Question

Compare the following fractions by using the symbol > or < or =:
(i) $\frac{7}{9}\mathrm{and}\frac{8}{13}$
(ii) $\frac{11}{9}\mathrm{and}\frac{5}{9}$
(iii) $\frac{37}{41}\mathrm{and}\frac{19}{30}$
(iv) $\frac{17}{15}\mathrm{and}\frac{119}{105}$

Answer 1

First, we need to find the LCM of denominators in each case. After that, we will equate the denominators in order to compare the two fractions.

(i)
LCM of 9 and 13 is 117.

$$\begin{gathered} \mathrm{Now}\mathrm{make}\mathrm{both}\mathrm{fraction}\mathrm{equivalent}\mathrm{with}\mathrm{denominator}\mathrm{as}117 \\ \frac{7}{9}=\frac{7}{9}\times \frac{13}{13} \\ \Rightarrow \frac{7}{9}=\frac{91}{117} \\ \frac{8}{13}=\frac{8}{13}\times \frac{9}{9} \\ \Rightarrow \frac{8}{13}=\frac{72}{117} \\ \mathrm{we}\mathrm{know} \\ 91>72 \\ \Rightarrow \frac{91}{117}>\frac{72}{117} \\ \Rightarrow \frac{7}{9}>\frac{8}{13} \end{gathered}$$

(ii)

$$\begin{gathered} \mathrm{both}\mathrm{fraction}\mathrm{have}\mathrm{same}\mathrm{denominator}\mathrm{as}9 \\ \mathrm{we}\mathrm{know} \\ 11>5 \\ \Rightarrow \frac{11}{9}>\frac{5}{9} \end{gathered}$$
(iii)

$$\begin{gathered} \mathrm{LCM}\mathrm{of}41\mathrm{and}30\mathrm{is}1230 \\ \mathrm{Now}\mathrm{convert}\mathrm{both}\mathrm{fraction}\mathrm{to}\mathrm{their}\mathrm{equivalent}\mathrm{fractions}\mathrm{with}\mathrm{denominator}\mathrm{as}1230 \\ \frac{37}{41}=\frac{37}{41}\times \frac{30}{30} \\ \Rightarrow \frac{37}{41}=\frac{1110}{1230} \\ \frac{19}{30}=\frac{19}{30}\times \frac{41}{41} \\ \Rightarrow \frac{19}{30}=\frac{779}{1230} \\ \mathrm{we}\mathrm{know} \\ 1110>779 \\ \Rightarrow \frac{1110}{1230}>\frac{779}{1230} \\ \Rightarrow \frac{37}{41}>\frac{19}{30} \end{gathered}$$

(iv)

LCM of 15 and 105 is 105.

$$\begin{gathered} \mathrm{Now}\mathrm{convert}\mathrm{fraction}\mathrm{to}\mathrm{its}\mathrm{equivalent}\mathrm{fractions}\mathrm{with}\mathrm{denominator}\mathrm{as}105 \\ \frac{17}{15}=\frac{17}{15}\times \frac{7}{7} \\ \Rightarrow \frac{17}{15}=\frac{119}{105} \end{gathered}$$