Fill in the blanks.

Question:

Fill in the blanks.

(i) $\frac{25}{8} \div(\ldots \ldots)=-10$.

(ii) $\frac{-8}{9} \times(\ldots \ldots)=\frac{-2}{3}$.

(iii) $(-1)+(\ldots \ldots)=\frac{-2}{9}$.

(iv) $\frac{2}{3}-(\ldots \ldots)=\frac{1}{15}$.

Solution:

(i) Let the number be $x$.

Now, we have :

$\frac{25}{8} \div x=-10$

$\Rightarrow \frac{25}{8} \times \frac{1}{x}=-10$

$\Rightarrow \frac{1}{x}=-10 \div \frac{25}{8}$

$\Rightarrow \frac{1}{x}=-10 \times \frac{8}{25}$

$\Rightarrow \frac{1}{x}=\frac{-80}{25}$

$\Rightarrow x=\frac{25}{-80}$

$\Rightarrow x=\frac{25 \times-1}{-80 \times-1}$

$\Rightarrow x=\frac{-25}{80}$

$\Rightarrow x=\frac{-25 \div 5}{80 \div 5}$

$\Rightarrow x=\frac{-5}{16}$

(ii) Let the number be $x$.

Now, we have:

$\frac{-8}{9} \times x=\frac{-2}{3}$

$\Rightarrow x=\frac{-2}{3} \div \frac{-8}{9}$

$\Rightarrow x=\frac{-2}{3} \times \frac{9}{-8}$

$\Rightarrow x=\frac{18}{24}=\frac{18 \div 6}{24 \div 6}$

$\Rightarrow x=\frac{3}{4}$

(iii) Let the blank space be $x$.

Now, we have :

$(-1)+x=\frac{-2}{9}$

$\Rightarrow x=\frac{-2}{9}+1$

$\Rightarrow x=\frac{-2+9}{9}$

$\Rightarrow x=\frac{7}{9}$

(iv) Let the blank space be $x$.

Now, we have:

$\frac{2}{3}-x=\frac{1}{15}$

$\Rightarrow-x=\frac{1}{15}-\frac{2}{3}$

$\Rightarrow-x=\frac{1-10}{15}$

$\Rightarrow-x=\frac{-9}{15}$

$\Rightarrow x=\frac{9}{15}=\frac{3}{5}$

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