RD Sharma solution class 7 chapter 5 Operations On Rational numbers Exercise 5.3

Exercise 5.3

Page-5.10

Question 1:

Multiply:
(i) $\frac{7}{11} \mathrm{by} \frac{5}{4}$
(ii) $\frac{5}{7} \mathrm{by} \left(\frac{-3}{4}\right)$
(iii) $\frac{(-2)}{9} \mathrm{by} \frac{5}{11}$
(iv) $\frac{-3}{17} \mathrm{by} \frac{-5}{-4}$

Answer 1:

$$\begin{gathered} \left(\mathrm{i}\right) \frac{7}{11}\times \frac{5}{4}= \frac{7\times 5}{11\times 4} = \frac{35}{44} \\ \left(\mathrm{ii}\right) \frac{5}{7}\times \frac{-3}{4}=\frac{5\times -3}{7\times 4} = \frac{-15}{28} \\ \left(\mathrm{iii}\right) \frac{-2}{9}\times \frac{5}{11}= \frac{-2\times 5}{9\times 11} = \frac{-10}{99} \end{gathered}$$

$\left(\mathrm{iv}\right) \frac{-3}{17}\times \frac{-5}{-4}= \frac{-3\times 5}{17\times -4} = \frac{-15}{68}$

Question 2:

Multiply:
(i) $\frac{-5}{17} \mathrm{by} \frac{51}{-60}$
(ii) $\frac{-6}{11} \mathrm{by} \frac{-55}{36}$
(iii) $\frac{-8}{25} \mathrm{by} \frac{-5}{16}$
(iv) $\frac{6}{7} \mathrm{by} \frac{-49}{36}$

Answer 2:

(i) $\frac{-5}{17}\times \frac{51}{-60}=\frac{-5}{17}\times \frac{17\times 3}{-5\times 3\times 4}=\frac{1}{4}$

(ii) $\frac{-6}{11}\times \frac{-55}{36}=\frac{-6}{11}\times \frac{-5\times 11}{6\times 6}=\frac{5}{6}$

$\left(\mathrm{iii}\right) \frac{-8}{25}\times \frac{-5}{16}=\frac{-8}{5\times 5}\times \frac{-5}{8\times 2}=\frac{1}{10}$

(iv) $\frac{6}{7}\times \frac{-49}{36}=\frac{6}{7}\times \frac{-7\times 7}{6\times 6}=\frac{-7}{6}$

Question 3:

Simplify peach of the following and express the result as a rational number in standard from:
(i) $\frac{-16}{21}\times \frac{14}{5}$
(ii) $\frac{7}{6}\times \frac{-3}{28}$
(iii) $\frac{-19}{36}\times 16$
(iv) $\frac{-13}{9}\times \frac{27}{-26}$

Answer 3:

$\left(\mathrm{i}\right) \frac{-16}{21}\times \frac{14}{5}=\frac{-16\times 14}{21\times 5}=\frac{-32}{15}$
$$\begin{gathered} \left(\mathrm{ii}\right) \frac{7}{6}\times \frac{-3}{28}=\frac{7\times -3}{6\times 28}=\frac{-1}{8} \\ \left(\mathrm{iii}\right) \frac{-19}{36}\times 16=\frac{-19\times 16}{36}=\frac{-76}{9} \end{gathered}$$

$\left(\mathrm{iv}\right) \frac{-13}{9}\times \frac{27}{-26}=\frac{-13\times 27}{9\times -26}=\frac{3}{2}$

Question 4:

Simplify:
(i) $\left(-5\times \frac{2}{15}\right)-\left(-6\times \frac{2}{9}\right)$
(ii) $\left(\frac{-9}{4}\times \frac{5}{3}\right)+\left(\frac{13}{2}\times \frac{5}{6}\right)$

Answer 4:

$$\begin{gathered} \left(\mathrm{i}\right) (-5\times \frac{2}{15})-(-6\times \frac{2}{9})=(-5\times \frac{2}{3\times 5})-(-6\times \frac{2}{3\times 3}) \\ =\left(\frac{-2}{3}\right)-\left(\frac{-4}{3}\right)=\frac{-2+4}{3}=\frac{2}{3} \\ \left(\mathrm{ii}\right) (\frac{-9}{4}\times \frac{5}{3})+(\frac{13}{2}\times \frac{5}{6})=(\frac{-3\times 3}{4}\times \frac{5}{3})+\left(\frac{65}{12}\right) \\ =\left(\frac{-15}{4}\right)+\left(\frac{65}{12}\right)=\frac{-15\times 3}{4\times 3}+\frac{65}{12}=\frac{-45+65}{12}=\frac{20}{12}=\frac{5\times 4}{3\times 4}=\frac{5}{3} \end{gathered}$$

Question 5:

Simplify:
(i) $\left(\frac{13}{9}\times \frac{-15}{2}\right)+\left(\frac{7}{3}\times \frac{8}{5}\right)+\left(\frac{3}{5}\times \frac{1}{2}\right)$
(ii) $\left(\frac{3}{11}\times \frac{5}{6}\right)-\left(\frac{9}{12}\times \frac{4}{3}\right)+\left(\frac{5}{13}\times \frac{6}{15}\right)$

Answer 5:

$$\begin{gathered} \left(\mathrm{i}\right) (\frac{13}{9}\times \frac{-15}{2})+(\frac{7}{3}\times \frac{8}{5})+(\frac{3}{5}\times \frac{1}{2}) \\ =(\frac{13}{3\times 3}\times \frac{-3\times 5}{2})+\left(\frac{56}{15}\right)+\left(\frac{3}{10}\right)=\frac{-65}{6}+\frac{56}{15}+\frac{3}{10} \\ =\frac{-65\times 5}{6\times 5}+\frac{56\times 2}{15\times 2}+\frac{3\times 3}{10\times 3}=\frac{-325}{30}+\frac{112}{30}+\frac{9}{30}=\frac{-325+112+9}{30}=\frac{-204}{30} = \frac{-34}{5} \\ \left(\mathrm{ii}\right) (\frac{3}{11}\times \frac{5}{6})-(\frac{9}{12}\times \frac{4}{3})+(\frac{5}{13}\times \frac{6}{15}) \\ =(\frac{3}{11}\times \frac{5}{2\times 3})-\left(\frac{3\times 3}{4\times 3}\times \frac{4}{3}\right)+\left(\frac{5}{13}\times \frac{3\times 2}{5\times 3}\right)=\frac{5}{22}-\frac{1}{1}+\frac{2}{13} \\ =\frac{5\times 13}{22\times 13}-\frac{1\times 286}{1\times 286}+\frac{2\times 22}{13\times 22}=\frac{65}{286}-\frac{286}{286}+\frac{44}{286}=\frac{65-286+44}{286}=\frac{-177}{286} \end{gathered}$$