Subtraction 127
Th is is useful for calculating the numbers to write in the circles when
you are using 100 or 1,000 as reference numbers for multiplication.
It is also useful for calculating change.
Th e method taught in North American and Australian schools has
you doing exactly the same calculation, but you have to work out
what you are carrying and borrowing with each step. Th e benefi t of
this method is that it becomes mechanical and can be carried out
with less chance of making a mistake.
CHECKING SUBTRACTION BY CASTING OUT NINES
For subtraction, the method used to check answers is similar to
that used for addition, but with a small diff erence. Let’s try an
example.
8 4 6 5
- 3 8 9 6
4 5 6 9
Is the answer correct? Let’s cast out the nines and see.
8 4 6 5 5 - 3 8 9 6 8
4 5 6 9 6
Five minus 8 equals 6? Can that be right? Obviously not. Although
in the actual problem we are subtracting a smaller number from a
larger number, with the substitutes, the number we are subtracting
is larger.
We have two options. One is to add 9 to the number we are subtracting
from. Five plus 9 equals 14. Th en the problem reads:
14 – 8 = 6
Th is answer is correct, so our calculation was correct.