Chapter 4.1A, Problem 18A

A test for checking arithmetic calculations 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 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. Try the check on the subtraction $1003-46$.

d. Try the check on the multiplication $345\cdot 56$.

e. Would it make sense to try the check on division? Why or why not?