Ratio and Proportion- Calculation Process

Question

How we arrived for for following:

$$\frac{441.66}{958.33}=\frac{441\cdot 3 +2}{958\cdot 3 +1}$$

I understand that $0.66$ is $\frac{2}{3}$ but want to know how we arrived at above relation.

Answer 1

The $2$ parts in the original "equation" are not actually equal to each other. Instead, assuming the "=" was meant to be "$\approx$", you get

$$\frac{441.66}{958.33} \approx \frac{441 + \frac{2}{3}}{958 + \frac{1}{3}} = \frac{441 \times 3 + 2}{958 \times 3 + 1} \tag{1}\label{eq1}$$

The approximation's numerator and denominator was multiplied by $3$, with $\frac{3}{3} = 1$, so the overall value doesn't change.