Question

The distance between the two islands showed on the map is 210 miles a ruler measure distance on the map as 3 1/2 inches how many miles would be represented by 1 3/4 inches on the map

Answer 1

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

`\bf \stackrel{mixed}{3(1)/(2)}\implies \cfrac{3\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{7}{2}}~\hfill \stackrel{mixed}{1(3)/(4)}\implies \cfrac{1\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{7}{4}} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} \stackrel{size}{actual~miles}&\stackrel{size}{map~inches}\\ \cline{1-2} 210&(7)/(2)\\\\ x&(7)/(4) \end{array} \implies \cfrac{210}{x}=\cfrac{~~(7)/(2)~~}{(7)/(4)}`

`\bf \cfrac{210}{x}=\cfrac{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}{~~\begin{matrix} 2 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\cdot \cfrac{\stackrel{2}{~~\begin{matrix} 4\\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{~~\begin{matrix} 7 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} \implies \cfrac{210}{x}=2\implies 210=2x\implies \cfrac{210}{2}=x\implies 105=x`