# Does it make sense to multiply slopes?

Multiplying fractions is a regular occurance. If those fractions are considered slopes, does it make any sense?

For example, if these fractions are slopes,$\frac{9}{8} \times \frac{49}{48},$ does the product have meaning in terms of slope?

Sure. Let $f(x)=ax+b, g(x)=cx+d$. Then the slope of $f(g(x))$ is $ac$.
• The product of two rising (i.e., positive) slopes isn't necessarily steeper: $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$. – Joshua Taylor Apr 18 '14 at 15:26