Express `1//3` as a percentage of `5//9`.

Options

A. `60%`
B. `(500)/(3)`
C. `30%`
D. `90%`

Answer

To express \( \frac{1}{3} \) as a percentage of \( \frac{5}{9} \), we can follow these steps:

### Step 1: Set up the percentage formula
To find \( \frac{1}{3} \) as a percentage of \( \frac{5}{9} \), we use the formula:
\[ \text{Percentage} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \]
In this case, the "Part" is \( \frac{1}{3} \) and the "Whole" is \( \frac{5}{9} \).

### Step 2: Substitute the values into the formula
Substituting the values into the formula gives us:
\[ \text{Percentage} = \left( \frac{\frac{1}{3}}{\frac{5}{9}} \right) \times 100 \]

### Step 3: Simplify the fraction
To simplify \( \frac{\frac{1}{3}}{\frac{5}{9}} \), we can multiply by the reciprocal of the denominator:
\[ \frac{\frac{1}{3}}{\frac{5}{9}} = \frac{1}{3} \times \frac{9}{5} = \frac{1 \times 9}{3 \times 5} = \frac{9}{15} \]

### Step 4: Reduce the fraction
Now, we can simplify \( \frac{9}{15} \):
\[ \frac{9}{15} = \frac{3}{5} \]

### Step 5: Convert to percentage
Now, we multiply by 100 to convert to a percentage:
\[ \text{Percentage} = \frac{3}{5} \times 100 = 60 \]

### Final Answer
Thus, \( \frac{1}{3} \) as a percentage of \( \frac{5}{9} \) is:
\[ \boxed{60\%} \]

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