How is (208 − 18y)/7 simplified to (29-2y) + (5-4y)/7?

[Gravitational]

In my textbook it simplifies (208 − 18y)/7 to (29-2y) + (5-4y)/7
How does this happen?

 

[DonAntonio]

In my textbook it simplifies (208 − 18y)/7 to (29-2y) + (5-4y)/7
How does this happen?

$29-2y+\frac{5-4y}{7}=\frac{7\cdot 29 - 7\cdot 2y + 5 - 4y}{7} = \frac{208-18y}{7}$

DonAntonio

 

[Gravitational]

Yes I know that, I also tried it in reverse. But how can it be done without doing it in reverse.

 

[DonAntonio]

Yes I know that, I also tried it in reverse. But how can it be done without doing it in reverse.

Errr...$208 = 29\cdot 7 + 5\,,\,\,and\,\,18 = 7\cdot 2 + 4$...what else?!

DonAntonio

 

[HallsofIvy]

It's just arithmetic. 7 divides into 208 29 times with remainder 5. 7 divides into 18 twice with remainder 4.