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casting out nines. Pamela Leutwyler. 9 goes into 36 four times with remainder 0. 3 + 6 = 9. 9 goes into 36 four times with remainder 0. 3 + 6 = 9. 9 goes into 99 eleven times with remainder 0. 9 + 9 = 18 1 +8 = 9. 9 goes into 36 four times with remainder 0. 3 + 6 = 9. - PowerPoint PPT Presentation
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Pamela Leutwyler
9 goes into 36 four times with remainder 0. 3 + 6 = 9
9 goes into 36 four times with remainder 0. 3 + 6 = 9
9 goes into 99 eleven times with remainder 0. 9 + 9 = 18 1 +8 = 9
9 goes into 36 four times with remainder 0. 3 + 6 = 9
9 goes into 99 eleven times with remainder 0. 9 + 9 = 18 1 +8 = 9
The sum of the digits of a multiple of 9 is 9 (or a multiple of 9).
9 goes into 36 four times with remainder 0. 3 + 6 = 9
9 goes into 99 eleven times with remainder 0. 9 + 9 = 18 1 +8 = 9
The sum of the digits of a multiple of 9 is 9 (or a multiple of 9).
9 goes into 29 three times with remainder 2. 2 + 9 = 11 1 +1 = 2
9 goes into 36 four times with remainder 0. 3 + 6 = 9
9 goes into 99 eleven times with remainder 0. 9 + 9 = 18 1 +8 = 9
The sum of the digits of a multiple of 9 is 9 (or a multiple of 9).
9 goes into 29 three times with remainder 2. 2 + 9 = 11 1 +1 = 2
9 goes into 49 five times with remainder 4. 4 + 9 = 13 1 +3 = 4
9 goes into 36 four times with remainder 0. 3 + 6 = 9
9 goes into 99 eleven times with remainder 0. 9 + 9 = 18 1 +8 = 9
The sum of the digits of a multiple of 9 is 9 (or a multiple of 9).
9 goes into 29 three times with remainder 2. 2 + 9 = 11 1 +1 = 2
9 goes into 49 five times with remainder 4. 4 + 9 = 13 1 +3 = 4
9 goes into 253 twenty eight times with remainder 1. 2+5+3 = 10 1 +0 = 1
9 goes into 36 four times with remainder 0. 3 + 6 = 9
9 goes into 99 eleven times with remainder 0. 9 + 9 = 18 1 +8 = 9
The sum of the digits of a multiple of 9 is 9 (or a multiple of 9).
9 goes into 29 three times with remainder 2. 2 + 9 = 11 1 +1 = 2
9 goes into 49 five times with remainder 4. 4 + 9 = 13 1 +3 = 4
9 goes into 253 twenty eight times with remainder 1. 2+5+3 = 10 1 +0 = 1
The sum of the digits of any whole number = the remainder when that number is divided by 9. If the sum of the digits is > 9, add the digits again.
9 goes into 36 four times with remainder 0. 3 + 6 = 9
9 goes into 99 eleven times with remainder 0. 9 + 9 = 18 1 +8 = 9
The sum of the digits of a multiple of 9 is 9 (or a multiple of 9).
9 goes into 29 three times with remainder 2. 2 + 9 = 11 1 +1 = 2
9 goes into 49 five times with remainder 4. 4 + 9 = 13 1 +3 = 4
9 goes into 253 twenty eight times with remainder 1. 2+5+3 = 10 1 +0 = 1
The sum of the digits of any whole number = the remainder when that number is divided by 9.
253 = 2x100 + 5x10 + 3 = 2x(99+1) + 5x(9+1) + 3 = 2x99 + 2x1 + 5x9 + 5x1 + 3
The sum of the digits of any whole number = the remainder when that number is divided by 9.
When dividing by 9,getting a remainder of 9 is the same as getting a remainder of 0.
The sum of the digits of any whole number = the remainder when that number is divided by 9.
When dividing by 9,getting a remainder of 9 is the same as getting a remainder of 0.
For example:
You could say that 9 goes into 27 two times with a remainder of 9
or
You could say that 9 goes into 27 three times with a remainder of 0
Casting out nines
an algorithm for checking computation
2 7 1
3 9 5
6 4 2
+ 9 7 7
2 2 8 5
Is the following sum correct?
2 7 1
3 9 5
6 4 2
+ 9 7 7
2 2 8 5
Is the following sum correct?
In theory, the sum of the remainders
should equal the remainder when the sum is divided by 9.
1
8
3
5
81+8+3+5=17 and 1+7 = 8
2 7 1
3 9 5
6 4 2
+ 9 7 7
2 2 8 5
Is the following sum correct?
In theory, the sum of the remainders
should equal the remainder when the sum is divided by 9.
1
8
3
5
8
Shorten the process:
All of these numbers are addedso there is no need to separate them
Also a remainder of 9 is the same as a remainder of 0. Where you see 9, cross it out.
2 7 1
3 9 5
6 4 2
+ 9 7 7
2 2 8 5
Is the following sum correct? Cast out NINES
2 7 1
3 9 5
6 4 2
+ 9 7 7
2 2 8 5
Is the following sum correct? Cast out NINES
2 7 1
3 9 5
6 4 2
+ 9 7 7
2 2 8 5
Is the following sum correct? Cast out NINES
2 7 1
3 9 5
6 4 2
+ 9 7 7
2 2 8 5
Is the following sum correct? Cast out NINES
2 7 1
3 9 5
6 4 2
+ 9 7 7
2 2 8 5
Is the following sum correct? Cast out NINES
The sum is probably correct.There is 1 chance in 9 that the numbers would match by chance.If the numbers do not match then you have found an error.
