why if we want to know if a number is divisible by 3 we add it's digits and if the sum of them is divisible by 3, the whole number will be too? for example 351 the sum of its digits is 9 so we say the whole number is divisible by 3.I mean I want a prove or reason of why we add them to know thought it is division .please help me please or I'll get mad of thinking.
2006-11-11 04:12:44 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
With all good things like this you need to state the obvious first.
A number divides by 3 if the remainder is zero if it divides by 3.
For numbers less than 10 this is obviously 3,6 and 9.
Look at remainders of 10,20 and 30 when divided by 3. 1,2 and zero respectively. Also notice that if you add two numbers together then to find the remainder when divided by three you only need to add remainders. So for example13 can be written as 10 + 3. Looking only at remainders this is 1+0 =1 so the remainder when 13 is divided by 3 is 1. You can reduce a number by 30 without affecting the remainder so higher numbers such as 50 can be reduced by 30 without affecting the remainder. So you can see how numbers below 100 can be checked this way.
Next notice that a number whose leading digit is one followed by zeros must have remainder 1 when divided by 3. Take one from this number to get a digit whose numbers are all 9 and this is obviously divisible by 3. This fact allows us to extend the reasoning we went through for 10, 20 etc to all higher numbers.
This explanation may be a bit hard going but hopefully it will be some sort of inspiration for your understanding.
2006-11-11 05:42:55 · answer #1 · answered by crazy_tentacle 3 · 0⤊ 0⤋
it is a math law... and also you can give examples to prove it, right? when the sum is divisible by 3, the whole number wil be devisible, all of the right examples will work. I know how to prove divisibility by7, 9 or 11, but not by 3!!!
2006-11-11 12:16:44 · answer #2 · answered by (^_^) CHiccaaqui(^_^) 4 · 0⤊ 0⤋
It is called the divisibility rules
2006-11-11 12:16:48 · answer #3 · answered by Anonymous · 0⤊ 0⤋
Sometimes to prove something, you try it and if it works it is right! Science and maths works a lot like this, you make an assumption and try to disprove it, if it works every time then you can assume that it is right.
2006-11-11 12:50:15 · answer #4 · answered by Mark G 2 · 0⤊ 0⤋
I dont know but I wonder who stayed up for days trying all the numbers to see if that was true.
OR maybe they were just really board in class.
2006-11-11 12:16:21 · answer #5 · answered by ellenrose219 3 · 0⤊ 1⤋
what?
2006-11-11 12:15:38 · answer #6 · answered by Anonymous · 0⤊ 0⤋