Patterns in numbers
Cast out nines from a given number to check if it is a multiple of nine.
Example
Is 46908 multiple of 9?
$$ 46908 = 4 + 6 + 0 + 8 $$
$$ = 18 $$
$$ = 1 + 8 $$
$$ = 9 $$
Let us Know
Any number or combination of digits in that number which add to 9 can be cast out from the given number. Then the sum of remaining digits of the number is divisible by 9 or multiple of 9.
Addition Check
In addition problem, we can check the sum by casting out nines.
Example 1
Check the following numbers whether it is a multiple of 9 or not
1. 24689
$$ 24689 = 2 + 4 + 6 + 8 = 20 $$
(It's not a multiple of 9.)
2. 9108
$$ 9108 = 0 $$
(It's a multiple of 9.)
3. 3165
$$ 3165 = 1 + 5 = 6 $$
(It's not a multiple of 9.)
Example 2
Check the addition fact
$$ 3356 + 4729 = 8085 $$
$$ 8 + 4 = 21 $$
$$ 12 = 21 $$
$$ 1 + 2 = 2 + 1 $$
$$ 3 = 3 $$
Subtraction Check
In subtraction problem, we can check the difference by casting out nines method.
(Remember that subtraction is nothing more than addition in reverse).
Example
$$ 4897 - 2186 = 2711 $$
$$ 19 - 8 = 2 $$
$$ 10 - 8 = 2 $$
$$ 2 = 2 $$
Let us Know
Think of a two digit number say 52, then subtract the reverse of its digits, 25 from 52.
$$ \text{Difference} = 52 - 25 = 27 $$
27 is a multiple of 9.
Activity
