Question

How much water will it take to simmer 1 3/4 quarts of barley using a water to barley ratio of 4 to 1

Answer 1

4 to 1 or 4:1, water to barley, simply means, the water will be 4 times as much as the barley.

well, convert the 1 and 3/4 from mixed to "improper" and check.

$\bf \cfrac{water}{barley}\qquad 4:1\qquad\cfrac{4}{1}=\cfrac{\stackrel{water}{w}}{\stackrel{barley}{1\frac{3}{4}}}\implies \cfrac{4}{1}=\cfrac{w}{\frac{1\cdot 4+3}{4}}\implies \cfrac{4}{1}=\cfrac{w}{\stackrel{improper}{\frac{7}{4}}} \\\\\\ \cfrac{4}{1}=\cfrac{\quad \frac{w}{1}\quad }{\frac{7}{4}}\implies \cfrac{4}{1}=\cfrac{w}{1}\cdot \cfrac{4}{7}\implies 4=\cfrac{4w}{7}\implies 28=4w \\\\\\ \cfrac{28}{4}=w\implies 7=w$