ffirs.indd

Using the Methods in the Classroom 205
Had you found you had made a mistake, you could cast out nines to
fi nd where you made it. You would fi nd the substitute number for
each part of the calculation. It would look like this.
355 4
× 52 7
710 8
17,750 20 2
18 ,460 10 1
To check, you would use the substitutes like this. First 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
Th e 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 fi nal 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 important, once you earn a reputation for being mathematically
gifted, no one will worry about your methods—they will expect you
to be diff erent.
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