Compatible numbers to estimate each difference 84-36 show me?


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Oddman answered
I would probably estimate the difference using 80 and 40, recognizing that I would have an error of 8 = 4 - (-4). These numbers are chosen by rounding to the nearest 10.

If I used 80 and 30, my error would be reduced to 2. These numbers are chosen by recognizing that 80 is less than 84, so a suitable compatible number for 36 will be the next multiple of 10 less than 36. By making both compatible number errors in the same direction for this subtraction problem, I reduce the error in the resulting estimate.

84 - 36
  = (80 + 4) - (30 + 6)    (the bold font indicates the "compatible numbers" I chose; the plain font indicates the error calculation)
  = (80 - 30) + (4 - 6)
  = 50 + (-2)
  = 48    (after error correction)

If I were doing an addition problem, I would choose the first set of compatible numbers (80, 40), because I want some positive errors and some negative errors to reduce the total error in my estimate.

The idea with compatible numbers is to simplify the problem. Computing the resulting error is a level of sophistication that comes later. However, if you cannot describe the error you have introduced, your answer cannot be trusted.

In my solution above, the problem is simplified by working with numbers that are multiples of 10. You could also recognize that changing the problem to 86 - 36 would simplify it as well. (As would changing it to 84 - 34.)  This is actually much easier, as it only requires changing one of the numbers by a small amount.

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