Question

Fill in the blanks:
(i) $\frac{9}{8}+\left(...\right)=\frac{-3}{2}$
(ii) $\left(...\right)÷\left(\frac{-7}{5}\right)=\frac{10}{19}$
(iii) $\left(...\right)÷\left(-3\right)=\frac{-4}{15}$
(iv) $\left(-12\right)÷\left(...\right)=\frac{-6}{5}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right) \\ \mathrm{Let}\frac{9}{8}÷\mathrm{x}=\frac{-3}{2} \\ \Rightarrow \frac{9}{8}\times \frac{1}{\mathrm{x}}=\frac{-3}{2} \\ \Rightarrow \frac{1}{\mathrm{x}}=\frac{-3}{2}÷\frac{9}{8} \\ \Rightarrow \frac{1}{\mathrm{x}}=\frac{-3}{2}\times \frac{8}{9} \\ \Rightarrow \frac{1}{\mathrm{x}}=\frac{-24}{18} \\ \Rightarrow \frac{1}{\mathrm{x}}=\frac{-4}{3} \\ \Rightarrow \mathrm{x}=\frac{-3}{4}[\mathrm{Reciprocal}\mathrm{of}\frac{-4}{3}] \end{gathered}$$

$$\begin{gathered} \left(\mathrm{ii}\right) \\ \mathrm{Let}\mathrm{x}÷\left(\frac{-7}{5}\right)=\frac{10}{19} \\ \Rightarrow \mathrm{x}\times \left(\frac{5}{-7}\right)=\frac{10}{19} \\ \Rightarrow \mathrm{x}=\left(\frac{10}{19}\right)÷\left(\frac{5}{-7}\right) \\ \Rightarrow \mathrm{x}=\frac{10}{19}\times \frac{-7}{5} \\ \Rightarrow \mathrm{x}=\frac{-70}{95} \\ \Rightarrow \mathrm{x}=\frac{-14}{19} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iii}\right) \\ \mathrm{Let}\mathrm{x}÷(-3)=\frac{-4}{15} \\ \Rightarrow \mathrm{x}\times \left({\displaystyle \frac{1}{-3}}\right)=\frac{-4}{15} \\ \Rightarrow \mathrm{x}=\frac{-4}{15}\times (-3) \\ \Rightarrow \mathrm{x}=\frac{12}{15} \\ \Rightarrow \mathrm{x}=\frac{4}{5} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iv}\right) \\ \mathrm{Let}(-12)÷\mathrm{x}=\frac{-6}{5} \\ \Rightarrow (-12)\times \frac{1}{\mathrm{x}}=\frac{-6}{5} \\ \Rightarrow \frac{1}{\mathrm{x}}=\frac{-6}{5}÷(-12) \\ \Rightarrow \frac{1}{\mathrm{x}}=\frac{-6}{5}\times \frac{1}{-12} \\ \Rightarrow \frac{1}{\mathrm{x}}=\frac{1}{10} \\ \Rightarrow \mathrm{x}=10 \end{gathered}$$