35 is what % of 105 ?

Options

A. `33%`
B. `30%`
C. `33 (1)/(3)%`
D. `33.30%`

Answer

To find out what percentage 35 is of 105, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We need to find out what percentage 35 is of 105. This can be expressed mathematically as:
\[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \]
Here, the "Part" is 35 and the "Whole" is 105.

2. **Set Up the Equation**: Plugging the values into the formula gives us:
\[ \text{Percentage} = \left( \frac{35}{105} \right) \times 100 \]

3. **Calculate the Fraction**: First, we need to simplify the fraction \( \frac{35}{105} \):
- Both 35 and 105 can be divided by 35:
\[ \frac{35 \div 35}{105 \div 35} = \frac{1}{3} \]

4. **Multiply by 100**: Now we can substitute this back into our percentage formula:
\[ \text{Percentage} = \left( \frac{1}{3} \right) \times 100 \]

5. **Calculate the Final Result**: To find \( \frac{1}{3} \times 100 \):
\[ \frac{100}{3} \approx 33.33 \]
This can also be expressed as \( 33 \frac{1}{3} \).

### Final Answer:
Thus, 35 is \( 33 \frac{1}{3} \% \) of 105.

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