`(25% of 50% of 100%)/(25/100 times 50% of 100)` is equal to

Options

A. `1.1%`
B. `0.1%`
C. `0.01%`
D. `1%`

Answer

To solve the expression \((25\% \text{ of } 50\% \text{ of } 100\%)/(25/100 \text{ times } 50\% \text{ of } 100)\), we will break it down step by step.

### Step 1: Calculate the numerator
The numerator is \(25\% \text{ of } 50\% \text{ of } 100\%\).

1. Convert percentages to fractions:
- \(25\% = \frac{25}{100} = \frac{1}{4}\)
- \(50\% = \frac{50}{100} = \frac{1}{2}\)
- \(100\% = 100\)

2. Calculate \(50\% \text{ of } 100\):
\[ 50\% \text{ of } 100 = \frac{1}{2} \times 100 = 50 \]

3. Now calculate \(25\% \text{ of } 50\):
\[ 25\% \text{ of } 50 = \frac{1}{4} \times 50 = \frac{50}{4} = 12.5 \]

So, the numerator is \(12.5\).

### Step 2: Calculate the denominator
The denominator is \( \frac{25}{100} \text{ times } 50\% \text{ of } 100\).

1. We already calculated \(50\% \text{ of } 100\) in Step 1, which is \(50\).

2. Now calculate \( \frac{25}{100} \text{ times } 50\):
\[ \frac{25}{100} \times 50 = \frac{1}{4} \times 50 = 12.5 \]

So, the denominator is also \(12.5\).

### Step 3: Divide the numerator by the denominator
Now we divide the numerator by the denominator:
\[ \frac{12.5}{12.5} = 1 \]

### Step 4: Convert to percentage
Since the answer is \(1\), to express it as a percentage:
\[ 1 = 1 \times 100\% = 100\% \]

### Final Answer
Thus, the value of the expression \((25\% \text{ of } 50\% \text{ of } 100\%)/(25/100 \text{ times } 50\% \text{ of } 100)\) is **1%**.

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