Which of the following fractions has a reciprocal that is a proper fraction ?
\( \frac{9}{7} \)
A proper fraction has its numerator smaller than its denominator. The reciprocal of \( \frac{a}{b} \) is \( \frac{b}{a} \), so the reciprocal is proper only when the original fraction is improper (a > b).
Reciprocals: \( \frac{9}{7} \to \frac{7}{9} \) (proper); \( \frac{2}{7} \to \frac{7}{2} \), \( \frac{5}{8} \to \frac{8}{5} \), \( \frac{2}{5} \to \frac{5}{2} \) (all improper).
Check: \( 7 \lt 9 \), so \( \frac{7}{9} \lt 1 \).
Hence, \( \frac{9}{7} \).
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Important Questions from Fractions
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
Number 0.232323 can be written in rational form as:
Solve: \(\frac{1}{2}\) [{-2(2 + 3)*20}/2]
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?
