The problem asks to select all ratios that are equivalent to the ratio $9:6$. The options are $18:12$, $40:30$, and $15:10$.

1. Problem Description

The problem asks to select all ratios that are equivalent to the ratio $9:6$. The options are $18:12$, $40:30$, and $15:10$.

2. Solution Steps

First, simplify the given ratio $9:6$ by dividing both numbers by their greatest common divisor, which is

3. $9 \div 3 = 3$

$6 \div 3 = 2$

So, the simplified ratio is $3:2$.

Now, check each of the options:

* $18:12$: Divide both numbers by their greatest common divisor, which is

6. $18 \div 6 = 3$

$12 \div 6 = 2$

So, the simplified ratio is $3:2$. This is equivalent to $9:6$.

* $40:30$: Divide both numbers by their greatest common divisor, which is

1

0. $40 \div 10 = 4$

$30 \div 10 = 3$

So, the simplified ratio is $4:3$. This is not equivalent to $9:6$.

* $15:10$: Divide both numbers by their greatest common divisor, which is

5. $15 \div 5 = 3$

$10 \div 5 = 2$

So, the simplified ratio is $3:2$. This is equivalent to $9:6$.

Therefore, the ratios equivalent to $9:6$ are $18:12$ and $15:10$.

3. Final Answer

$18:12, 15:10$