Mathematics ACT Aspire Practice Test

If there are M ways to do one thing and N ways to do another, how many ways are there to do both?

1. M + N

2. M - N

3. M * N

4. M / N

The correct answer is: M * N

When considering the number of ways to perform two distinct tasks, the correct approach is to multiply the number of ways of doing each task. If there are M ways to complete the first task and N ways to complete the second task, then for each way of doing the first task, there exist all N ways of performing the second task. This can be visualized as follows: if you choose one of the M methods for the first task, you can pair it with any of the N methods for the second task. Therefore, the total combinations of completing both tasks are calculated as M * N. The logic behind the other options does not apply to this situation. Adding the ways (M + N) would only give the total number of ways to do one task or the other, but not both in combination. Subtracting the ways (M - N) does not have a mathematical basis for this scenario and would not yield a relevant count. Division (M / N) represents a completely different relationship, typically used to determine how many times one quantity is contained within another, which doesn't fit here. Thus, multiplying the number of ways to perform each task gives the total number of ways to do both tasks, reinforcing why multiplication is the