To check, you would use the substitutes like this. Firstly you multiplied 355 by 2 to get 710. Now you
multiply the substitute.
4 × 2 = 8
Our substitute answer is 8, so this part of the calculation is correct.
Next, we multiplied 355 by 5 (or 50) to get 17,750. Multiply the substitutes again.
5 × 4 = 20
The substitute answer is the same, so you can accept this part of the calculation as correct.
Next you added 710 and 17,750 to get your final answer of 18,460. We add the substitutes of 8 + 2 =
10, and this checks with your calculation. In this case your answer is correct but, if you had made a
mistake, you not only would have found it, but you would also know where you made it. You would
know if the mistake was in the multiplication, and which part, or if the mistake was in the addition.
I would make these checks with pencil and then erase them.
In practice, I think any teacher would be intrigued by your method of checking. I have never heard of
these methods causing problems for students in the classroom.
Most importantly, once you earn a reputation for being mathematically gifted, no-one will worry
about your methods — they will expect you to be different.