Question

Carry out the following subtarctions involving rational numbers.

(i) $\frac{7}{11}-\frac{3}{7}$

(ii) $\frac{13}{36}-\frac{2}{40}$

(iii) $1\frac{2}{3}-3\frac{5}{6}$

(iv) $4\frac{1}{2}-3\frac{1}{3}$

Answer 1

$\left(\mathrm{i}\right)\frac{7}{11}-\frac{3}{7}$
Now, LCM of 11 and 7 is 77.
$$\begin{gathered} \frac{7}{11}-\frac{3}{7} \\ =\frac{7\times 7}{11\times 7}-\frac{3\times 11}{7\times 11} \\ =\frac{49}{77}-\frac{33}{77} \\ =\frac{49-33}{77} \\ =\frac{16}{77} \end{gathered}$$
$\left(\mathrm{ii}\right)\frac{13}{36}-\frac{2}{40}$
Now, LCM of 36 and 40 is 360.
$$\begin{gathered} \frac{13}{36}-\frac{2}{40} \\ =\frac{13\times 10}{36\times 10}-\frac{2\times 9}{40\times 9} \\ =\frac{130}{360}-\frac{18}{360} \\ =\frac{130-18}{360} \\ =\frac{112}{360} \\ =\frac{112÷8}{360÷8}\left(\mathrm{since},\mathrm{HCF}\mathrm{of}112\mathrm{and}360\mathrm{is}8\right) \\ =\frac{14}{45} \end{gathered}$$
$$\begin{gathered} \left(\mathrm{iii}\right)1\frac{2}{3}-3\frac{5}{6} \\ =\frac{1\times 3+2}{3}-\frac{3\times 6+5}{6} \\ =\frac{5}{3}-\frac{23}{6} \end{gathered}$$
Now, LCM of 3 and 6 is 6.
$$\begin{gathered} \frac{5}{3}-\frac{23}{6} \\ =\frac{5\times 2}{3\times 2}-\frac{23\times 1}{6\times 1} \\ =\frac{10}{6}-\frac{23}{6} \\ =\frac{10-23}{6} \\ =-\frac{13}{6} \end{gathered}$$
$$\begin{gathered} \left(\mathrm{iv}\right)4\frac{1}{2}-3\frac{1}{3} \\ =\frac{4\times 2+1}{2}-\frac{3\times 3+1}{3} \\ =\frac{9}{2}-\frac{10}{3} \end{gathered}$$
Now, LCM of 2 and 3 is 6.
$$\begin{gathered} \frac{9}{2}-\frac{10}{3} \\ =\frac{9\times 3}{2\times 3}-\frac{10\times 2}{3\times 2} \\ =\frac{18}{6}-\frac{20}{6} \\ =\frac{18-20}{6} \\ =-\frac{2}{6} \\ =-\frac{1}{3} \end{gathered}$$