Let the length of rope be 1 unit.Given Joshua used [tex] \frac{1}{4} [/tex] of a coil of rope to hold a shelf to the wall.
Remainder rope = [tex] 1-\frac{1}{4} =\frac{3}{4} [/tex]
Joshua kept [tex] \frac{4}{9} [/tex] of the remainder
Rope kept by Joshua =[tex] \frac{3}{4} .\frac{4}{9} =\frac{12}{36} =\frac{1}{3} [/tex]
Rope left =[tex] \frac{3}{4} -\frac{1}{3} =\frac{9-4}{12} =\frac{5}{12} [/tex]
With this Joshua ties two parcels
a) Fraction of rope used to tie each parcel =[tex] \frac{5}{12} [/tex]÷2
=[tex] \frac{5}{12} .\frac{1}{2} =\frac{5}{24} [/tex]
b)Joshua has 240 cm of rope .
Rope used to tie each parcel = [tex] 240.\frac{5}{24} [/tex] =50cm.
