Final answer:
To determine if two ratios or rates are equivalent, compare their simplified forms or unit rates. They are equivalent if these match; otherwise, they are not. Sometimes additional information may be required for a clear determination.
Step-by-step explanation:
Whether two ratios or rates are equivalent can be determined by comparing their values after simplification or finding a common unit rate or scale factor.
- A) If both ratios are $4 per paperback book, they are equivalent because they have the same unit rate.
- B) Ratios are not equivalent if they have different rates, which means their unit rates or simplified forms don't match.
- C) Ratios that simplify to the same terms, such as $4 per paperback book in both cases, are equivalent.
- D) Sometimes, more information may be required to determine equivalency if the values or terms provided are incomplete or unclear.
As an example, considering a proportion like 1/2 = 3/6, we can see that both sides of the equation represent the same value when simplified, hence they are equivalent. Similarly, a unit scale like 1 inch = 100 feet on a map represents a specific comparison between two measurements. In order to determine if ratios are equivalent, each pair needs to be examined individually.