Question

Why can you tell that a digit is divisible by 9 if the digits add up to 9?

Answer 1

because we write out numbers in base ten

Answer 2

for example the number 324 means \(3\times 10^2+2\times 10+4\)
if you divide \(300\) by \(9\) the remainder is \(3\) because \(9\) goes in to \(100\) 11 times with a remainder of 1, and so it goes in to \(300\) 33 times with a remainder of 3
9 goes in to 10 one time with a remainder of 1, and so it goes in to 20 2 times with a remainder of 2
9 goes in to 4 no times with a remainder of 4
so the remainder when you divide 324 by 9 is \(3+2+4=9\) and a remainder of 9 is the same as a remainder of 0