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Delvig [45]
3 years ago
15

Prove that the sum of ab and ba is divisible by the sum of a and b

Mathematics
1 answer:
Likurg_2 [28]3 years ago
5 0

Answer:

It is divisible by 11 and (a + b) !

Step-by-step explanation:

Given a two digit number $ ab $, the digits written in reverse order is $ba $.

Note that a two digit number ab  = 10a + b.

For example: 24 = 10(2) + 4

Similarly, ba = 10(b) + a

Now, the sum of the numbers ab and ba = 10a + b + 10b + a

= 11a + 11b

= 11(a + b)

Hence, the sum of any two digit number ab and the reverse of the number ba,  is divisible by 11 and (a + b).

Hence, proved.

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