$ are in $\frac{2}{3}$ of a pizza. This is a "how many times does one quantity fit into another" problem, which is represented by division: $\frac{2}{3} \div \frac{1}{6}$. This matches the given expression.

Answer:

D. How many portions that are $\frac{1}{6}$ of a whole pizza can be made with $\frac{2}{3}$ of a pizza?