# Math algebra question?

How would I divide the following integers

(-120)(31)/(-5)(-8)(9)

My result is -3720/360 but my book tell me it is zero?

-
James, your notation is not quite clear: Do you mean $\frac{-120 \cdot 31}{-5 \cdot (-8) \cdot 9}$? If yes, your answer is correct. – Johannes Kloos Mar 20 '12 at 16:50
Your fraction simplifies to $-31/3$. But it is definitely not $0$. – André Nicolas Mar 20 '12 at 16:50
Any fraction which numerator is non-zero can't be zero regardless of all other things. – Ilya Mar 20 '12 at 17:06
Could you give us the problem exactly as it appears in your book (perhaps as a photograph)? – jwodder Mar 20 '12 at 17:15
There is only one answer $-\frac{31}{3}$ like Andre mentioned. – Kirthi Raman Mar 20 '12 at 19:09

## 1 Answer

The expression is somewhat ambiguous. It be read either as

$$\frac{(-120)(31)}{(-5)(-8)(9)}$$

or as

$$\frac{(-120)(31)(-8)(9)}{-5}$$

When writing expressions like this, you should always place brackets to make the grouping of terms obvious.

In any case, the answer is certainly negative, since none of the factors in the numerator are zero, and there are three minus signs.

In the first case, the fraction simplifies to

$$-\frac{3720}{360} = -\frac{31}{3}$$

which is presumably how you arrived at your answer, and in the second case it simplifies to

$$-53568$$

-
I think you are mistaken that it is ambiguous; I think $ab/cd$ always means $(ab)/(cd)$, and never $(ab/c)d$. – MJD Mar 20 '12 at 17:16
I agree that almost everyone reads $a/bc$ as $a/(bc)$ rather than $(a/b)c$, but since the possibility for ambiguity exists, it seems prudent to be explicit rather than implicit (following the principle that you should always be twice as explicit as you think necessary) – Chris Taylor Apr 20 '12 at 8:55