Question

The recorded lengths of 3 bluegills caught by a fisherman were 21/4 inches, 3/8 of a foot, and 4 15/16 inches. Order the lengths of the bluegills from least to greatest.

Answer 1

$\text{The recorded lengths of 3 bluegills cought by a fisher man were}\\ \frac{21}{4}\text{ inches, }\frac{3}{8} \text{ of a foot,  and }4\frac{15}{16} \text{ inches}.\\ \\ \text{so first we write these lengths with same unit and in simplified form.}\\ \\ \text{the first length is already in simplified form and is in inches.}\\ \\ \text{second bluegill length is in foot, so we convert it in inches. so}\\ \\ \frac{3}{8}\text{ foot}=\frac{3}{8}(12 \text{ inches})=\frac{9}{2} \text{ inches}$

$\text{and for the length of third bluegill, we convert the mix fraction to improper}\\ \text{fraction. so we have}\\ \\ 4\frac{15}{16}\text{inches}=\frac{64+15}{16} \text{ inches}=\frac{79}{16 }\text{ inches}\\ \\ \text{now in order to arrange the lengths of the bluegills from least to largest,}\\ \text{we make the denominators equal for all the lengths and then arrange as}\\ \text{per the increasing order of numerator.}\\ \\ \text{Observe that the Least common Denominator (LCD) of 4,2 and 16 is 16.}$

$\text{so we multiply up and down the first length by 4, so we get}\\ \\ \frac{21}{4}\times\frac{4}{4}=\frac{84}{16}, \\ \\ \text{to the second length, we multiply up and down by 8, so}\\ \\ \frac{9}{2}\times \frac{8}{8}=\frac{72}{16}\\ \\ \text{So now with same denominators, the lengths are }\frac{84}{16}, \ \frac{72}{16} \text{ and }\frac{79}{16}$

$\text{Hence the order of length of bluegills from least to greatest is:}\\ \\ \frac{3}{8}\text{ of a foot }< 4\frac{15}{16 }\text{ inches} < \frac{21}{4}\text{ inches}$