The correct answers are:
1. The amount of change is different for the percent increase and the percent decrease.
2. The ratio of the percent increase is not the same as the percent decrease.
3. The ratio for the percent increase has a smaller denominator than the percent decrease.
Let's take these one at a time:
1. The amount of change is different for the percent increase and the percent decrease.
To calculate a percent change, you subtract the original amount from the new amount, and then divide that difference by the original amount. So when we increase from 45 to 75, the difference is 30. When we decrease from 75 to 45, the difference is also 30. However, the original amounts are different, so the percent changes are not going to be equivalent.
2. The ratio of the percent increase is not the same as the percent decrease.
Expanding on the previous point, the ratios are going to be different because for the percent increase, the denominator (original amount) is 45, but for the percent decrease, the denominator is 75. This naturally results in two different results when calculated.
3. The ratio for the percent increase has a smaller denominator than the percent decrease.
This is just reinforcing what was discussed in the previous point. The ratio's denominator for the percent increase is 45 and for the percent decrease, is 75. Smaller denominators result in larger fractions, so the percent change from 45 to 75 (increase) is going to be greater than the percent change from 75 to 45 (decrease).
Therefore, even though the actual amount change (30) is the same in both cases, the percent changes are not equivalent due to the differences in the initial amounts and the resulting ratios.
Hopefully, this provides a clear understanding of percent changes. Remember, a percent change is essentially a ratio that compares the change in an amount to the original amount.