# Question

If *abc/def* = *a/d* * *b/e* * c/f, then why doesn't (*a* * *b*)*/c* = (*a/c*)(*b/c*)? The quiz solution says (*a* * *b*)*/c* = (*a/c*)*b*...but shouldn't *b* have a denominator of *c*?

# Answer

Dividing by a value is the same as multiplying by its reciprocal. So dividing by 2 is the same as multiplying by (1/2), or for this problem, dividing by *c* is the same as multiplying by (1/*c*). One way you could think about the *a ** *b/c* term is to split it up with parentheses into a set of multiplications:

*a ** *b/c* = (*a*) * (*b*) * (1/*c*)

Since you can re-order multiplications, all these are equivalent statements:

(*a*)(*b*)(1/*c*) = (*a*)(1/*c*)(b) = (*a/c*) * (*b*)

If you want, we can try plugging in some numbers to make sure that (*a* * *b*)*/c* = (*a/c*) * *b*

For example, let's try *a* = 3, *b* = 4, and *c* = 6

(*a* * *b*)*/c* = (3 * 4)/6 = 2

(*a/c*) * *b* = (3/6) * 4 = 2

2 = 2

However, for *ab/c*=(*a/c*)(*b/c*), we can't separate out both (*a/c*) and (*b/c*). Let's try it with the same numbers above:

*a* = 3, *b* = 4, and *c* = 6

(*a* * *b*)*/c* = (3 * 4)/6 = 2

(*a/c*)(*b/c*) = (3/6)(4/6) = (1/2) * (2/3) = 1/3

2 does not equal 1/3

When you simplify fractions, there are a few rules you have to stick to regarding numerators and denominators, the following video lessons may be of help:

# Link

http://gre.magoosh.com/questions/2619

## Comments

1 comment

Could you also do b/c * a?

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