Problem 13

Explanation

To determine which number is greater, we will convert all options to a form similar to the problem, which is $0.44 \times \frac{17}{18}$. Note that $\frac{17}{18} = \frac{34}{36}$.

So, the comparison value is $0.44 \times \frac{34}{36}$.

Let's analyze each expression:

1. Analyzing $0.11 \times \frac{35}{9}$

   $$0.11 \times \frac{35}{9} = (0.11 \times 4) \times \left(\frac{35}{9} \times \frac{1}{4}\right) = 0.44 \times \frac{35}{36}$$

   Since $\frac{35}{36} > \frac{34}{36}$, this value is greater.

2. Analyzing $0.22 \times \frac{17}{9}$

   $$0.22 \times \frac{17}{9} = (0.22 \times 2) \times \left(\frac{17}{9} \times \frac{1}{2}\right) = 0.44 \times \frac{17}{18} = 0.44 \times \frac{34}{36}$$

   This value is equal.

3. Analyzing $0.33 \times \frac{34}{27}$

   $$0.33 \times \frac{34}{27} = \left(0.33 \times \frac{4}{3}\right) \times \left(\frac{34}{27} \times \frac{3}{4}\right) = 0.44 \times \frac{34}{36}$$

   This value is equal.

4. Analyzing $0.55 \times \frac{34}{45}$

   $$0.55 \times \frac{34}{45} = \left(0.55 \times \frac{4}{5}\right) \times \left(\frac{34}{45} \times \frac{5}{4}\right) = 0.44 \times \frac{34}{36}$$

   This value is equal.

5. Analyzing $0.66 \times \frac{17}{27}$

   $$0.66 \times \frac{17}{27} = \left(0.66 \times \frac{2}{3}\right) \times \left(\frac{17}{27} \times \frac{3}{2}\right) = 0.44 \times \frac{17}{18} = 0.44 \times \frac{34}{36}$$

   This value is equal.

Thus, the number that is greater is $0.11 \times \frac{35}{9}$.