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# 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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