Final Answer:
a, c, e This process helps find ratios that maintain the same relative size or proportionality. In this case, ratios 3:2 and 18:12 share equivalence with the initial ratio of 9:6, as they represent the same relative quantities in simplified forms. Ratio 5:2 or 13:10 do not match the simplified 3:2, hence they are not equivalent to the given ratio.
Step-by-step explanation:
Ratios equivalent to 9:6 are determined by simplifying the ratio to its simplest form. For 9:6, both terms share a common factor of 3, resulting in the simplified ratio of 3:2 (option c). Similarly, for 18:12, reducing it to its simplest form yields 3:2 (option e). The ratio 5:2 (option d) cannot be simplified to match 9:6, as there is no common factor between the terms.
When identifying equivalent ratios, the goal is to find ratios that share a proportional relationship, representing the same relative quantities. To determine equivalence, the given ratios are simplified by dividing both terms by their greatest common factor until no further simplification is possible.
This process helps find ratios that maintain the same relative size or proportionality. In this case, ratios 3:2 and 18:12 share equivalence with the initial ratio of 9:6, as they represent the same relative quantities in simplified forms. Ratio 5:2 or 13:10 do not match the simplified 3:2, hence they are not equivalent to the given ratio. Understanding how to simplify ratios aids in recognizing equivalent ratios across varying representations.