Simplify : c. `(3)/(5)` of `((1)/(15) xx 3 (2)/(5))`

Answer

To simplify the expression \(\frac{3}{5}\) of \(\left(\frac{1}{15} \times 3 \frac{2}{5}\right)\), we will follow these steps:

### Step 1: Convert the mixed fraction to an improper fraction
The mixed fraction \(3 \frac{2}{5}\) can be converted to an improper fraction.

To convert \(3 \frac{2}{5}\):
- Multiply the whole number (3) by the denominator (5): \(3 \times 5 = 15\)
- Add the numerator (2) to this result: \(15 + 2 = 17\)
- The improper fraction is \(\frac{17}{5}\).

So, \(3 \frac{2}{5} = \frac{17}{5}\).

### Step 2: Rewrite the expression
Now, we can rewrite the expression:
\[ \frac{3}{5} \text{ of } \left(\frac{1}{15} \times \frac{17}{5}\right) \]
This can be expressed as:
\[ \frac{3}{5} \times \left(\frac{1}{15} \times \frac{17}{5}\right) \]

### Step 3: Multiply the fractions
Now, we will multiply the fractions:
\[ \frac{1}{15} \times \frac{17}{5} = \frac{1 \times 17}{15 \times 5} = \frac{17}{75} \]

### Step 4: Multiply by \(\frac{3}{5}\)
Next, we multiply \(\frac{3}{5}\) by \(\frac{17}{75}\):
\[ \frac{3}{5} \times \frac{17}{75} = \frac{3 \times 17}{5 \times 75} = \frac{51}{375} \]

### Step 5: Simplify the fraction
Now, we need to simplify \(\frac{51}{375}\). We can find the greatest common divisor (GCD) of 51 and 375:
- The factors of 51 are 1, 3, 17, 51.
- The factors of 375 are 1, 3, 5, 15, 25, 75, 125, 375.
- The GCD is 3.

Now, divide both the numerator and the denominator by 3:
\[ \frac{51 \div 3}{375 \div 3} = \frac{17}{125} \]

### Final Answer
Thus, the simplified form of the expression is:
\[ \frac{17}{125} \]

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