`a:b=(1)/(2) : (1)/(3)`, Find `a:b=?`

Answer

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

### Step 1: Understand the Ratio
We start with the given ratio:
\[ a:b = \frac{1}{2} : \frac{1}{3} \]

### Step 2: Express the Ratio in Fraction Form
We can express the ratio \( \frac{1}{2} : \frac{1}{3} \) as a fraction:
\[ \frac{1/2}{1/3} \]

### Step 3: Simplify the Fraction
To simplify \( \frac{1/2}{1/3} \), we multiply by the reciprocal of the denominator:
\[ \frac{1}{2} \div \frac{1}{3} = \frac{1}{2} \times \frac{3}{1} = \frac{3}{2} \]

### Step 4: Write the Result as a Ratio
Now, we can express this result in the form of a ratio:
\[ a:b = 3:2 \]

### Final Answer
Thus, the final answer is:
\[ a:b = 3:2 \]

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