If P = 96/ (95 × 97), Q = 97/ (96 × 98) and R = 1/97, then which of the following is TRUE?
R < Q < P
Rewrite using \((n-1)(n+1)=n^2-1\): \(P=\tfrac{96}{96^2-1}\), \(Q=\tfrac{97}{97^2-1}\).
P vs Q: The function \(f(x)=\tfrac{x}{x^2-1}\) decreases for \(x>1\), so \(P>Q\).
Q vs R: \(Q=\tfrac{97}{97^2-1}>\tfrac{97}{97^2}=\tfrac{1}{97}=R\).
Therefore R < Q < P.
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Important Questions from Fractions
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Match the following.
Column I
Column II
a.
Equivalent fraction of \(\frac{7}{12}\) is
i.
Proper fraction
b.
Equivalent fraction of \(\frac{9}{15}\) is
ii.
Improper fraction
c.
\(\frac{7}{11}\) is
iii.
\(\frac{21}{36}\)
d.
\(\frac{19}{5}\) is
iv.
\(\frac{3}{5}\)
Among the fractions \(\frac{7}{12}\) , \(\frac{8}{15}\) , \(\frac{17}{24}\) and \(\frac{13}{18}\) , which is the smallest?
