Casting out Nines
There are many little tricks in mathematics can make solving problems much easier. Casting out the 9s is one of the tricks can help make sure your answer is right much easier. Many people check the digit sum of the answers to make sure that their answers are correct. Casting out the 9s can make checking the answers and getting digit sums much easier.
Let’s start with Digit Sums. It is possible to take a number regardless of how big it is and transform it into a single digit. You can start with the number 15. In order to get it down to just one digit, you would add the two numbers together which would equal 6. This means that the digit sum of 15 is 6. It is also possible to do this with larger numbers such as 547. You would begin by adding 5 and 4 together which would be 9 then you would add 9 and 7 together which would be 16. However, you still got two digits so you would need to add 1 and 6 together which would be 7. With a bigger number such as 72546 you would add 7 and 2 which is 9 then 9 and 5 which is 14. 14 and 4 would equal 18 and finally 18 and 6 would equal 24. Finally, 2 plus 4 equals 6 so the digit sum of 72546 equals 6. This can be rather frustrating with larger numbers.
Thankfully, there is another way to shorten it down and make it easier.
Okay, now you’re probably wondering where casting out the 9s comes into play in this situation. When it comes to digit sums, it is possible to regard 9 as a 0. This basically means that you can cast out the 9s when working with digit sums. Then you would add the remaining digits together to get the digit sum. Let’s work with the numbers mentioned above. Let’s look at 547. 5 plus 4 is equal to 9. We can quickly eliminate these two numbers since they are equal to 9 when added together. Therefore, we are left with 7. This is the same answer we got above.
We just got with much easier and quicker when casting out the 9s. Okay, now let’s look at 72546 which was rather complicated to break down and get the digit sum earlier. 7 plus 2 is equal to 9 which can be casted out. 5 and 4 is also equaled to 9 and can also be casted out. This leaves us with 6 which is the same sum digit that we received using the more complicated method above.
