# Algebraic Expressions : clarify

The Length of an iron bar is $p$ cm . It is melted and recast into a thin bar whoose length is $q$ cm longer than $n$ times its original length . The thin bar is then cut into $m$ sticks of equal length . Express , in terms of $p$ , $q$ , $m$ and $n$ , the length of each stick

My workings-

Length of thin bar - $pn + q$

I'm now a little confuse with how to find the length of each stick. Since $m$ sticks is the total number of sticks , is the length of each stick = length of the thin bar divide by $m$ ?

• Yes, it seems like you are correct, in which case you will get $\frac{pn+q}{m}$ Commented Aug 30, 2016 at 8:35

## 1 Answer

The length of the thin bar is $pn+q$, you are correct.

Then, you split the thin bar into $m$ parts. Well, think in concrete terms:

If I have a $200$cm stick and I split it into $4$ pieces of equal length, how long are the $4$ pieces?

You probably see the answer is $50$cm, and you got it by dividing $200$ by $4$...

You should see that indeed, the length of each stick is the length of the whole stick, divided by $m$. So the answer should be

$$\frac{pn+q}{m}.$$

• ...'into 4 pieces of equal lengths'. Commented Aug 30, 2016 at 8:38