We can use estimation to check multiplication problems for reasonableness because it will give us a "roundabout" answer that should be close to the correct one. For example, if we have 15 times 18, then the final answer should be 270:
To make sure this is reasonable, we can round one of the numbers to a close number that will make the answer close to the correct one:
`15*20=300 ` In this case, we rounded 18 to 20 since 15*20 was a simple problem that we could probably do in our heads. But since we rounded up from 18 to 20, this answer should be just a little bit bigger than the correct original one.
Let's look at a more complex example:
If we have 723*998, the result should be 721,554
We can round 998 to 1,000 and do a simple calculation in our head:
`723*1000=723,000 ` Since we rounded up from 998 to 1,000, this new answer should just be a little bit larger than the correct answer. Since we added 2 to get from 998 to 1,000, this new answer should just be the result of 723 times 2 larger than the correct answer. Since 723*2 is about 1,500, and our new answer (723,000) is pretty close to 1,500 more than the original (721,554) we could say that after using this estimation, that this answer is reasonable.