Name the compatible numbers used to find the estimate.

1. 725/19 estimate:35

2. 3,641/34 estimate:120

Please show me how to work out these problems.

first one: what is 700/20 ?

second one: what is 3600/30?

Thank you!

To find compatible numbers for estimating, you need to identify numbers that are easy to work with mentally and close to the given numbers. Here's how you can find compatible numbers for the two given problems:

1. 725 ÷ 19 estimate: 35
Compatible numbers can be chosen based on the nearest multiples of 19. You can start by finding a multiple of 19 close to 725. Since 19 × 38 = 722, you can use 38 as a compatible number.
Now, divide 722 by 38 to verify your compatible number:
722 ÷ 38 = 19
Since the division result closely matches the estimate of 35, we have found compatible numbers.

2. 3,641 ÷ 34 estimate: 120
For this problem, you can choose a multiple of 34 closest to 3,641. The closest multiple is 34 × 107 = 3,638. Hence, you can take 107 as a compatible number.
Now divide 3,638 by 107 to check the compatibility:
3,638 ÷ 107 ≈ 34
The division result of approximately 34 matches the estimate of 120, so 107 can be considered a compatible number.

It's important to note that compatible numbers may result in an approximation and might not yield an exact answer, but they can be helpful in quickly estimating calculations mentally.