Question

A recipe calls for 3/5 cup of sugar for every 2 1/3 teaspoons of vanilla. What is the unit rate in cups per teaspoon?

Answer 1

the unit rate is simply the units/units, namely cups/teaspoons.

let's firstly convert the mixed fraction to improper fraction.

$\bf \stackrel{mixed}{2\frac{1}{3}}\implies \cfrac{2\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{7}{3}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{\textit{sugar cups}}{\textit{vanilla spoons}}\qquad \qquad \cfrac{~~\frac{3}{5}~~}{\frac{7}{3}}\implies \cfrac{3}{5}\cdot \cfrac{3}{7}\implies \cfrac{9}{35}\implies 9\div 35\quad \approx \quad 0.257$