`2/3` of `3/4` of `4/9` of `(1)/(60)` of 120 of a number will be what percentage of that number?

Options

A. 44.44
B. 33.33
C. 22.22
D. 11.11

Answer

To solve the problem step by step, we need to calculate the expression given and then find out what percentage it is of the original number.

### Step 1: Understand the Expression
We need to calculate:
\[ \frac{2}{3} \text{ of } \frac{3}{4} \text{ of } \frac{4}{9} \text{ of } \frac{1}{60} \text{ of } 120 \text{ of a number } x. \]

### Step 2: Calculate Each Fraction Step-by-Step
1. **Calculate \(\frac{1}{60} \text{ of } 120\)**:
\[ \frac{1}{60} \times 120 = \frac{120}{60} = 2. \]

2. **Now calculate \(\frac{4}{9} \text{ of } 2\)**:
\[ \frac{4}{9} \times 2 = \frac{8}{9}. \]

3. **Next, calculate \(\frac{3}{4} \text{ of } \frac{8}{9}\)**:
\[ \frac{3}{4} \times \frac{8}{9} = \frac{3 \times 8}{4 \times 9} = \frac{24}{36} = \frac{2}{3}. \]

4. **Finally, calculate \(\frac{2}{3} \text{ of } \frac{2}{3}\)**:
\[ \frac{2}{3} \times \frac{2}{3} = \frac{4}{9}. \]

### Step 3: Find What Percentage \(\frac{4}{9}\) is of \(x\)
To find out what percentage \(\frac{4}{9}\) of \(x\) is, we use the formula:
\[ \text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100. \]
Here, the part is \(\frac{4}{9}x\) and the whole is \(x\):
\[ \text{Percentage} = \left(\frac{\frac{4}{9}x}{x}\right) \times 100 = \frac{4}{9} \times 100. \]

### Step 4: Calculate the Final Percentage
\[ \frac{4}{9} \times 100 = \frac{400}{9} \approx 44.44\%. \]

### Final Answer
So, \(\frac{2}{3}\) of \(\frac{3}{4}\) of \(\frac{4}{9}\) of \(\frac{1}{60}\) of 120 of a number will be approximately \(44.44\%\) of that number.