What percentage drop is this? Can someone help a student who is terribly bad at math answer this question? Between 1998 and 2014, in New Mexico, Birth rates for teens 18-19 years of age fell from a rate of 108.8 per 1000 to 69.3 per 1,000 females. What percentage had the teen birth rate dropped?
So in my mind all of these answers pop up. The figure 69.3 is 44% lower than 108.8. However, when comparing 108.8/1000 to 69.3/1000 the drop between the two is 13.28%. Then again, simply taking 108.8 and subtracting it by 69.3 would give us 39.5.
 A: $108.8$ became $69.3$ so what will $100\%$ become? Write
\begin{align}108.8 &\longmapsto 69.3\\ 100\% &\longmapsto x\%\end{align} Can you learn the following rule: Multiply diagonally and equate! $$x\%\cdot108.8=69.3\cdot100\% \implies x\%=\frac{69.3}{108.8}\cdot100\%=63.69\%$$ So $100\%$ will become $63.69\%$ which means that it will be reduced by $100\%-63.69\%=36.31\%$. That is your number.
A: The previous teen birth rate was $108.8/1000$ and the new birth rate was $69.3/1000$. 
The percentage decrease is, by definition, the difference between the old and new values, divided by the old value. 
In this case, the old birth rate is $108.8/1000$ and the new birth rate is $69.3/1000$. So the percentage decrease is
$$
\frac{\left(\frac{108.8}{1000} - \frac{69.3}{1000} \right)}{\frac{108.8}{1000}},
$$
which simplifies to 
$$
\frac{108.8 - 69.3}{108.8}.
$$
The value of that fraction is about 0.363, so the birth rate decreased by about 36.3%. 
The key point is to remember the definition of "percent decrease". It is not merely the amount of decrease (which would be $39.5/1000$). 
A sometimes confusing topic is that we can look at the old and new rates as percentages themselves. The old birth rate was $10.88\%$ and the new birth rate is $6.93\%$. If you subtract these, you get a difference of $3.95\%$. That is not the "percent change" - it is just the difference between the percentages. To keep this clear, we say that the birth rate decreased by $\mathbf{3.95}$ percentage points. Of course, it also decreased by $\mathbf{36.3}$ percent.  
