Final answer:
To estimate 1,578 divided by 42 using compatible numbers, one can use the numbers 1,600 and 1,560 divided by 40, resulting in estimates of 40 and 39, respectively.
Step-by-step explanation:
To estimate 1,578 divided by 42 using compatible numbers, we want to choose numbers that are close to the actual numbers but easier to divide. A good estimate for 42 is 40 because 40 is a multiple of 10, which makes it easier to divide. So, for the first estimate, let's use 1,600 (which is close to 1,578 and also a multiple of 40) divided by 40. For the second estimate, we can choose 1,560 (also a multiple of 40 and slightly less than 1,578) divided by 40.
First Estimate: 1,600 divided by 40 equals 40.
Second Estimate: 1,560 divided by 40 equals 39.
Both estimates provide us with reasonable approximations for 1,578 divided by 42, which can be helpful in mental calculations or when a calculator is not available.