2510.11 – Defined Operation no. 1

Define an operation $D$ for positive real numbers so that $a D b = \frac{ab}{(a + b)}$ .

Then $4 D (4 D 4)$ = what?

Solution

In evaluating $4 D (4 D 4)$ , we start inside the parentheses, as usual.

So $4 D (4 D 4) = 4 D \frac{16}{8} = 4 D 2 = \frac{8}{6} = \frac{4}{3}$ .