Question

Joshua used 1/4 of a coil of rope to hold a shelf to the wall, kept 4/9 od the remainder and uses the rest equally to tie 2 parcels.
(a) What fraction of the rope did Joshua use to tie each parcel? Give your answer as a fraction in it's simplest form.

(b) Joshua had 240 cm of rope at first. How Ong was the rope he used to tie each parcel?

Answer 1

Let the length of rope be 1 unit.Given Joshua used $\frac{1}{4}$ of a coil of rope to hold a shelf to the wall.

Remainder rope = $1-\frac{1}{4} =\frac{3}{4}$

Joshua kept $\frac{4}{9}$ of the remainder

Rope kept by Joshua =$\frac{3}{4} .\frac{4}{9} =\frac{12}{36} =\frac{1}{3}$

Rope left =$\frac{3}{4} -\frac{1}{3} =\frac{9-4}{12} =\frac{5}{12}$

With this Joshua ties two parcels

a) Fraction of rope used to tie each parcel =$\frac{5}{12}$÷2

=$\frac{5}{12} .\frac{1}{2} =\frac{5}{24}$

b)Joshua has 240 cm of rope .

Rope used to tie each parcel = $240.\frac{5}{24}$ =50cm.

Answer 2

a)the fraction of rope that joshua used for each parcel is 16 2/3
b)the answer is 16.6 cm