ffirs.indd

Checking Your Answers 41
Th is method won’t fi nd all mistakes. For instance, say we had
3,789,360 for our last answer; by mistake we put a 0 on the end.
Th e fi nal 0 wouldn’t aff ect our check by casting out nines and
we wouldn’t know we had made a mistake. When it showed we
had made a mistake, though, the check defi nitely proved we had
the wrong answer. It is a simple, fast check that will fi nd most
mistakes, and should get you 100% scores on most of your math
tests.
Do you get the idea? If you are unsure about using this method
to check your answers, we will be using the method throughout
the book so you will soon become familiar with it. Try it on your
calculations at school and at home.
Why does the method work?
You will be much more successful using a new method when you
not only know that it does work, but you understand why it works
as well.
First, 10 is 1 times 9 with 1 remainder. Twenty is 2 nines with 2
remainder. Twenty-two would be 2 nines with 2 remainder for the
20 plus 2 more for the units digit.
If you have 35¢ in your pocket and you want to buy as many candies
as you can for 9¢ each, each 10¢ will buy you one candy with 1¢
change. So, 30¢ will buy you three candies with 3¢ change, plus the
extra 5¢ in your pocket gives you 8¢. So, the number of tens plus
the units digit gives you the nines remainder.
Second, think of a number and multiply it by 9. What is 4 × 9? Th e
answer is 36. Add the digits in the answer together, 3 + 6, and you
get 9.
Let’s try another number. Th ree nines are 27. Add the digits of the
answer together, 2 + 7, and you get 9 again.