Question

Find the reciprocal of each of the following fractions and classify them as proper, improper and whole numbers:
(i) $\frac{3}{7}$
(ii) $\frac{5}{8}$
(iii) $\frac{9}{7}$
(iv) $\frac{6}{5}$
(v) $\frac{12}{7}$
(vi) $\frac{1}{8}$

Answer 1

Reciprocal of a non-zero fraction $\frac{\mathrm{a}}{\mathrm{b}}\mathrm{is}\frac{\mathrm{b}}{\mathrm{a}}$
(i)
$$\begin{gathered} \mathrm{Reciprocal}\mathrm{of}\frac{3}{7}\mathrm{is}\frac{7}{3} \\ \mathrm{It}\text{'}\mathrm{s}\mathrm{improper}\mathrm{fraction}\mathrm{because}\text{n}\mathrm{umerator}\mathrm{is}\mathrm{greater}\mathrm{than}\mathrm{denominator} \end{gathered}$$

(ii)
$$\begin{gathered} \mathrm{Reciprocal}\mathrm{of}\frac{5}{8}\mathrm{is}\frac{8}{5} \\ \mathrm{It}\text{'}\mathrm{s}\mathrm{improper}\mathrm{fraction}\mathrm{because}\mathrm{n}\mathrm{umerator}\mathrm{is}\mathrm{greater}\mathrm{than}\mathrm{denominator} \end{gathered}$$

(iii)
$$\begin{gathered} \mathrm{Reciprocal}\mathrm{of}\frac{9}{7}\mathrm{is}\frac{7}{9} \\ \mathrm{It}\text{'}\mathrm{s}\mathrm{proper}\mathrm{fraction}\mathrm{because}\text{n}\mathrm{umerator}\mathrm{is}\mathrm{less}\mathrm{than}\mathrm{denominator} \end{gathered}$$

(iv)
$$\begin{gathered} \mathrm{Reciprocal}\mathrm{of}\frac{6}{5}\mathrm{is}\frac{5}{6} \\ \mathrm{It}\text{'}\mathrm{s}\mathrm{proper}\mathrm{fraction}\mathrm{because}\text{n}\mathrm{umerator}\mathrm{is}\mathrm{less}\mathrm{than}\mathrm{denominator} \end{gathered}$$

(v)
$$\begin{gathered} \mathrm{Reciprocal}\mathrm{of}\frac{12}{7}\mathrm{is}\frac{7}{12} \\ \mathrm{It}\text{'}\mathrm{s}\mathrm{proper}\mathrm{fraction}\mathrm{because}\text{n}\mathrm{umerator}\mathrm{is}\mathrm{less}\mathrm{than}\mathrm{denominator} \end{gathered}$$

(vi)
$$\begin{gathered} \mathrm{Reciprocal}\mathrm{of}\frac{1}{8}\mathrm{is}\frac{8}{1}=8 \\ \mathrm{It}\mathrm{i}\mathrm{s}\mathrm{a}\text{w}\mathrm{hole}\mathrm{number} \end{gathered}$$