3/7:9/14

To simplify the ratio \( \frac{3/7}{9/14} \), you can perform the following steps:

1. Rewrite the ratio as a division of fractions:

   \[ \frac{3/7}{9/14} = \frac{3}{7} \div \frac{9}{14} \]

2. Dividing by a fraction is equivalent to multiplying by its reciprocal:

   \[ \frac{3}{7} \times \frac{14}{9} \]

3. Now, multiply the numerators and the denominators:

   \[ = \frac{3 \times 14}{7 \times 9} = \frac{42}{63} \]

4. Simplify the fraction \( \frac{42}{63} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 21:

   \[ = \frac{42 \div 21}{63 \div 21} = \frac{2}{3} \]

So, the simplified ratio of \( \frac{3/7}{9/14} \) is \( 2:3 \).