Find the fraction which bears the same ratio to \(\frac{1}{27}\) that \(\frac{3}{11}\) does to \(\frac{5}{9}\).
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\frac{1}{55}\)
‘Bears the same ratio’ means the two ratios are equal (a proportion). Calling the fraction \(x\):
\(\displaystyle x:\frac{1}{27}=\frac{3}{11}:\frac{5}{9}\)
Writing each ratio as a division: \(\displaystyle x=\frac{1}{27}\times\frac{3}{11}\div\frac{5}{9}=\frac{1}{27}\times\frac{3}{11}\times\frac{9}{5}\)
The 27 cancels: \(\displaystyle x=\frac{27}{27\times55}=\frac{1}{55}\)