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Verifying the Outcome

After solving a problem, it can often be useful to make sure you have the correct answer, and didn't make any silly mistakes. You don't want to simply repeat the solution using the same method, since you might repeat the same mistake. It is best to verify your answer through a different technique than originally used to solve the problem.

 
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In addition and subtraction we verify the outcome using estimation (obtained by rounding).

Example 1:   660 + 880 = 1540

First pass estimate:

660 is rounded to 700
880 is rounded to 900

Therefore, the estimate is 700 + 900 = 1600.

Refining the estimate:

660 was rounded up by 40
880 was rounded up by 20

Amount of rounding = 40 + 20 = 60 (greater than 50)

Therefore, subtract 100 from the estimate to eliminate some of the rounding error.

A closer estimate would be 1600 - 100 = 1500.

Example 2:

We know that division and multiplication are inverse operations.

            132 ÷ 2 = 66 can be verified by 2 × 66 =132;

            24 ÷ 3 = 8 can be verified by 3 × 8 =24;

So, we verify the outcome of a problem or experiment by using the inverse operation from that originally used to solve the problem.

 
 
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