Question

greatest to least​

Answer 1

first off, is noteworthy that on the denominators, 17 and 37 are prime numbers, so we can't quite factor them, and denominators of 15 and 22, have no common factors so the LCD of all denominators is simply their product, 15*22*37*17.

what we do is, turn all fractions with the same denominator, so they all represent the same division of the whole, and from there we can simply look at which numerator is larger or smaller to sort them.

we'll do so by using the LCD of all denominators, and dividing the LCD by each denominator, our quotient we'll use to multiply the fraction, let's do so

`\bf \cfrac{7}{15} \qquad \cfrac{17}{22}\qquad \cfrac{22}{37} \qquad \cfrac{5}{17}~\hspace{5em} \stackrel{\textit{so the LCD for those denominators is}}{15\cdot 22\cdot 37\cdot 17\implies 207570} \\\\[-0.35em] ~\dotfill`

`\bf \stackrel{207570/ 15 ~=~ 13838}{\cfrac{7\cdot 13838}{15\cdot 13838}}\qquad \stackrel{207570/ 22 ~=~ 9435}{\cfrac{17\cdot 9435}{22\cdot 9435}}\qquad \stackrel{207570/ 37 ~=~ 5610}{\cfrac{22\cdot 5610}{37\cdot 5610}}\qquad \stackrel{207570/ 17 ~=~ 12210}{\cfrac{5\cdot 12210}{17\cdot 12210}} \\\\[-0.35em] ~\dotfill`

`\bf \cfrac{96866}{207570}\qquad \cfrac{160395}{207570}\qquad \cfrac{123420}{207570}\qquad \cfrac{61050}{207570} \\\\\\ \stackrel{\textit{and if we sort them from greatest to least}}{\cfrac{160395}{207570}\qquad \cfrac{123420}{207570}\qquad \cfrac{96866}{207570}\qquad\cfrac{61050}{207570}}`