Question

The new length of a stick is \(\dfrac{57}{66}~\text{ m}\). The old length of the stick was \(\dfrac{3}{11}~\text{ m}\) shorter than the new stick. Which of the following measures is greater than the old length of the stick?

Answer 1

Detailed step-by-step solution:
The new length of the stick is \(\dfrac{57}{66}~\text{ m}\)

The old length of the stick was \(\dfrac{3}{11}~\text{ m}\) shorter.

Old length of the stick = New length − \(\dfrac{3}{11}~\text{ m}\)

\( = \dfrac{57}{66}-\dfrac{3}{11}\)

\( = \dfrac{57}{66}-\dfrac{3 \times 6}{11 \times 6}\)

\( = \dfrac{57}{66}-\dfrac{18}{66} = \dfrac{57-18}{66} \)

Old length of the stick = \( \dfrac{13}{22}\)

Option A

Given fraction \(=\dfrac{54}{66} \)

Old length of the stick \(= \dfrac{13}{22} = \dfrac{13 \times 3}{22 \times 3} = \dfrac{39}{66} \)

\(54 > 39 \)

So, the given fraction is greater than the old length of the stick.
Option B
Given fraction \(= \dfrac{ 9}{22}\)

Old length of the stick \(= \dfrac{13}{22}\)
\(13 > 9\)
So, the given fraction is not greater than the old length of the stick.

Option C
Given fraction = \( \dfrac{13}{66}\)

Old length of the stick \( = \dfrac{13}{22} =\dfrac{ 13 \times 3}{ 22 \times 3} = \dfrac{39}{66}\)

\(39 > 13\)
So, the given fraction is not greater than the old length of the stick.

Option D
Given fraction \(= \dfrac{11}{22}\)
Old length of the stick \(= \dfrac{13}{22}\)
\(13 > 11\)
So, the given fraction is not greater than the old length of the stick.
Hence, Option A is correct.