Question

One half liter of lemonade concentrate is added to 3 liters of water. how many one thirds liter servings of lemonade are made.

Answer 1

So, 3 liters of water, add 1/2 liter of lemonade, that's 3 and 1/2 liters of lemonade.

so in short, how  many times does 1/3 go into 3 and 1/2?

let's change the mixed to "improper" and divide then.

$\bf \stackrel{mixed}{3\frac{1}{2}}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}\\\\ -------------------------------\\\\ \cfrac{\quad \frac{7}{2}\quad }{\frac{1}{3}}\implies \cfrac{7}{2}\cdot \cfrac{3}{1}\implies \cfrac{21}{2}\implies 10\frac{1}{2}$