Numbers that are close to the original numbers but easier to add are called compatible numbers.
One way to find compatible numbers is to round.
295 rounded to the nearest 10 or 100 is 300. That estimate is off by 5 ones.
112 rounded to the nearest 10 is 110. That estimate is off by 2, but in the opposite direction from our other estimate.
All together the estimate is only 3 ones away from the actual sum.
Instead of rounding, you can adjust the numbers to be easier to work with. These are called compatible numbers.
Exact:
$625 + $239 = $864
Adjust $239 to $240:
$625 + $240 = $865
- This strategy is even more accurate than rounding to the nearest ten.
- $625 is already easy to work with.
- Adjusting $239 up by $1 gives us an estimate that is just $1 more than the exact answer.
Example #1
Use compatible numbers to find the sum 356 and 224.
If we make compatible numbers by rounding, we might make an estimate of 360 + 220 = 580, which is also our exact answer!
Example #2
Micaville Elementary is having an assembly for their kindergarten through 3rd grade parents. 245 parents have signed up for kindergarten & 1st grade, and 269 parents have signed up for 2nd & 3rd grade. If the principal wants to buy donuts for the parents, about how many should he buy?
245 + 270 = ?
This problem requires regrouping in the ones and tens places. One way to make compatible numbers would be to adjust 269 up to 270.
245 + 270 = 515
There are many ways to make these into compatible numbers.
We can adjust 269 up to 300 and take 30 away from 245.
215 + 300 = 515
Making compatible numbers is your choice.
Remember to think about the accuracy of your estimate.
Practice Problems
How important is an accurate estimate for this problem?
Round to the nearest hundred to solve the word problem.
Will we get a good estimate if we use the compatible numbers 350 and 250 to solve this problem?
