Find the order of the element 5 + <3> in the quotient group II18/ <3>.
OK, and 18=0=the identity in II18.II18 = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18}
<3> = {3,6,9,12,15,18}
5 + <3> = {5,8,11,14,17,2}
order is the number of elements
I am thinking this II18/ <3> equals {3,6,9,12,15,18} and I have to find the order of that plus 5.
So I got the order as 6.
This statement refers to the mathematical concept of order of operations, where the expression inside the parentheses (5 + <3>) is evaluated first, followed by the division (II18/<3>), resulting in a final answer of 6.
In mathematics, the standard order of operations is PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This means that in the given expression, the addition inside the parentheses is evaluated first, followed by the division.
The order of operations is important because it dictates the sequence in which mathematical expressions should be evaluated. Following the correct order ensures that everyone arrives at the same answer when solving a given expression. Without it, there would be ambiguity and confusion in mathematical calculations.
If the order of operations is not followed, the result of a mathematical expression may be incorrect. For example, if the expression 5 + 3 x 2 is evaluated without following the order of operations, the result will be 16 instead of the correct answer of 11. This is because multiplication should be performed before addition.
No, the order of operations cannot be changed in this expression. It is a fundamental rule in mathematics that must be followed in order to get the correct answer. However, the order of operations can be changed if parentheses are used to group certain parts of the expression differently.