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##