Final answer:
The ratios 4:11 and 44:110 are not equivalent because when the second ratio is simplified or the first is scaled up, they do not match. Simplifying 44:110 by dividing by the GCD, which is 22, results in 2:5, which is different from 4:11.
Step-by-step explanation:
To determine if 4:11 and 44:110 are equivalent ratios, one approach is to simplify the second ratio.
To do this, we find the greatest common divisor (GCD) of the numbers in the second ratio, which in this case is 22 (because 22:11:22 also reduces to 2:1:2).
Dividing both terms of the ratio 44:110 by 22, we get 2:5, which is not equivalent to 4:11. Therefore, the ratios are not equivalent.
Another method is to scale up the first ratio. Multiplying both terms of the ratio 4:11 by 4, we get 16:44, which is not equal to 44:110, further confirming that the ratios are not equivalent.
We use these coefficients and the idea of proportions to compare ratios and determine equivalency.