Question

The directions for mixing an insect spray say to use 1 1/2 ounces of chemical in each gallon of water. How many ounces of chemical should be mixed with 3 4/5 gallons of​ water? First, estimate the answer to the application problem. Then find the exact answer.

Answer 1

1 1/2 oz to each gallon.  
Total required for 3 4/5 gal is the product of 1 1/2 and 3 4/5, which is approximately 4*1 1/2 = 6 oz.

Exact answer
1 1/2 * 3 4/5
=3/2 * 19/5
=57/10
=5.7 oz

Answer 2

$\bf \begin{array}{ccllll} chemical&water\ gallons\\ -----&-------\\ 1\frac{1}{2}&1\\\\ x&3\frac{4}{5} \end{array}\implies \cfrac{1\frac{1}{2}}{x}=\cfrac{1}{3\frac{4}{5}} \\\\\\ \cfrac{\frac{1\cdot 2+1}{2}}{x}=\cfrac{\frac{1}{1}}{\frac{3\cdot 5+4}{5}}\implies \cfrac{\frac{3}{2}}{\frac{x}{1}}=\cfrac{\frac{1}{1}}{\frac{19}{5}}\implies \cfrac{3}{2}\cdot \cfrac{1}{x}=\cfrac{1}{1}\cdot \cfrac{5}{19}\implies \cfrac{3}{2x}=\cfrac{5}{19}$

$\bf 3\cdot 19=2x\cdot 5\implies 57=10x\implies \cfrac{57}{10}=x\implies \boxed{5\frac{7}{10}=x} \\\\\\ \cfrac{5\cdot 10+7}{10}\implies \cfrac{57}{10}$