A man measures a room for a wallpaper border and find he needs lengths of 10 ft 6 3/8in., 14 ft. 9 3/4 in., 6 ft. 5 1/2 in., and 3 ft. 2 7/8 in. What total length of wallpaper border does he need to purchase?

1 Answer
Oct 8, 2016

The man needs to purchase #35#ft #1/2#in of wallpaper border.

Explanation:

The lengths needed should be added together. To do this, we can first convert everything to one unit of measure (change everything to either inches or feet, but not both) or we can add the like parts together and then convert as needed. In this case, I suggest we add the like parts and convert as needed.

First, we will add all the foot lengths:
#10 + 14 + 6 + 3 = 33#ft

Now, add the whole inch lengths:
#6 + 9 + 5 + 2 = 22#in

Next add the partial inch lengths. Remember you must have common denominators to combine fractions, so converting the fractions to have common denominators will be your first order of business in this step. The final answer should be in proper form and reduced.
#3/8 + 3/4 + 1/2 + 7/8 =#
#3/8 + 6/8 + 4/8 + 7/8 = 20/8#
#20/8 = 2 4/8 = 2 1/2#

Now we will combine the two inch length answers and convert to feet and inches as possible. Remember there are #12# inches in one foot.
#22 + 2 1/2 = 24 1/2#in
#24 1/2# in #= 2#ft #1/2#in

Now combine the foot length answer with the ft & inch answer:
#33#ft #+ 2#ft #1/2#in #= 35#ft #1/2#in

So, the man needs to purchase #35#ft #1/2#in of wallpaper border.