Final answer:
The ratios 16:8 and 4:2 are equivalent; both simplify to 2:1. To confirm this, one can divide the numbers of each ratio by their greatest common divisors or set up a proportion showing that the two ratios are equal.
Step-by-step explanation:
Yes, the ratios 16:8 and 4:2 are equivalent. To verify the equivalence of two ratios, you can simplify both to their lowest terms by dividing both components of each ratio by their greatest common divisors. For the ratio 16:8, divide both numbers by 8, and you get 2:1. Similarly, for the ratio 4:2, divide both numbers by 2, and you get 2:1. Since both simplified ratios are the same, the original ratios are indeed equivalent.
Proportions can also be used to compare ratios. For example, by setting up a proportion 16/8 = 4/2 and cross-multiplying, you find that 16*2 = 8*4, which simplifies to 32 = 32, confirming that the two ratios are equal.
The concept of equivalent ratios is closely related to the process of finding scale factors in problems involving models or drawings. For instance, a problem might ask for an actual dimension when given a scale dimension and factor, expressed as a proportion, like 1:2=4:x, which can be solved for 'x' the actual dimension.