ffirs.indd

Checking Your Answers 35
Mathematicians have known this method of checking answers for
about 1,000 years, although I have made a small change I haven’t seen
anywhere else. It is called the digit sum method. I have taught this
method of checking answers in my other books, but this time I am
going to teach it diff erently. Th is method of checking your answers
will work for almost any calculation. Because I still make mistakes
occasionally, I always check my answers. Here is the method I use.
SUBSTITUTE NUMBERS
To check the answer to a calculation, we use substitute numbers
instead of the original numbers we were working with. A substitute
on a football team or a basketball team is somebody who takes
another person’s place on the team. If somebody gets injured, or
tired, they take that person off and bring on a substitute player.
A substitute teacher fi lls in when your regular teacher is unable to
teach you. We can use substitute numbers in place of the original
numbers to check our work. Th e substitute numbers are always low
and easy to work with.
Let me show you how it works. Let us say we have just calculated
12 × 14 and come to an answer of 168. We want to check this
answer.
12 × 14 = 168
Th e fi rst number in our problem is 12. We add its digits together to
get the substitute:
1 + 2 = 3
Th ree is our substitute for 12. I write 3 in pencil either above or
below the 12, wherever there is room.
Th e next number we are working with is 14. We add its digits:
1 + 4 = 5