Question

Compare the following fractions using the symbol > ro <:

(i) $\frac{6}{7}$and $\frac{6}{11}$
(ii) $\frac{3}{7}$and $\frac{5}{7}$
(iii) $\frac{2}{3}$and $\frac{8}{12}$
(iv) $\frac{1}{5}$and $\frac{4}{15}$
(v) $\frac{8}{3}$and $\frac{8}{13}$
(vi) $\frac{4}{9}$and $\frac{15}{8}$

Answer 1

(i) $\frac{6}{7}>\frac{6}{11}$ because if the numerator is the same, then the fraction with smaller denominator is greater.
(ii) $\frac{3}{7}<\frac{5}{7}$ because 3 < 5 and the denominator is the same.

(iii)
$$\begin{gathered} \frac{8}{12}=\frac{2\times 2\times 2}{2\times 2\times 3}=\frac{2}{3} \\ so\frac{2}{3}=\frac{8}{12} \end{gathered}$$

(iv)
$$\begin{gathered} \frac{1}{5}=\frac{1}{5}\times \frac{3}{3}=\frac{3}{15} \\ \frac{3}{15}<\frac{4}{15} \end{gathered}$$ (Because 3 < 4 and the denominator is the same. Therefore, $\frac{1}{5}<\frac{4}{15}$.)

(v)
$\frac{8}{3}>\frac{8}{13}$ because if the numerator is the same, then the fraction with smaller denominator is greater.

(vi)
$$\begin{gathered} \frac{4}{9}=\frac{4}{9}\times \frac{8}{8}=\frac{32}{72} \\ \frac{15}{8}=\frac{15}{8}\times \frac{9}{9}=\frac{135}{72} \\ \frac{32}{72}<\frac{135}{72} \end{gathered}$$ (Because 135 > 32 and the denominator is the same)

∴$\frac{4}{9}<\frac{15}{8}$