Addition of Two Numbers in Case One of the Numbers Ends With Repeated 9s or 8s 

You can add two numbers in your mind without doing much effort from your side if you see one of them has repeated 9s or 8s.               

Example : – a)  98765+999 =?                                              b)  78976+9998 = ?

Rule : – Round off one of the number into multiple of 10s and do the balancing act.

Solution : – 98765+999                                                        -1|     |+1                                                           = 98764   1000                                              =98764+1000= 99764

Example : – 78976+9998 = ?                             

Solution : – 78976+9998                                                     -2 |       |+2                                                    = 78974    10000                                              =  78974+10000= 88974

Here I discuss a variety of math tricks and math skill so you are join my site to learn variety math tricks addition, subtraction, multiplication and division tricks are there.

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 digit 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:-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

When adding two numbers where one of them ends with repeated 9s or 8s, there is a special consideration to keep in mind. Let’s explore each case separately:

1. Addition when one number ends with repeated 9s: When adding a number that ends with repeated 9s (e.g., 19, 29, 99, etc.), there is a possibility of carrying over a digit to the left. Here’s a step-by-step process:

   a. Align the numbers: Write down the two numbers, aligning them vertically based on their place values (ones, tens, hundreds, etc.).

   b. Begin the addition: Start adding the digits from the rightmost column (the ones column). If the digits sum up to a value less than 9, write down the sum in the result column.

   c. Carry over: If the sum of the digits in the ones column is 9 or greater, write down the ones digit of the sum and carry over the tens digit to the next column.

   d. Continue adding: Proceed to the next column (tens column) and add the carried-over value (if any) to the sum of the digits in that column. Repeat the process of carrying over if necessary.

   e. Repeat the process: Continue adding and carrying over, if needed, until you have added all the columns.

   f. Write the final sum: Once you have added all the columns, write down the final sum as the result.

2. Addition when one number ends with repeated 8s: The process is similar to the case of repeated 9s, but with a slight difference. When adding a number ending in repeated 8s (e.g., 18, 28, 88, etc.), the sum of the ones digit will always be 10. Here’s the step-by-step process:

   a. Align the numbers: Write down the two numbers, aligning them vertically based on their place values (ones, tens, hundreds, etc.).

   b. Begin the addition: Start adding the digits from the rightmost column (the ones column). Write down the sum of the digits in the ones column as 0 and carry over the tens digit to the next column.

   c. Carry over: Proceed to the next column (tens column) and add the carried-over value (which will be 1) to the sum of the digits in that column. Repeat the process of carrying over if necessary.

   d. Repeat the process: Continue adding and carrying over, if needed, until you have added all the columns.

   e. Write the final sum: Once you have added all the columns, write down the final sum as the result.

By following these steps, you can accurately perform addition when one of the numbers ends with repeated 9s or 8s. Remember to take care when carrying over and ensure that you correctly add all the digits in each column.