Why is the sum of multiples of 9 9?

The main thing that the digits of multiples of 9 add up to 9 because we use a base-10 system. First, let’s take 9 and re-write it as 09. When we add a 9, the value of the 10’s place will go up by 1, but the value of the one’s place will go down by 1 because there wasn’t a “complete 10 for the 9.”

Why is 9 magic number?

The number 9 is revered in Hinduism and considered a complete, perfected and divine number because it represents the end of a cycle in the decimal system, which originated from the Indian subcontinent as early as 3000 BC. In the Christian angelic hierarchy there are 9 choirs of angels.

How do you check if a number is a multiple of 9?

The most simple way to check for n’s divisibility by 9 is to do n\%9. Another method is to sum the digits of n. If sum of digits is multiple of 9, then n is multiple of 9.

What happens when you add 9 to a number?

When you add 9 to a number, if the 1’s place digit is 0, you add 9 to the sum (ex., 40 summed is 4, 40+9=49 which when summed is 4+9). For integers, this is always the case. The sum of the digits of any multiple of nine (other than zero) equals another multiple of 9, and repeated summing of digits eventually leads to 9.

How do you find the sum of the digits added to 9?

Take 9 and add any number to it. What you have observed: The sum of the digits of the number added to 9 is always equal to the sum of the digits of the result. Take any four digit number and try the trick.

What happens when you add two multiples of 9?

So whenever you add 9 to a number, the sum can only change by a multiple of 9. Through the distributive property, when you add or subtract two multiples of 9, the result is also a multiple of 9. For numbers 10 and larger, summing the digits results in a smaller number (ex., 35 summed is 3+5<35).

What is the sum of the digits of the difference?

You see how fascinating and enjoying it is. In each case the difference is divisible by 9 (i.e. the common factor is 9) and the sum of the digits of the difference is always 9. Do you think this will also work for three digit number or four-digit number.