Question

From a rope of length $$20\dfrac{1}{2}$$ m, a piece of length $$3\dfrac{5}{8}$$ m is cut off. Find the length of the remaining rope.

Answer 1

Total length of rope $$= 20\dfrac{1}{2}m$$
Length cut off $$= 3\dfrac{5}{8}$$
Remaining rope$$= \left[20 \dfrac{1}{2} - 3\dfrac{5}{8}\right]m$$
$$= \left[ \dfrac{41}{2} - \dfrac{29}{8}\right]m$$

2	$$|2,8$$
4	$$|1,4$$
	$$|1,1$$

$$\therefore$$ LCM of 2 and 8 is 8
$$= \dfrac{41\times 4 - 29 \times 1}{8} \left[ \dfrac{164 - 29}{8}\right]m$$
$$= \left[ \dfrac{135}{8}\right]m = 16\dfrac{7}{8}m$$
$$\therefore $$Length of the remaining rope $$= 16\dfrac{7}{8} m $$