Question

From a rope of length 20 1/2 m, a piece of length 3 5/8 m is cut off. Find the length of remaining rope.​

Answer 1

Answer:

135/8m

Step-by-step explanation:

total length of rope- 20 1/2 m

length of rope cut- 3 5/8m

length of remaining rope- length of rope- length of rope cut

20 1/2 = 41/2

3 5/8= 29/8

41/2-29/8

taking LCM of 2 and 8

LCM= 8

164-29/8

135/8m

Answer 2

• The length of the remaining rope = $16 \dfrac{7}{8} \: m$

Given :

• Total length of a rope = $\sf 20 \dfrac{1}{2} \: m$
• The length of one piece of a rope = $\sf 3 \dfrac{5}{8} \: m$

To Find :

• The length of the remaining rope.

Solution :

First, we need to convert the mixed fraction to simple fraction.

• Total length of a rope.

$\implies \rm20 \dfrac{1}{2} \: m \\ \\ \implies \rm \dfrac{20 \times 2 + 1}{2} \: m \\ \\ \implies \rm \frac{40 + 1}{2} \: m \\ \\ \implies \rm \dfrac{41}{2} \: m$

Hence,

The total length of a rope is $\sf \dfrac{41}{2} \: m$

• The length of one piece of a rope.

$\implies \rm3 \dfrac{5}{8} \: m \\ \\ \implies \rm \dfrac{3 \times 8 + 5}{8} \: m \\ \\ \implies \rm \dfrac{24 + 5}{8} \: m \\ \\ \implies \rm \dfrac{29}{8} \: m$

Hence,

The length of one piece of a rope is $\sf \dfrac{29}{8} \: m$

Now, we have to find the length of the remaining rope.

The length of the remaining rope = Total length – Length of a piece

Now we have,

$\star \: \: \: \tt Total \: \: length = \dfrac{41}{2} \: m \\ \\ \star \: \: \: \tt Length \: \: of \: \: a \: \: piece = \dfrac{29}{9} \: m$

$\implies \rm\dfrac{41}{2} \: m - \dfrac{29}{8} \: m \\ \\ \implies \rm \dfrac{41 \times 4 - 29 \times 1}{8} \: m \\ \\ \implies \rm \dfrac{164 - 29}{8} \: m \\ \\ \implies \rm \dfrac{135}{8} \: m$

Now, we have to convert it into mixed fraction.

$\sf\Large\qquad\quad16\\ \begin{array}{cc} \cline{2 - 2}\sf 8 )&\sf \ \ 135\\&\sf - \: \: \: 8\downarrow\\ \cline{2-2}& \sf \ \ \ \ \: \: 55\ \ \\ &\sf \ - \: 48 \\ \cline{2-2} & \sf \ \ \: \: 007 \\ \cline{2-2} \end{array}$

• Divisor = 8.
• Quotient = 16.
• Remainder = 7.

So, the mixed fraction is,

$\implies \rm16 \dfrac{7}{8} \: m$

Hence,

The length of the remaining rope is $16 \dfrac{7}{8} \: m$