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}\\ (21)/(4)\text{ inches, }(3)/(8) \text{ of a foot,  and }4(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}\\ \\ (3)/(8)\text{ foot}=(3)/(8)(12 \text{ inches})=(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(15)/(16)\text{inches}=(64+15)/(16) \text{ inches}=(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}\\ \\ (21)/(4)*(4)/(4)=(84)/(16), \\ \\ \text{to the second length, we multiply up and down by 8, so}\\ \\ (9)/(2)* (8)/(8)=(72)/(16)\\ \\ \text{So now with same denominators, the lengths are }(84)/(16), \ (72)/(16) \text{ and }(79)/(16)`

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