I want to create two math mode binary operation symbols:

#### (1) A combination of `-` (minus symbol) and `*` (asterisk)

#### (2) A combination of `/` (slash symbol) and `*` (asterisk)

The desired result would be something that looks like the following but is kerned and centered properly and has the left-right spacing of a typical binary operation:

[![a \minusast b = c \slashast d.](https://i.stack.imgur.com/sFbqa.png)](https://i.stack.imgur.com/sFbqa.png)

```
\documentclass[12pt]{article}

\begin{document}
\Huge\[a \mathbin{-\mkern-11.5mu*} b = c \mathbin{/\mkern-8.875mu*} d.\] % my makeshift solution
\end{document}

```

```
\[a \minusast b = c \slashast d.\] % desired macro names and syntax

```

My question is:

### How do I create the custom math mode binary relation symbols (1) and (2)?

It would also be nice if there's a version of (2) where the `/` symbol is adjusted to be a diagonal axis of symmetry of the `*` symbol.

### If it's also possible, how do I generally create a custom math mode binary operation symbol that is a combination of two binary operation symbols?

Thank you.