An angle measuring (468n)° is in standard position. for which value of n will the terminal side fall along the negative portion of the x-axis?
n = 4
n = 5
n = 6
n = 7

To fall along the negative portion of the x-axis means that the angle has to be a multiple of 180°.

So 468n is k*180, where n and k are integers, such that k/n = 468/180 or (the same) k = 468n/180

468=(2^2)(3^2)(13)

180=(2^2)(3^2)(5)

Then 468/180 = 13/5 and k =13n/5

To make K an integer n has to be a multiple of 5. Use 5 and you get

k = 13
n=5
468n = 468(5) = 2340

2340/180 = 13. which means that 2340 is multiple of 180.

Then the solution is n =5.

To make the numerator divisible by the denominator, you need to multiply

Add the cents that add the left overs to get the first number