Question

I need help with Modulos, I wasn't in class when they taught it, so I need a little help.

1. 98mod29
2. 32mod17
3. 17mod 35
4. -47mod45
5. 42mod100
6. 0mod20
7. 52mod26
8. -2mod10
9. 62mod4

Answer 1

@mathstudent55 @mathmath333

Answer 2

@dan815

Answer 3

u have to find the reaminder when 98 is divided by 29
example
\(\large\tt \begin{align} \color{black}{98 (mod 29)\equiv 11}\end{align}\)

Answer 4

32 divided by 17 gives remainder 15
\(\large\tt \begin{align} \color{black}{32 (mod17)\equiv 15}\end{align}\)

Answer 5

don't you mean subtract or add

Answer 6

It does get trickier with negative numbers though.
So it is best to recall the divison theorem:
For any two integers a and b there exist q and r such that
a=bq+r
where 0<=r<|b|
So this means r has to be positive.
a mod b should result in a positive integer
so for example
13 mod 5=3 since 13=5(2)+3
-13 mod 5=2 since -13=5(-3)+2

Answer 7

if there is a negative number u can simply add the divisor to the dividend untill it gets positive
example in case of \(-47~~(mod45)\)-

\(\large -47+45=-2\implies -2+45=43\)
so
\(\large\tt \begin{align} \color{black}{-47 (mod45)\equiv 43}\end{align}\)


\(\large\tt \begin{align} \color{black}{-2 ~~(mod ~10)\equiv 8-----(-2+10=8)}\end{align}\)

Answer 8

what do I put on #5. I think the answer is 45

Answer 9

I meant 42

Answer 10

\(\large\tt \begin{align} \color{black}{ 42~~(mod~100)\equiv 42}\end{align}\)

as \(42<100\)

\(a~~(mod~b)\equiv a\)
\(if~~a<b\)

Answer 11

@agent0smith #6 0mod20; I think the answer is 0, but I am not for sure if it's the right answer.

Answer 12

\(\large\tt \begin{align} \color{black}{6.)\\ 0~~(mod~20)\equiv 0}\end{align}\)
as i stated \( 0<20\)