ffirs.indd

170 Speed Math for Kids
We divide by 5 and just use the remainder. Again, we are only working
with the units digits. Five divides once into 7 with 2 remainder; it
divides once into 8 with 3 remainder, and, just using the 6 of 56, we
see there is 1 remainder.
Does it check? Let’s see: 2 × 3 = 6 (which is the same as the units
digit of 56), and 6 has a fi ves remainder of 1, just like our check. Th e
problem with this is that 36, or even 41, would also have checked as
correct using this method.
Let’s try casting out sevens to check 9 × 8 = 72.
Nine and 8 have substitutes of 2 and 1, and 2 × 1 = 2. Two is our
check answer.
We can cast out the 7 from 72, as it represents seven tens (7 × 10),
which leaves us with 2. Our answer is correct. Casting out sevens was
a better check than casting out twos, tens or fi ves because it involved
all of the digits of the answer, but it is still too much trouble to be
useful. Casting out nines makes far more sense, but it is still fun to
experiment.
CASTING OUT NINES WITH
MINUS SUBSTITUTE NUMBERS
Can we use our method of casting out nines (substitute numbers)
to check a simple calculation like 7 times 8? Is it possible to check
numbers below 10 by casting out nines?
7 × 8 = 56
Th e substitutes for 7 and 8 are 7 and 8, so it doesn’t help us very
much.
Th ere is another way of casting out nines that you might like to play
with. To check 7 × 8 = 56, you can subtract 7 and 8 from 9 to get
minus substitute numbers.
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