Question

[(5 - 9) ∙ 3] (mod 5)

Answer 1

first do the math for (5-9)3

Answer 2

5 - 9 = ??

Answer 3

help

Answer 4

5 - 9 = ??

Answer 5

-4

Answer 6

help

Answer 7

what is a mod

Answer 8

a mod is a remainder .....

Answer 9

essentially; you want to know what remainer is of:

[(5 - 9) ∙ 3] /5

Answer 10

5-9=-4
-4x3=-12

Answer 11

and -12/5 gives us a whole number and a remainder

Answer 12

how do i do that

Answer 13

you divide .... longhand style like back in the 4th grade

Answer 14

since 5*-2 = -10, lets go for a smaller value and use 5*-3 = -15

-3
-----------
5 ) -12
-(-15)
------
3 <-- our remainder

Answer 15

so r2

Answer 16

the negative can be offputting; we want a value of 5*n such that it is less than -12

Answer 17

but how did you get -15

Answer 18

another trick is to count backlwards with a proper setup

place your remainders in a row

0 1 2 3 4

now count backwards to -12


-12 -11
-10 -9 -8 -7 -6
-5 -4 -3 -2 -1
0 1 2 3 4 <-- poosible remianders of dividing by 5
^^
-12 falls int his stack

Answer 19

5*-1 = -5 ; -5 is bigger than -12

5*-2 = -10 ; -10 is bigger than -12

5*-3 = -15; -15 is smaller than -12 so use -3

Answer 20

we cant get a remainder if we are trying to subtract a large from a small; which is why you have to be cognizant of the negative

Answer 21

ok

Answer 22

if we have 12 mod 5, can you tell me what they would have been?

Answer 23

i dont understand

Answer 24

we just went thru how we defined mods ...

Answer 25

we can look at it this way as well

12 = 5n + R

12 = 5(2) + R

12 = 10 + 2

12 mod 5 = 2 since we get a Remainder of 2
----------------------------

-12 mod 5:

-12 = 5n + R

-12 = 5(-3) + R

-12 = -15 + 3

-12 mod 5 = 3 since we get a Remainder of 3

Answer 26

(11 x 4. + 6] (mod 8)
so i
11x4=44
44+6=50
r is 6

Answer 27

the 50 is good; lets write it out now as:

50 mod 8

50 = 8n + R

well 8(6) = 48
8(7) = 56 .... too big, lets use the 6

50 = 8(6) + R

50 = 48 + R
R has to equal 2

50 mod 8 = 2

Answer 28

o so 8x7=56 but 6 is to much
so i do 8x6=48 but it is 2 to small
so the R is 2 2+48=50
50=50

Answer 29

i can understand that thought process, yes :)

Answer 30

cool i understand mods

Answer 31

but what is a (clock 7)

Answer 32

2 + (5 - 2) (clock 7)

Answer 33

5-2=3
2+2=4

Answer 34

clock arithemetic is another name for mods;

normally a clock has 12 hours: clock 12 would then be mod12

clock 7 is just another expression for mod7

http://www-math.ucdenver.edu/~wcherowi/clockar.html

Answer 35

2 + (5 - 2) (clock 7)

2 + (3) (clock 7)

5 (clock 7)

Answer 36

5 = 7n + R

7(0) = 0
7(1) = 7 .. too big, go with 0

5 = 7(0) + R
5 = R

Answer 37

thanks you are a "big help"

Answer 38

youre welcome, im sure im going to go thru these in the Fall; gonna be taking number theory ....

Answer 39

o well i bet you are good at it

Answer 40

lol, i can be :)

goood luck, i have to get