Main Answer:
The ideas included in the explanation are. a. No, they are not equivalent. b. In the ratios 2:3, 2 is multiplied by 2, but 3 is not. c. The same number must be multiplied by both parts in the ratio, not added to them.
Therefore, the correct answer is a) b) c).
Step-by-step explanation:
In mathematics, the equivalence of ratios is a crucial concept. The statement "No, they are not equivalent" (a) emphasizes that not all ratios are equal, and understanding this distinction is fundamental. Moving on to the second idea (b), it delves into the specific operation applied to each part of a ratio. In the example of the ratio 2:3, we highlight that 2 is multiplied by 2, but 3 is not, showcasing the unique treatment of each component. This underscores the precision required when manipulating ratios.
The third idea (c) reinforces a fundamental principle of ratio manipulation. It asserts that when altering a ratio, the same number must be multiplied by both parts, not added. This guards against distorting the original relationship between the two quantities. By elucidating these ideas, the explanation provides a comprehensive understanding of the nuanced rules governing ratios.
In summary, the explanation elucidates the non-equivalence of ratios and delves into the intricacies of ratio manipulation. Each idea contributes to a holistic grasp of this mathematical concept, ensuring clarity in handling ratios.
Therefore, the correct answer is a) b) c).