Question

when I make macaroni and cheese for my brother and me, I use 2 2/3 tablespoons of butter. how much butter will I n need to make my macaroni and cheese dish for Thanksgiving dinner if 15 people are attending?

Answer 1

You would need about 34  2/3 tablespoons of butter. Convert the fraction into an improper fraction, so 8/3. Then multiply that by 13 (you and your brother are included in the 15 people I suppose) and you get 104/3. Simplify that to get a mixed number and you have 34  2/3.

Answer 2

if you use 2 2/3 tablespoons for you and your brother, that means, you need 2 2/3 tablespoons for two servings, how many tablespoons for 15 servings then?

well  $\bf 2\frac{2}{3}\implies \cfrac{2\cdot 3+2}{3}\implies \cfrac{8}{3}\\\\ -------------------------------\\\\ \begin{array}{ccllll} \textit{butter spoons}&servings\\ -----&-----\\ \frac{8}{3}&2\\ x&15 \end{array}\implies \cfrac{\frac{8}{3}}{x}=\cfrac{2}{15}\implies \cfrac{\frac{8}{3}}{\frac{x}{1}}=\cfrac{2}{15} \\\\\\ \cfrac{8}{3}\cdot \cfrac{1}{x}=\cfrac{2}{15}\implies \cfrac{8}{3x}=\cfrac{2}{15}\implies 8\cdot 15=3x\cdot 2\implies 120=6x \\\\\\ \cfrac{120}{6}=x\implies 20=x$