ffirs.indd

Checking Answers (Division) 169
BONUS: CASTING OUT TWOS, TENS AND FIVES
Just as it is possible to check a calculation by casting out the nines,
you can cast out any number to make your check.
Casting out twos will only tell you if your answer should be odd or
even. When you cast out twos, the only substitutes possible are 0
when the number is even and 1 when the number is odd. Th at is
not very helpful.
When I was in primary school I sometimes checked answers by
casting out the tens. All that did was check if the units digit of the
answer was correct. Casting out the tens means you ignore every
digit of a number except the units digit. Again, it is not very useful,
but I did use it for multiple-choice tests where a check of the units
digit was sometimes enough to let me recognize the correct answer
without doing the whole calculation.
Let’s try an example. Which of these is correct?
34 × 72 =
a) 2,345 b) 2,448 c) 2,673 d) 2,254
Multiplying two even numbers can’t give an odd number for an
answer. (Th at is casting out twos.) Th at eliminates a) and c). To
check the other two answers, we multiply the units digits of our
problem together and get an answer of 8 (4 × 2 = 8). Th e answer
must end with 8, so the answer must be b).
Casting out fi ves is another option. For the calculation above, the
substitute numbers would be exactly the same. But it can have its
uses for checking multiplication by small numbers.
Let’s try 7 × 8 = 56 as an example.
Casting out fi ves, we get 2 × 3 = 1.
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