A test for checking computations is called casting out nines. Consider the sum 193 + 24 + 786 = 1003. The remainders when 193, 24, and 786 are divided by 9 are 4, 6, and 3, respectively. The sum of the remainders, 13, has a remainder of 4 when divided by 9, as does 1003. Checking the remainders in this manner provides a quasi-check for the computation. Find the following sums and use casting out nines to check the sums:
a. 12,343 + 4546 + 56
b. 987 + 456 + 8765
c. 10,034 + 3004 + 400 + 20
d. Try the check on the subtraction 1003 – 46
e. Try the check on the multiplication 345 # 56
f. Would it make sense to try the check on division? Why or why not?
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