The area of a rectangle is ##5 4/5## square meters. The width of the rectangle is ##2 1/4## meter. How long is the rectangle?

##2 26/45## ##"meters"##

First, convert the mixed numbers into improper fractions.

##"area"=5 4/5=5+4/5=25/5+4/5=29/5##

##"width"=2 1/4=2+1/4=8/4+1/4=9/4##

Next, we need to know that the area of a rectangle is equal to its length times its width, expressed algebraically as

##A=lw##

From the question, we know that

##29/5=lxx9/4##

To find just ##l##, the length, multiply both sides by ##4/9## (the reciprocal of ##9/4##).

##29/5xx4/9=lxxcolor(red)(cancel(color(black)(9)))/color(blue)(cancel(color(black)(4)))xxcolor(blue)(cancel(color(black)(4)))/color(red)(cancel(color(black)(9##

##l=(29xx4)/(5xx9)=116/45=2 26/45##