Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers.
(i) $\frac{3}{7}$
(ii) $\frac{5}{8}$
(iii) $\frac{9}{7}$
(iv) $\frac{6}{5}$
(v) $\frac{12}{7}$
(vi) $\frac{1}{8}$
(vii) $\frac{1}{11}$
To do:
We have to find the reciprocal of each of the given fractions and classify the reciprocals as proper fractions, improper fractions and whole numbers.
Solution:
Proper fraction:
A proper fraction is a fraction in which the denominator is greater than the numerator of the fraction.
Improper fraction:
An improper fraction is a fraction in which the numerator is greater than the denominator.
Whole number:
Whole numbers include all natural numbers and 0.
Reciprocal of $\frac{a}{b}$ is $\frac{b}{a}$
Reciprocal of $a$ is $\frac{1}{a}$ and vice versa.
Therefore,
(i) $\frac{3}{7}$
Reciprocal of $\frac{3}{7}$ is $\frac{7}{3}$
$\frac{7}{3}$ is an improper fraction.
(ii) $\frac{5}{8}$
Reciprocal of $\frac{5}{8}$ is $\frac{8}{5}$
$\frac{8}{5}$ is an improper fraction
(iii) $\frac{9}{7}$
Reciprocal of $\frac{9}{7}$ is $\frac{7}{9}$
$\frac{7}{9}$ is a proper fraction.
(iv) $\frac{6}{5}$
Reciprocal of $\frac{6}{5}$ is $\frac{5}{6}$
$\frac{5}{6}$ is a proper fraction.
(v) $\frac{12}{7}$
Reciprocal of $\frac{12}{7}$ is $\frac{7}{12}$
$\frac{7}{12}$ is a proper fraction.
(vi) $\frac{1}{8}$
Reciprocal of $\frac{1}{8}$ is $8$
$8$ is a whole number.
(vii) $\frac{1}{11}$
Reciprocal of $\frac{1}{11}$ is $\frac{11}{1}$ or $11$
$11$ is a whole number.
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