Math - Single Digit Sum

An easy technique to reduce any number to a single digit sum

What does Single Digit Sum mean?

Any number (say 3456) to be equated to a single digit sum, we just add all the digits together (3+4+5+6 = 18) until they become a single digit (1+8=9). i.e. less than 10

What is this article trying to achieve?

This article explains a shortcut method to find the single sum for any number through a simple mind math.

The magic number 9

The shortcut method is that you can skip all the 9’s from the digits, also by excluding all the numbers that adds up to 9.

For example: 12789, Single Sum = (Skipping the digit 9) 1+2+7+8 => (because 1+8 is 9, skipping the digits 1 & 8) 2+7 => 9

Technique: Adding any number to 9 will result in a single sum of the added number.

9+3 = 3,

9+24 = 6,

9+9999 = 9,

and likewise.

If there are no easy 9's

If there are no numbers that easily adds up to 9 at a single glance (say 786), then start the manipulation by considering the number closest to 9 (number 8 in this case). Then to make it a 9 how much ever is the difference, subract that difference from the other digits and eventually make the calculation simpler (7+6-1 because 9-1=8), until you arrive at smaller numbers (-2+6-1 because 9-2=7) and ultimately the single sum (6–2–1=3).

So, 8 means subtract 1 from any other number, 7 means subtract 2 from any other number and so on.

Practise

As you practise this technique well, finding the single sum for even large numbers will look easy. Just be well versed with the numbers that adds to 9. i.e. 5+4, 6+3, 8+1, 7+2.

543=?

9321=?

12345=?

201305=?

9690194889=?

Kindly let me know if the article needs correction / improvement. TIA.

learner. seeker.