I need help understanding this math problem.

Question

Hi, I'm trying to pass my GED Math test. It's literally the only test I need to pass, but math problems like this one really tend to discourage me.

48x+32y

32

The way I have it is as the long division format.

x+y

32 |48x+32y

-32x+32y

16x

Am I doing this correctly?

I checked the answer key, and apparently the answer looks like this;

3x +y

2

I don't know how to get the answer 3x over 2, but I do have the +y correct, it seems.

Please help me understand.

Thank you.

Answer 1

The easier way to do a problem like this is by factoring instead of long division.

With ^{(48x + 32y)}/₃₂ , all the terms (48, 32, and 32 in the denominator) can be divided by 16. If we factor out a 16 from top and bottom we would get

^{16 (3x + 2y)}/₁₆₍₂₎

Since 16/16 = 1, we can reduce the equation to ^{(3x + 2y)}/₂

We can now write the equation as addition of two fractions

^3x/₂ + ^2y/₂

Since 2y/2 = y, we can write the answer as

^3x/₂ + y