Rusty's hair grows at the rate of 1 over 4 inch per month.
how many months will it take rusty's hair to grow 5 over 8 inch?
explain your answer using words, and show your work using fractions.

1/4 = 2/8. Remember that. This means that 1/8 is equal to half of a month. It there is 5/8, you can add a half month for every eights. In this case, it will take 2 and a half months
Easy Way:If your hair were to grow 1/4 inches a month, it would also grow 2/8 inches a month, since 1/4 = 2/8. How long with it take 1/8 (0.5/4)inches to grow? It would take a half of a month for your hair to grow 1/8 inches.
Now that we know 1/8 inches grows in a half of a month, we add a half of a month for every eigths. Since we are trying to figure out how long it would take for it to grow 5/8 inches, we add 5 half months to get the answer of 2 and a half months. Kind of confusing, but that is the best way I can describe it.

(1/4)in/month

Now let's make an equation for this. 

They already sortah set this up. For every month we grow 1/4 inches. So our variable will be m for month. 

1/4m = 5/8

So what we are going to do is solve for m, the number of months it will take to get to 5/8 inches. 

To do so we need to remove the 1/4 by multiplication. (Also you can think of 1/4m as m/4. They are both correct forms) 

(1/4m)*4 = (5/8)*4

It will cancel out on the left side. 

m = 20/8

Reduce the number!

m = 10/4

Reduce it more!!

m = 5/2

So it will take 5/2 months for it to grow that long. 

My guess by the wording of the question it wants us to use fractions to find that answer. So we'll do that too. 

Find a common denominator. 
1/4 * 2/2 = 2/8

As we go up the number of months increases by 1. Each time I multiply the original number (2/8 per month) by the number of months. 

2/8, 4/8, 6/8

So we are now above our answer of 5/8. We are going up by 2 each month. But we need half of that. So we do this: m/2. In other words half of a month. So in order to get to 5/8 we will need to wait 2 and a half months. 

So 2.5 months. Or in fraction form 5/2. 

Explanation: 
The given answer is due to the rate given of 1/4 of an inch per one month. So, we need to find a common denominator to make this easier. After multiplying the fraction by two over two to get a common denominator I then begin to multiply it by the number of months. After multiplying by three we see that the number exceeds our number of 5/8 inches. So three is too much, because we only need 1/8 more instead of 2/8 more. So we take half of a month instead of a full month to give us the answer of 2.5 or 5/2.