Digit Sums have unique property: The operation done in any mathematical calculation (involving addition, subtraction and multiplication) is valid for the same operation when done on their digit sums.

In simple words, digit sums help to check if answers are right in case of addition, subtraction or multiplication.

For example:

digit sum

However, there is a situation when digit sums will give incorrect answers. If the number itself or result of the operation on the number is increased by 9 or any multiple of 9, or 0 is  replaced by 9, then also the digit sum does not change. This may give us incorrect answers.

For example,

digit sum-1

For below questions, solve and check using digit sums:

a. 765 x 12                    b. 983 x 2               c. 889 x 5                d. 796 x 11            e. 89 x 9

f. 9 + 4                           g. 94 + 10                h. 76 + 16                i. 8 + 102               j. 7 + 997