I just dont understand how i got that answer
It seems to me like the presence of so many variables is what's confusing you. Let's dispense with as many of them as we can. What if we replace \(k\) by 2, \(w\) by 3, and \(v\) by 4. Then you'd have:
\(\displaystyle 2a = \frac{3}{4}\)
How would you solve this equation for \(a\)? Well, you'd divide both sides of the equation by 2, so as to isolate \(a\) on one side:
\(\displaystyle a = \frac{3}{4} \div 2\)
Now, can we clean that up a bit? Dividing by 2 is the same as multiplying by \(\frac{1}{2}\) (why?):
\(\displaystyle a = \frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8}\)
Let's do it again, still replacing \(w\) by 3, and \(v\) by 4, but this time replacing \(k\) by 7:
\(\displaystyle 7a = \frac{3}{4}\)
How would you solve this equation for \(a\)? Well, you'd divide both sides of the equation by 7 (i.e. multiply by \(\frac{1}{7}\)), so as to isolate \(a\) on one side:
\(\displaystyle a = \frac{3}{4} \times \frac{1}{7} = \frac{3 \times 1}{4 \times 7} = \frac{3}{28}\)
That seems like it should be sufficient to get the core concept down, so now let's re-introduce our variables, one at a time. First, re-introduce \(v\):
\(\displaystyle a = \frac{3}{v} \times \frac{1}{7} = \frac{3 \times 1}{v \times 7} = \frac{3}{7v}\)
Next, re-introduce \(w\):
\(\displaystyle a = \frac{w}{v} \times \frac{1}{7} = \frac{w \times 1}{v \times 7} = \frac{w}{7v}\)
And finally, re-introduce \(k\):
\(\displaystyle a = \frac{w}{v} \times \frac{1}{k} = \frac{w \times 1}{v \times k} = \frac{w}{kv}\)
In each of the two cases with "real" values, you simply divided by the value of \(k\) which undid the multiplication. Any reason to believe the exact same process wouldn't apply here? You may not know the exact value of \(k\), but you can still work with it all the same.