Final answer:
To create an equivalent ratio to 2:3 by multiplying both sides by 3, we get 6:9. The proportional relationship stays the same, meaning the ratios are indeed equivalent.
Step-by-step explanation:
The initial ratio given is 2:3. To find a new ratio that is equivalent to this, we can multiply each side of the ratio by the same number. In this case, we are asked to multiply by 3.
The principle of equivalent ratios is simple: Just as multiplying both sides of an equality doesn't alter the truth of the equality, multiplying both sides of a ratio doesn't change the inherent proportional relationship represented by the ratio.
So, let's perform the multiplication: 2 * 3 = 6 and 3 * 3 = 9. So, our equivalent ratio becomes 6:9, which maintains the same proportional relationship as the 2:3.
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