# Modulo

Can any one please tell me how
7 mod 10 = 7
and
-2 mod 10 =8

Thanks.
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Commented:
8 + 2  = 10
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Commented:
modulo is the remainder after dividing and is always positive.

a mnemonic to help remember them is to think of it is as a circle of values

``````7  8   9 0 1 2 3 4 5 6 7 8 9 0  1   2  3  4
-3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

``````

and the pattern of 0-9 loops forever in both positive and negative direction
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Author Commented:
if i divide 10 by 7 the reminder is 3 not 7
if i divide 2 by 10 the reminder is 0 not 8
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Commented:
For positive integers:    7, 17, 27, 37, ...    all equal 7 mod 10.   They have remainder of 7 when divided by 10.

Another way to look at this is to start with 7,  and add 10 as many times as you like.    Since 10 = 0 mod 10

Once you see this you can also subtract 10 as many times as you like.  This can get you into negative numbers.

So  8 = 8 mod 10.     And   (8 -10) = -2 = 8 mod 10      and      (8 -10 - 10) = -12 = 8 mod 10
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Commented:
>> if i divide 10 by 7 the reminder is 3 not 7

Wrong.   Divde 7 by 10 to get 0 and remainder 8

You have to understand the positive numbers before you tackle the negative.
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Commented:
>> if i divide 10 by 7 the reminder is 3 not 7

Wrong.   Divde 7 by 10 to get 0 and remainder 7
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Author Commented:
7/10 = .7
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Author Commented:
7/10 = .7 with reminder 0
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Author Commented:
im sory i think i have a thick head.
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Commented:
Integer division is not the same as division.

27 divided by 10  ==>  2 with remainder 7.       2 * 10 + 7  =  27

7 divided by 10  ==>  0 with remainder 7.        0 * 10 + 7  =   7
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Author Commented:
ok now i understand. Can you please tell me one  more time the case of negative number.
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Commented:
Isn't a split in order?
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Commented:
modulo is basically the remainder of a division problem
7/10 is 0 with 7 left over (0*10 + 7 = 7) so 7 mod 10 is 7
16/10 is 1 with 6 left over (1*10 + 6 = 16) so 16 mod 10 is 6
-2/10 is 0 with -2 left over, but we don't want negative answers so let's fix it

-2/10 is -1 with 8 left over (-1*10 + 8 = -2) so -2 mod 10 is 8

That's how I explain the reasons.

I don't see the need for a split. http:#a36718497 basically just showed him what he already knew (the answers) not why they are the answers.
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