How does one get from y=(x+4)/3 to y=1/3*x+4/3?

Question

help!

Answer 1

You can separate out the top portion of a quotient to create two separate quotients.
In this problem, you can split the top into two, by dividing each part by 3, so you'd get
(x/3) + (4/3) = y.
You can check by setting x = 1.
(1 + 4) / 3 = 5/3 = (1/3) + (4/3).

Beware that you can't do this the opposite way!
If it had been y = 3 / (x + 4), you would NOT be able to switch the function to be y = 3/x + 3/4.

Answer 2

since the numerator is a sum, the 3 can divide into each number:

simple example:

(2 +4) / 2 = 6/2 = 3
2/2 + 4/2 = 1 +2 = 3

And since these are equal, the general rule can be created:
(a+b)/c = a/c+b/c
BUT keep in mind that this is only for a sum in the NUMERATOR, not the denominator!

So x/3 + 4/3 = (x+4)/3
and x/3 = 1/3*x

Answer 3

(x+4)/3
=(x+4)*(1/3)
Distribute 1/3 to x and 4
=x*1/3+4*1/3
=1/3*x+4/3

Answer 4

y = (x + 4)3

Open the brackets and divide x and 4 by 3.

y = x/3 + 4/3

1/3*x is same as x/3

Answer 5

Distributive propertry

(a+b)/c = 1/c * (a+b) = a/c + b/c

Answer 6

you break the bracket by dividing each element by 3