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(1)/(2)}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}\\\\ -------------------------------\\\\ \cfrac{\quad (7)/(2)\quad }{(1)/(3)}\implies \cfrac{7}{2}\cdot \cfrac{3}{1}\implies \cfrac{21}{2}\implies 10(1)/(2)`