Question

Which is another way to check the sum of 104+34+228+877?

Answer 1

A simple method of checking the sum of arithmetic problems is by using the "digit sum" method. The digit sum can be obtained by adding the digits of a number together, until you get a single-digit number. In case you get a double-digit number, just add them again until you get a single digit number.

Let's try it with an example.

Given the numbers 143, 876, and 534, their digit sums would be:
144 : 1 + 4 + 3 = 9 (same as 0)
876 : 8 + 7 + 6 = 21; 2 + 1 = 3
534 : 5 + 3 + 4 = 12; 1 + 2 = 3

Getting the digit sum is actually getting the number modulo 9, which in other words, is the remainder of that number divided by 9. Since you now have an understanding of the digit sum, how can it be used to check the sum of the problem above?

By comparing the sum of the digit sums of the addends and the digit sum of the obtained sum, you can determine if the arithmetic process was done correctly. Let us do this below:

104 + 34 + 228 + 877 = 1243

Using the digit sum method:

104 : 1 + 0 +4 = 5
34 : 3 + 4 = 7
228 : 2 + 2 + 8 = 12; 1 + 2 = 3
877 : 8 + 7 + 7 = 22; 2 + 2 = 4

adding the digit sums of the addends:

5 + 7 + 3 + 4 = 19; 1 + 0 = 1

Comparing with the digit sum of the sum (1243):

1 + 2 + 4 + 3 = 10; 1 + 0 = 1 (OK)

As we can see, the digit sums are the same, so we can say that the arithmetic process has been done correctly.