I want to get clarified with numbers ending with 9. I have considered 2 digit numbers and not extending it further as of now.

```
If we have 2 digit numbers of the form 10a + b and ending with 9,
```

Then, \(ab + a+b= 10a+b \).

I want to get clarified with numbers ending with 9. I have considered 2 digit numbers and not extending it further as of now.

```
If we have 2 digit numbers of the form 10a + b and ending with 9,
```

Then, \(ab + a+b= 10a+b \).

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TopNewestI assume that \(a\) is a single digit positive integer and \(b\) is a non-negative single digit integer, then obviously \(b=9\) and so your equation holds true. – Pi Han Goh · 7 months, 2 weeks ago

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– Ashwin K · 7 months, 2 weeks ago

Yes..I considered only 2 digit numbers. I need to know how it works!Log in to reply

– Pi Han Goh · 7 months, 2 weeks ago

After you know that \(b=9\), what happens when you substitute \(b=9\) into the equation \(ab + a +b = 10a + b\)?Log in to reply

For instance a =1, the equation becomes 1*9 + 1 + 9 = 19 = 10(1) + 9 = 19. – Ashwin K · 7 months, 2 weeks ago

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I asked you to substitute \(b=9\) alone only, nothing else. What happens to the equation \(ab+ab+b=10a+b\) after you substitute \(b=9\)? – Pi Han Goh · 7 months, 2 weeks ago

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– Ashwin K · 7 months, 2 weeks ago

Got you. both side equations are becoming equal. Can we extend this for 3 digit numbers. Do u have any idea?Log in to reply

– Pi Han Goh · 7 months, 2 weeks ago

Hmmm, yes we can, by assuming your last digit is already given, then you can make up any equation as you like. But I doubt any of these identity are useful, because it is too specific and are not applicable in the first place.Log in to reply

– Ashwin K · 7 months, 2 weeks ago

9 always been a magic number. Knowing it's property will always be handy. I made up this note after solving a problem of this kind.Log in to reply

– Pi Han Goh · 7 months, 2 weeks ago

No, it's not. What is so special about 9?Log in to reply

– Ashwin K · 7 months, 2 weeks ago

It is magical number because we consider base 10 in our number system and thus last number '9' has to be Special. In general, last digit in that number system will carry special properties.Log in to reply

– Pi Han Goh · 7 months, 2 weeks ago

That made no sense, I could call the number 8 special because "the second last number '8' has to be special".Log in to reply

– Ashwin K · 7 months, 2 weeks ago

There are interesting properties on it buddy. This is not my judgement. I think I am not convincing you. Just Google it for yourselves and check.Log in to reply

– Pi Han Goh · 7 months, 2 weeks ago

The number 8 also has interesting properties.Log in to reply

– Ashwin K · 7 months, 2 weeks ago

Wow..let me know that.Log in to reply

application of divisibility rules. – Pi Han Goh · 7 months, 2 weeks ago

Read upLog in to reply

– Ashwin K · 7 months, 2 weeks ago

Cool..I agree all numbers got it's own properties.Log in to reply