Express the ratio in simplest form :
`1/15 : 1/25`

Answer

To express the ratio \( \frac{1}{15} : \frac{1}{25} \) in simplest form, follow these steps:

### Step 1: Write the ratio in fraction form
The ratio \( \frac{1}{15} : \frac{1}{25} \) can be expressed as a fraction:
\[ \frac{\frac{1}{15}}{\frac{1}{25}} \]

### Step 2: Simplify the fraction
To simplify the fraction, we can multiply by the reciprocal of the denominator:
\[ \frac{1}{15} \div \frac{1}{25} = \frac{1}{15} \times \frac{25}{1} = \frac{25}{15} \]

### Step 3: Reduce the fraction to simplest form
Now, we need to simplify \( \frac{25}{15} \). We can do this by finding the greatest common divisor (GCD) of 25 and 15. The GCD is 5. We divide both the numerator and the denominator by 5:
\[ \frac{25 \div 5}{15 \div 5} = \frac{5}{3} \]

### Step 4: Write the final ratio
Thus, the ratio \( \frac{1}{15} : \frac{1}{25} \) in simplest form is:
\[ 5 : 3 \]

### Final Answer:
The simplest form of the ratio \( \frac{1}{15} : \frac{1}{25} \) is \( 5 : 3 \).

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