Alvin has some marbles in a box. He keeps 1/3 of them and gives the remainder to Joyce and Sean. Joyce gets 5/8 of the remainder. What fraction of the marbles does Sean get?

n marbles

n/3 ---> Alvin

2 n /3 ---> J and S

(5/8)(2n/3) ---> J
so
(3/8)(2n/3) ----> S

which is (1/4)n

patience, patience , plug and chug

To find out what fraction of the marbles Sean gets, we need to calculate the fraction that Joyce gets first, and then subtract that fraction from 1 (since Sean gets the remainder).

Let's start with the information given:
- Alvin keeps 1/3 of the marbles.
- The remainder is given to Joyce and Sean.
- Joyce gets 5/8 of the remainder.

To find out what fraction of the marbles Joyce gets, we need to calculate the fraction of the marbles that are the remainder. We can do this by subtracting the fraction Alvin keeps from 1:

1 - 1/3 = 2/3 (This is the fraction that is the remainder)

Now we can find out what fraction of the remainder Joyce gets by multiplying the fraction of the remainder by 5/8:

(2/3) * (5/8) = 10/24

So, Joyce gets 10/24 of the marbles.

To find what fraction of the marbles Sean gets, we need to subtract the fraction that Joyce gets from 1:

1 - 10/24 = 14/24

Therefore, Sean gets 14/24 of the marbles.

To find the fraction of marbles that Sean gets, we need to calculate his share from the remainder that Joyce receives. Let's break down the problem step by step:

Step 1: Calculate the fraction of marbles that Alvin keeps.
Alvin keeps 1/3 of the marbles, which means he doesn't give away 2/3 of them.

Step 2: Calculate the remainder that Alvin gives away.
The remainder is obtained by subtracting the fraction Alvin keeps (1/3) from 1 (the whole). So, the remainder is 1 - 1/3 = 2/3.

Step 3: Calculate the fraction of the remainder that Joyce gets.
Joyce gets 5/8 of the remainder. So, we multiply the remainder (2/3) by 5/8 to find Joyce's share: (2/3) * (5/8) = 10/24 or simplified 5/12.

Step 4: Calculate the fraction of the remainder that Sean gets.
Since Sean gets the remainder that is left after Joyce takes her share, we subtract Joyce's share (5/12) from the remainder (2/3).
The calculation is: (2/3) - (5/12) = 8/12 - 5/12 = 3/12 or simplified 1/4.

Therefore, Sean gets 1/4 of the marbles.