The problem asks to select all ratios equivalent to 2:3 from the given options: 13:30, 14:21, and 8:9.

1. Problem Description

The problem asks to select all ratios equivalent to 2:3 from the given options: 13:30, 14:21, and 8:

9.

2. Solution Steps

To determine if a ratio is equivalent to 2:3, we can write it as a fraction and simplify it. If the simplified fraction is equal to $\frac{2}{3}$, then the ratios are equivalent.

* Check 13:

3

0. $\frac{13}{30}$ cannot be simplified. Since $\frac{13}{30} \neq \frac{2}{3}$, the ratio 13:30 is not equivalent to 2:

3.

* Check 14:

2

1. $\frac{14}{21}$ can be simplified. Both 14 and 21 are divisible by

7. $\frac{14}{21} = \frac{14 \div 7}{21 \div 7} = \frac{2}{3}$.

Since $\frac{14}{21} = \frac{2}{3}$, the ratio 14:21 is equivalent to 2:

3.

* Check 8:

9. $\frac{8}{9}$ cannot be simplified. Since $\frac{8}{9} \neq \frac{2}{3}$, the ratio 8:9 is not equivalent to 2:

3.

3. Final Answer

14:21