Question

an oatmeal recipe calls for 1 1/2 cups of oat and 2 1/2 cups of water. A If you have 3 cups of oats,how many cups of oats water do you need? 3 cups oat •________= ___________ cups water. B if you have 2 cups of oats,how many cups of oats water do you need? 2 cups oat •________= ___________ cups water. C if you have 5 cups of water, how many cups of oats do you need? 5 cups water • ________=_______cups of oat. D If you have 3 cups of water, how many cups of oats do you need? 3 cups water •___________=_________cups of oat.

Answer 1

$\bf \stackrel{mixed}{1\frac{1}{2}}\implies \cfrac{1\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{3}{2}}~\hfill \stackrel{mixed}{2\frac{1}{2}}\implies \cfrac{2\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{5}{2}}\\\\[-0.35em]\rule{34em}{0.25pt}$

A)

$\bf \begin{array}{ccll}oats&water\\\cline{1-2}\frac{3}{2}&\frac{5}{2}\\[0.8em]3&x\end{array}\implies \cfrac{~~\frac{3}{2}~~}{3}=\cfrac{~~\frac{5}{2}~~}{x}\implies \cfrac{~~\frac{3}{2}~~}{\frac{3}{1}}=\cfrac{~~\frac{5}{2}~~}{\frac{x}{1}}\implies \cfrac{3}{6}=\cfrac{5}{2x}\\\\\\6x=30\implies x=\cfrac{30}{6}\implies \blacktriangleright x=5 \blacktriangleleft$

B)

$\bf \begin{array}{ccll}oats&water\\\cline{1-2}\frac{3}{2}&\frac{5}{2}\\[0.8em]2&x\end{array}\implies \cfrac{~~\frac{3}{2}~~}{2}=\cfrac{~~\frac{5}{2}~~}{x}\implies \cfrac{~~\frac{3}{2}~~}{\frac{2}{1}}=\cfrac{~~\frac{5}{2}~~}{\frac{x}{1}}\implies \cfrac{3}{4}=\cfrac{5}{2x}\\\\\\6x=20\implies x=\cfrac{20}{6}\implies x=\cfrac{10}{3}\implies \blacktriangleright x=3\frac{1}{3} \blacktriangleleft$

C)

$\bf \begin{array}{ccll}oats&water\\\cline{1-2}\frac{3}{2}&\frac{5}{2}\\[0.8em]5&x\end{array}\implies \cfrac{~~\frac{3}{2}~~}{5}=\cfrac{~~\frac{5}{2}~~}{x}\implies \cfrac{~~\frac{3}{2}~~}{\frac{5}{1}}=\cfrac{~~\frac{5}{2}~~}{\frac{x}{1}}\implies \cfrac{3}{10}=\cfrac{5}{2x}\\\\\\6x=50\implies x=\cfrac{50}{6}\implies x=\cfrac{25}{3}\implies \blacktriangleright x=8\frac{1}{3} \blacktriangleleft$

D)

$\bf \begin{array}{ccll}oats&water\\\cline{1-2}\frac{3}{2}&\frac{5}{2}\\[0.8em]x&3\end{array}\implies \cfrac{~~\frac{3}{2}~~}{x}=\cfrac{~~\frac{5}{2}~~}{3}\implies \cfrac{~~\frac{3}{2}~~}{\frac{x}{1}}=\cfrac{~~\frac{5}{2}~~}{\frac{3}{1}}\implies \cfrac{3}{2x}=\cfrac{5}{6}\\\\\\18=10x\implies \cfrac{18}{10}=x\implies \cfrac{9}{5}=x\implies \blacktriangleright 1\frac{4}{5}=x \blacktriangleleft$