A fraction which bears the same ratio to \(\frac{1}{27}\) as \(\frac{3}{11}\)…
2023
A fraction which bears the same ratio to \(\frac{1}{27}\) as \(\frac{3}{11}\) bears to \(\frac{5}{9}\) is equal to
Answer: C. \(\frac{1}{55}\) — ConceptA proportion states that two ratios are equal. If an unknown fraction x bears to a reference fraction a the same ratio that b bears to c, then x/a =…
- A.
\(\frac{1}{11}\)
- B.
55
- C.
\(\frac{1}{55}\)
- D.
More than one of the above
- E.
None of the above
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Correct answer: C
Concept
A proportion states that two ratios are equal. If an unknown fraction x bears to a reference fraction a the same ratio that b bears to c, then x/a = b/c, so x = a × (b/c).
Application
Let the required fraction be x. The statement gives x/(1/27) = (3/11)/(5/9).
Divide by a fraction by multiplying by its reciprocal: (3/11)/(5/9) = (3/11) × (9/5) = 27/55.
Therefore x = (1/27) × (27/55) = 1/55.
Cross-check
(1/55)/(1/27) = 27/55, which is the same as (3/11)/(5/9). Hence the required fraction is 1/55.