Checking Answers (Division) 167
To check the answer to the problem 578 ÷ 17 = 34, we would use
substitute numbers.
578 ÷ 17 = 34
20 8 7
2
Substituting, we have 2 ÷ 8 = 7. Th at doesn’t make sense. So, we do
the calculation in reverse. We multiply: 7 × 8 = 2. Does 7 times 8
equal 2 with our substitute numbers?
7 × 8 = 56
5 + 6 = 11
1 + 1 = 2
Seven times 8 does equal 2; our answer is correct.
Handling remainders
How would we handle 581 ÷ 17 = 34, with 3 remainder? We would
subtract the remainder from 581 to make the calculation correct
without a remainder. We could either subtract the remainder fi rst to
get 578 ÷ 17 = 34, which is the problem we already checked, or we
do it in the casting out nines, like this:
(581 – 3) ÷ 17 = 34
Reversed, this becomes 17 × 34 = 581 – 3.
Writing in the substitutes, we get:
17 × 34 = 581 – 3
8 7 5 3
Or, 8 × 7 = 5 – 3.
8 × 7 = 56
5 + 6 = 2
5 – 3 = 2
cc17.indd Sec1:167 17 .indd Sec 1 : 167 1/9/07 8:40:53 AM 1 / 9 / 07 8 : 40 : 53 AM
brent
(Brent)
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