Addition of Similar Digits Repeated

Addition of similar digits with digits repeated in ascending order sometimes creates problem as you have to arrange them according to their place value before adding. Let me simplify this problem to make such addition a child's play.

Example: 5 + 55 + 555 =?

Rule: a) Take the digit repeated and replace all the repeated digits with 1

b) Count number of digits in each number.

c) Multiply the result 123… by the repeated digit.

Solution: a) Take 5 common and replace all 5 with 1 5 (1 + 11 + 111)

b) Count number of digits in each number. Here the digit 1 has been repeated 1, 2 and 3 times.

c) Multiply 123 by 5

Hence, 5 + 55 + 555 = 5 × 123 = 615

Example: 5 + 55 + 555 + 5555 + 55555 =?

Solution: a) Take 5 common and replace all 5 with 1 5 (1 + 11 + 111 + 1111 + 11111)

b) Count number of digits in each number. Here the digit 1 has been repeated 1, 2, 3, 4 and 5 times.

c) Multiply 12345 by 5

Hence, 5 + 55 + 555 + 5555 + 55555 = 5 × 12345 = 61725

Example: 9 + 99 + 999 + 9999 + 99999 + 999999 =?

Solution: a) Take 9 common and replace all 9 with 1

9 (1 + 11 + 111 + 1111 + 11111 + 111111)

b) Count number of digits in each number. Here the digit 1 has been repeated 1, 2, 3, 4, 5 and 6 times.

c) Multiply 123456 by 9

Hence, 9 + 99 + 999 + 9999 + 99999 + 999999 = 9 × 123456 = 1111104.