To determine which of the given fractions is the largest, we can compare them by converting each to a decimal or bringing them to a common denominator. I will convert the fractions to their decimal equivalents to make comparison easier:

1. $\frac{67}{144} \approx 0.4653$
2. $\frac{7}{18} \approx 0.3889$
3. $\frac{17}{36} \approx 0.4722$
4. $\frac{135}{288} \approx 0.4688$
5. $\frac{33}{72} \approx 0.4583$

Now, let's compare the decimal values:

• $0.4653$
• $0.3889$
• $0.4722$
• $0.4688$
• $0.4583$

The largest value is $\frac{17}{36}$, which equals approximately 0.4722.

So, the largest fraction is c) $\frac{17}{36}$.

Do you want details or have any questions?

Here are five related questions to expand your understanding:

1. How do you convert a fraction to a decimal?
2. What is the process of finding a common denominator?
3. How can you simplify fractions for easier comparison?
4. How do you compare fractions without converting them to decimals?
5. What is the greatest common divisor, and how is it used in fraction simplification?

Tip: When comparing fractions, converting to decimals is quick, but using a common denominator can be more precise.