# What identity is this? (Division to multiplication )

1. Nov 30, 2012

### musiclover55

This isn't a homework help issue, I just want to know what identity(?) this is.

a/b to ab

or A^2/B^2 to (A^2)(B^2)

2. Nov 30, 2012

### Staff: Mentor

There is no identity that converts a/b to ab, nor is there one to convert A2/B2 to A2B2.

What you might be thinking of is this one:

$$\frac{a}{b} = a \cdot \frac{1}{b}$$

In other words, dividing by a number b is the same as multiplying by the reciprocal of b (1/b).

3. Nov 30, 2012

### LCKurtz

Or maybe this one:$$\frac a {\frac 1 b} = ab$$

4. Nov 30, 2012

### rcgldr

Although this probably isn't what you're looking for, there is a way to implement division or more specifically 1/b by iterating multiplications and additions via Newton Raphson method, but this seems unlikely to be what you're looking for.

For 1/b the iternation is:

xi+1 = xi (2 - b xi)

This converges quadratically. For integers, usually a table of bytes is used to get the initial approximation.

5. Nov 30, 2012

### musiclover55

Yea, thanks everyone. I thought that was possible, but obviously it's not lol.

6. Dec 1, 2012

### HallsofIvy

Staff Emeritus
Yet another possibility: A/B= AB-1