Inversing fraction

Question

I'm having a little trouble understanding the logic behind solving the following equation:

$(24/25)\times a = b \times \cos(12)$ we need to seperate a from the equation so it becomes $a = (b \times \cos(12) \times 25)/24$

1. Why does $24/25$ become $25/24$ ?
2. Why can't the answer be: $a = (b \times \cos(12)) / (24/25)$

Answer 1

Note that $$\frac{A}{\frac{24}{25}}=\frac{A\times 25}{24}$$ because $$\frac{A}{\frac{24}{25}}=\frac{A}{\frac{24}{25}}\times 1=\frac{A}{\frac{24}{25}}\times \frac{25}{25}=\frac{A\times 25}{\frac{24}{25}\times 25}=\frac{A\times 25}{24}.$$ So, $$\frac{b\times \cos(12)}{\frac{24}{25}}=\frac{b\times \cos(12)\times 25}{24}.$$

Answer 2

Firstly, You should know that 1/2 is the same as 2/4, where in 2/4 , both the top and bottom is multiplied by 2 of the number 1/2.

Now-

You answer (2) is also correct, they are both the same thing. What they have done is taken your equation -

^^ They have taken this and multiplied both top and bottom of the Right hand side with 25, which then gives-