Test 8 Section 3 #12

This one comes down to fraction manipulation. You’re asked for the value of \dfrac{b}{a}. You’re given the value of \dfrac{2a}{b}, which is different from what you want in a couple ways. First, it has a 2 in it that you’ll need to get rid of. Second, it’s flipped. Luckily, we have operations available to us to resolve both of those differences!

Let’s get rid of the 2 first. To do so, we’ll multiply both sides of the given equation by \dfrac{1}{2}.

    \begin{align*}\dfrac{2a}{b}&=\dfrac{1}{2}\\\\\dfrac{2a}{b}\times\dfrac{1}{2}&=\dfrac{1}{2}\times\dfrac{1}{2}\\\\\dfrac{a}{b}&=\dfrac{1}{4}\end{align*}

Now we’re almost home. We know what \dfrac{a}{b} equals, so all we need to do is flip it to find out what \dfrac{b}{a} equals!

    \begin{align*}\dfrac{a}{b}&=\dfrac{1}{4}\\\\\dfrac{b}{a}&=4\end{align*}