Question

(i) Provide the number in the box $[]$, such that $\frac{2}{3}\times []=\frac{10}{30}$

(ii) The simplest form of the number obtained in $[]$ is

Answer 1

Step-1 The number in the box $[]$

(i) Let the number inside $[]$be $m$

So $\frac{2}{3}\times \mathrm{m}=\frac{10}{30}$

$\Rightarrow \mathrm{m}=\frac{10}{30}\times \frac{3}{2}$

$\Rightarrow \mathrm{m}=\frac{10}{30}\times \frac{3}{2}$

$\Rightarrow \mathrm{m}=\frac{5}{10}$

Hence the number inside$[]$ should be $\frac{5}{10}$

Step-2 The simplest form of the number:

(ii) As we know $\mathrm{m}=\frac{5}{10}$

$m$ can be simplified by dividing both the numerator and denominator by $5$.

$\Rightarrow \mathrm{m}=\frac{{\displaystyle \frac{5}{5}}}{{\displaystyle \frac{10}{5}}}$

$\Rightarrow \mathrm{m}=\frac{1}{2}$

Hence the simplest form of the number obtained in the box is $\frac{1}{2}$.