Question

Fill in the blanks.
(i) $\frac{25}{8}÷\left(.......\right)=-10.$
(ii) $\frac{-8}{9}\times \left(.......\right)=\frac{-2}{3}.$
(iii) $\left(-1\right)+\left(.......\right)=\frac{-2}{9}.$
(iv) $\frac{2}{3}-\left(.......\right)=\frac{1}{15}.$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right) \\ \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{be}x. \\ \mathrm{Now},\mathrm{we}\mathrm{have}: \\ \frac{25}{8}÷x=-10 \\ \Rightarrow \frac{25}{8}\times \frac{1}{x}=-10 \\ \Rightarrow \frac{1}{x}=-10÷\frac{25}{8} \\ \Rightarrow \frac{1}{x}=-10\times \frac{8}{25} \\ \Rightarrow \frac{1}{x}=\frac{-80}{25} \\ \Rightarrow x=\frac{25}{-80} \\ \Rightarrow x=\frac{25\times -1}{-80\times -1} \\ \Rightarrow x=\frac{-25}{80} \\ \Rightarrow x=\frac{-25÷5}{80÷5} \\ \Rightarrow x=\frac{-5}{16} \end{gathered}$$

(ii)
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{number}\mathrm{be}x. \\ \mathrm{Now},\mathrm{we}\mathrm{have}: \\ \frac{-8}{9}\times x=\frac{-2}{3} \\ \Rightarrow x=\frac{-2}{3}÷\frac{-8}{9} \\ \Rightarrow x=\frac{-2}{3}\times \frac{9}{-8} \\ \Rightarrow x=\frac{18}{24}=\frac{18÷6}{24÷6} \\ \Rightarrow x=\frac{3}{4} \end{gathered}$$

(iii)
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{blank}\mathrm{space}\mathrm{be}x. \\ \mathrm{Now},\mathrm{we}\mathrm{have}: \\ (-1)+x=\frac{-2}{9} \\ \Rightarrow x=\frac{-2}{9}+1 \\ \Rightarrow x=\frac{-2+9}{9} \\ \Rightarrow x=\frac{7}{9} \end{gathered}$$

(iv)
$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{blank}\mathrm{space}\mathrm{be}x. \\ \mathrm{Now},\mathrm{we}\mathrm{have}: \\ \frac{2}{3}-x=\frac{1}{15} \\ \Rightarrow -x=\frac{1}{15}-\frac{2}{3} \\ \Rightarrow -x=\frac{1-10}{15} \\ \Rightarrow -x=\frac{-9}{15} \\ \Rightarrow x=\frac{9}{15}=\frac{3}{5} \end{gathered}$$