The ratio $6:9$ simplifies to $2:3$.

To simplify a ratio, you need to determine the greatest common divisor (GCD) of the two numbers involved. The GCD is the largest integer that divides both numbers without leaving a remainder. For the ratio $6:9$, we will first find the GCD of $6$ and $9$.

Begin by listing the factors of each number. The factors of $6$ are $1, 2, 3,$ and $6$, while the factors of $9$ are $1, 3,$ and $9$. The largest common factor in these sets is $3$.

Next, divide both terms of the ratio by their GCD. Thus, $6$ divided by $3$ equals $2$, and $9$ divided by $3$ equals $3$. Therefore, the simplified form of the ratio $6:9$ is $2:3$.

Simplifying ratios is akin to simplifying fractions; it makes comparisons more straightforward and comprehensible. For instance, if you have $6$ apples and $9$ oranges, the simplified ratio of apples to oranges is $2:3$. This means that for every $2$ apples, there are $3$ oranges. This simplification process is valuable in various mathematical contexts, including proportions, rates, and scaling.