Best solutions to - "The value of the operation [16]+[9] in Z6..."

High School
Geometry
High school geometry
Congruence

Mylo O'Moore

Answered question

2021-04-17

The value of the operation [16]+[9] in $Z_{6}$ and to write the answer in the form [r] with $0 \leq r < m$ .

Answer & Explanation

coffentw

Skilled2021-04-19Added 103 answers

Definition used:
Congruence.
Let m be an integer greater than 1. If x and y are integers, then x is congruent to y modulo m if x - y is divisible by m. It can be represented as

x = y \pm o d m

. This relation is called as congruence modulo m.
Calculation:
It is known that, [x] + [y] = [x+y].
Then, the value of the expression becomes as follows.
[16] + [9] = [16 + 9] = [25]
Since

25 \equiv 1 \pm o d 6

. Thus [16] + [9] = [1] in

Z_{6}

.
Therefore, the value of the expression is [1].

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