Category: Arithmetic
"Published in Vacaville, California, USA"
Divisibility by 11:
How
do you know that a number is divisible by 11? Well, a number is divisible by 11 if the difference of the two groups is a multiple of 11. Each group is the sum of the alternate digits of a given number.
Example 1:
The
first thing that we need to do is to inspect the given number if it is
divisible by 11 or not.
The first group of alternating digits is 2, 7, and 6 and the second group of alternating digits is 0 and 3.
Hence, the difference of the two group is
Since
the difference of the two groups is not a multiple of 11, then the given number is not
divisible by 11. There's a remainder of 1 in the division. The answer or a quotient must be a whole number itself. You should not have a fraction or a remainder in the final answer.
Example 2:
The
first thing that we need to do is to inspect the given number if it is
divisible by 11 or not.
The first group of alternating digits is 8, 5, and 7 and the second group of alternating digits is 0, 3, and 6.
Hence, the difference of the two group is
Since
the difference of the two groups is a multiple of 11, then the given number is divisible by 11. There's no remainder or a fraction in the division.
You
should consider in studying the divisibility of a number because you
will use these principles later when you will study higher Math subjects
that involves the division of a number, simplifying fractions, and even
factoring.
This
method can also be used for negative integers as long as the difference of the two groups of the sum of alternating digits of a given number is a multiple of 11. Again, there should be no remainder or a
fraction in the division.