Question

(i) Provide the number in the box [ ], such that$\frac{3}{5}\times []=\frac{24}{75}$

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

Answer 1

Step 1: Find the required number:

Let the number inside the box [ ] be $m$

So $\frac{3}{5}\times \mathrm{m}=\frac{24}{75}$

$\Rightarrow \mathrm{m}=\frac{24}{75}\times \frac{5}{3}$

$\Rightarrow \mathrm{m}=\frac{8}{15}$

So $\frac{3}{5}\times []=\frac{24}{75}$ to be true, the number in the box should be $\frac{8}{15}$

Step 2: Simplified form of number:

The number in the box is $\frac{8}{15}$

As $8$ and $15$ are both co-prime so $\frac{8}{15}$ cannot be further simplified.

Hence the simplest form of the number in the box is $\frac{8}{15}$.