`a:b:c=(1)/(3):(1)/(5):(1)/(2)`, `a:b:c`

Answer

To solve the problem where the ratio \( a:b:c = \frac{1}{3}:\frac{1}{5}:\frac{1}{2} \), we will follow these steps:

### Step 1: Convert the given ratios to a common form
We start with the given ratios:
\[ a:b:c = \frac{1}{3}:\frac{1}{5}:\frac{1}{2} \]
To make calculations easier, we will find a common denominator for the fractions. The denominators are 3, 5, and 2. The least common multiple (LCM) of these numbers is 30.

### Step 2: Express each ratio in terms of the common denominator
Now, we convert each fraction to have the denominator of 30:
- For \( \frac{1}{3} \):
\[ \frac{1}{3} = \frac{10}{30} \]
- For \( \frac{1}{5} \):
\[ \frac{1}{5} = \frac{6}{30} \]
- For \( \frac{1}{2} \):
\[ \frac{1}{2} = \frac{15}{30} \]

### Step 3: Write the ratios with the common denominator
Now we can rewrite the ratios:
\[ a:b:c = 10:6:15 \]

### Step 4: Simplify the ratios if necessary
We can simplify the ratio \( 10:6:15 \) by finding the greatest common divisor (GCD) of the numbers. The GCD of 10, 6, and 15 is 1, so the ratio is already in its simplest form.

### Final Answer
Thus, the final ratio is:
\[ a:b:c = 10:6:15 \]

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