Change HTML class based on select option value through JavaScript/jQuery

I have a long list of options in a select menu.

<select name="top-menu" id="menu-selector">
	<option value="#">Choose a category</option>
	<option value="ABC">ABC</option>
	<option value="DEF">DEF</option>
	<option value="GHI">GHI</option>
</select>

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When an option is selected, jQuery will fade in a new select menu based on the value of that option. In other words, choosing ABC will fade in another select menu where id="ABC". As of right now, I have this.

$(document).ready(function (){
	$("#menu-selector").change(function() {
		document.getElementById($(this).val()).fadeIn('slow');
	});
});

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However, that's not working. It throws this error:

Uncaught TypeError: Object #<HTMLSelectElement> has no method 'fadeIn'

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How can I fix this?