Best Answer

Suppose the two digits of the first number are x and y where 0<=x,y<10.

[Strictly speaking, if it is a two digit number then x>0, but the proof still works.]

Then the first number is 10x + y

and the second number, therefore, is 10y + x

Taking the second number away from the first gives: (10x + y) - (10y + x)

= 10x + y - 10y - x = 9x - 9y = 9(x-y)

Now, since x and y are integers, x-y must be an integer.

That is, the result of the subtraction is 9*an integer ie it is a multiple of 9.

Q: How do you prove algebraically that if you write down a two-digit number then reverse the order of the digits and take it away from the first number that you end up with a multiple of 9?

Write your answer...

Submit

Still have questions?

Continue Learning about Other Math

If the sum of the digits of a given number equals nine or a multiple of nine, nine is a factor of that number.

34.

By 'after 8000' it looks like 'greater than 8000' is what you want.So to get multiple of 4, last 2 digits must be a multiple of 4. {This is because 100 and every multiple of 100 are multiples of 4, so you only have to look at the last two digits}.For multiple of 9, digits must sum up to 9 (or multiple of 9). So 8001 sums up to 9, but it's not multiple of 4. 8010 doesn't work either. So let's look at digits sum to 18. We already have 8, so the last 2 digits sum to 10 would work, and the last 2 digits multiple of 4:19 : 1+9 = 10, but not multiple of 4.28 : 2+8 = 10, and yes it's a multiple of 4.8028 is the answer.

Yes.A number is divisible by 9 if the sum of the digits is a multiple of 9.18324 = 1 + 8 + 3 + 2 + 4 = 18 (18 is a multiple of 9)A number is divisible by 4 if the last two digits is a multiple of 4.18324 = the last two digits are 24 & it is a multiple of 4.18324 ÷ 9 = 203618324 ÷ 4 = 4581

The sum of the digits is also a multiple of 9. And, if the sum of the digits is too large, you can sum those digits and keep going.

Related questions

63

72 reverse the digits divide by 3 = 24

Yes, yes, and no. 3- sum of digits must be multiple of 3. 6- sum of digits must be multiple of 3 and number must be even (multiple of 2). 9- sum of digits must be multiple of 9. (The sum of the digits here is 21.)

22

Yes If a numbers last two digits (assuming that it has at least two) is a multiple of 4, the whole number is also a multiple of 4. If the last two digits are 00 (assuming in this case it has at least three digits), the number is also a multiple of 4. For example, 100 and 200 are multiples of 4.

A number is divisible by 3 if the sum of its digits is a multiple of 3. A number is divisible by 6 if the sum of its digits is a multiple of 3 and it's even. A number is divisible by 9 if the sum of its digits is a multiple of 9.

231

No factor of 9 has three digits. 450 is a three-digit multiple of 150 (and of 9) with a digit sum of 9.

If the sum of the digits of a given number equals nine or a multiple of nine, nine is a factor of that number.

34.

16

No