Let's break down the problem:

1. You have a rectangle containing 16 squares.
2. Each square is divided into 3 equal parts (thirds).
3. The total number of parts (thirds) in the rectangle is: $16 \, \text{squares} \times 3 \, \text{thirds per square} = 48 \, \text{thirds}$
4. You are told that 40 of these 48 thirds are shaded.

To find what portion of the rectangle is shaded, you need to calculate the ratio of the shaded area to the total area: $\frac{40 \, \text{thirds shaded}}{48 \, \text{total thirds}} = \frac{40}{48}$

Now simplify the fraction: $\frac{40}{48} = \frac{5}{6}$

Thus, $\frac{5}{6}$ of the rectangle is shaded.

Would you like further clarification, or do you have any questions?

Here are 5 related questions to explore further:

1. How do you calculate the area of a rectangle if dimensions are given?
2. If only half of the squares were divided into thirds, how would that affect the shading?
3. How can we convert fractions into percentages to describe the shaded portion?
4. What would be the area of the shaded region if the total area of the rectangle was 24 square units?
5. How do you find the fraction of a shape shaded when multiple divisions exist?

Tip: When simplifying fractions, always look for the greatest common divisor (GCD) of the numerator and denominator to reduce the fraction efficiently.