ffirs.indd

Checking Answers (Division) 171
Seven is 9 minus 2 and 8 is 9 minus 1, so our substitute numbers
are –2 and –1. So long as they are both minus numbers, when you
multiply them you get a plus answer, so you can treat them as simply
2 and 1.
Let’s check our answer using the minus substitutes.
7 × 8 = 56
2 1 2
Th is checks out. Our substitute numbers, 2 and 1, multiplied give
us the same answer as our substitute answer, 2.
If you weren’t sure of the answer to 7 × 8, you could calculate the
answer using the circles, or you can cast out the nines to double-check
your answer.
You can have fun playing with this method. Let’s check 2 × 8 = 16.
Th e minus substitutes are 7 and 1. Seven times 1 is 7. Seven is our
check answer. Th e real answer adds to 7 (1 + 6 = 7), so our answer
is correct.
Every number has two substitutes when you cast out the nines—a
plus and a minus substitute. Th e number 25 has a positive substitute
of 7 (2 + 5 = 7) and a negative substitute of –2 (9 – 7 = 2).
Let’s try it with 8 × 8 = 64.
Eight is 9 minus 1, so –1 is our substitute for 8.
Th e substitute for 64 is 6 + 4 = 10; then, 1 + 0 = 1.
8 × 8 = 64
1 1 1
Th is only has a limited application, but you can play and experiment.
You could use it to check a subtraction where the substitute for
the number you are subtracting is larger than the number you are
cc17.indd Sec1:171 17 .indd Sec 1 : 171 1/9/07 8:40:53 AM 1 / 9 / 07 8 : 40 : 53 AM