5x/10 equals 1(x)/2 which equals (5/10) x or (1/2)x its just manipulating the numbers, all they did is factor the x out
think of it like this:
if x =2 then
5(2)/10
=(5/10)(2)
=1
right?
so 5x/10 = (5/10) (x)
So I am doing an equation for straight line graphs and one of the expressions simplified out to:
5x/10.
It then said this could simply again to (5/10)x.
Why does this work?
I understand if I do it in my calculator (substituting x = 3)
5 * 3 = 15
15 / 10 = 1.5
and
5/10 = 0.5
0.5 * 3 = 1.5
They both give the same answer.
But I am trying to UNDERSTAND why this works as I am still confused.
I thought this only worked with terms that started with a + or - (where we could re-arrange them any way we wanted).
Why does it work here?
5x/10 equals 1(x)/2 which equals (5/10) x or (1/2)x its just manipulating the numbers, all they did is factor the x out
think of it like this:
if x =2 then
5(2)/10
=(5/10)(2)
=1
right?
so 5x/10 = (5/10) (x)
I am not sure I can help you understand, but I can deduce this equality from basic axioms (properties) of real numbers. Usually this is what is meant by "understanding" a mathematical fact. Of course, it is possible not to understand why those axioms hold, but this is a different issue.
First, axioms don't deal with division directly. Instead, they deal with the reciprocal function that maps an x into 1 / x, which is also often denoted by . Then x / y is an abbreviation of x * (1 / y). Thus, there is the reciprocal function with one argument and multiplication with two arguments.
Next, the basic properties of multiplication include
associativity: (x * y) * z = x * (y * z) and
commutativity: x * y = y * x.
Then we have
Does this answer your question?