Dividing fractions just got so much easier!

Note that

$\begin{aligned} A \div B \div C &= D\\ \implies \dfrac{A}{BC}&=D\\ \implies A &= BCD \end{aligned}$

Thus, if we substitute this in the second statement, we have

$\begin{aligned} \dfrac{1}{BCD} \div \dfrac{1}{B} \div \dfrac{1}{C} &= \dfrac{BC}{BCD}\\ &= \dfrac{1}{D} \end{aligned}$

Therefore, the result must be true.

For this particular problem, you must remember that:

$A ÷ B ÷ C = D$ can be rewritten as follows:

$A * 1/B * 1/C = D$ , which can be simplified as:

$A/BC = D$

Also keep in mind that $1/A ÷ 1/B ÷ 1/C = 1/D$ is equal to:

$1/A * B/1 ÷ 1/C = 1/D$ , which can be written as:

$B/A ÷ 1/C = 1/D$ , which once again can be written as:

$BC/A = 1/D$ . Finding the reciprocal of both sides gives you:

$A/BC = D$