The difference of three-digit number and the number obtained by putting the digits in reverse order is always divisible by 9 and___________. Fill in the blank to make the statement true
Solution:
Let the three digit number be abc where a, b, and c are the digits in the same hundreds, tens and ones places respectively.
When abc is reversed the number becomes cba and the digits c, b and a are in the hundreds, tens and ones places respectively.
abc = 100a + 10b + c
cba = 100c + 10b + a
Therefore,
abc - cba = 100a - a + b - b + c - 100c = 99a - 99c = 99(a - c)
Since 99 is divisible by 9 and 11 it can be concluded that the difference of the two three digit numbers is divisible by 9 and 11.
✦ Try This: If the three digit number cab is subtracted from abc then the resultant number will be divisible by ___________
The number abc can be written as:
100a + 10b + c
The number cab can be written as:
100c + 10a + b
Therefore,
abc - cab = 100a + 10b + c - (100c + 10a + b) = 90a + 9b - 99c = 9(10a + b - 11c)
Hence we can say that the difference of abc and cab is always divisible by 9.
If the three digit number cab is subtracted from abc then the resultant number will be divisible by 9 only.
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 16
NCERT Exemplar Class 8 Maths Chapter 13 Problem 23
The difference of three-digit number and the number obtained by putting the digits in reverse order is always divisible by 9 and___________. Fill in the blank to make the statement true.
Summary:
The difference of three-digit number and the number obtained by putting the digits in reverse order is always divisible by 9 and 11.
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