Correction - perhaps not so obscure, and colloquial would be a better description than slang.

NB context is everything:

"More than 100 mph" = better, if speed is what you want
"More than 30 mpg" = better in terms of fuel economy
"Less than half price" = better for the buyer

Consider how "better than asking price" can mean "more than" or "less than", depending on context (these are all from the first page at Google Search)

"I think it will do better than the asking price - if there are two collectors it could sky-rocket." = more than
"My aim as a professional photographer is make your property look $50K-$100K better than the asking price" = more than
"I bought mine on ebay and only paid about $95 for it which is much better than the asking price" = less than
"I asked one of the sales people if they could do better than the asking price of $30 on the tag, which they could. ($20)" = less than

@Skeeter Lewis - I still don't know why you assume advertisers have picked up 'better-than-half-price' from a relatively obscure piece of American slang and 'got it wrong'? This expression makes perfect sense on its own, and there's no need at all to attribute it to the misunderstanding of anything. Except perhaps it allows you to get in a dig at 'the sort of people who write advertising copy'.

An afterthought: couldn't these expressions be referring both to intelligence and the physical organ? I don't think the difference is so clear cut.

@jayles the unwhateverwillitbenext - as a general idea, I'd agree with you:

"She's the brains of the family"

But Wiktionary gets it wrong when it says plural only for British English to mean intelligence. Oxford and Longman have 'usually plural', Macmillan 'often plural'.

And there are quite a few exceptions:
"She has an amazing brain" (more likely than "amazing brains")

"to blow somebody's brains out"

I don't see much difference in the meaning of brain(s) in the two expressions Dyske is talking about, yet in British English "rack your brains" is much more common in books than the singular version (according to Ngram) , whereas "use your brain" is marginally more common than the plural in BrE, and much more common in AmE .

What is also evident is that there is a movement towards the singular for "intelligence", especially in American English, where "use your brain" is nearly three times as common (in Ngram books) as the plural version, and even "rack your brain" is overtaking the plural version in AmE. In fact over the whole history of this idiom "rack your brains" and "rack your brain" have jockeyed for poll position.

http://books.google.com/ngrams/graph?content=use+your+brain%3Aeng_us_2012%2Cuse+your+brains%3Aeng_us_2012%2Cuse+your+brain%3Aeng_gb_2012%2Cuse+your+brains%3Aeng_gb_2012&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cuse%20your%20brain%3Aeng_us_2012%3B%2Cc0%3B.t1%3B%2Cuse%20your%20brains%3Aeng_us_2012%3B%2Cc0%3B.t1%3B%2Cuse%20your%20brain%3Aeng_gb_2012%3B%2Cc0%3B.t1%3B%2Cuse%20your%20brains%3Aeng_gb_2012%3B%2Cc0

@Hairy Scot - Ngram agrees with you, about two to one, in both BrE and AmE.

@Skeeter Lewis - As Brits, there are some who run writing courses who might disagree with you, in line with one of the definitions of 'mechanics' at Oxford Dictionaries Online - "The way in which something is done or operated":

"Postgraduates today, at least in the UK, experience increasing pressure to publish in ... These can range from issues to do with the mechanics of writing for publication." - Glasgow University

"The mechanics of writing"- University of York Computer Sciences Dept

"Mechanics of Writing a Literature Review"- uk-student.met

"Style and the Mechanics of Writing" - University College London

"Introduction to Mechanics of Writing (3 credits)" - City College Norwich

"on the mechanics of writing (e.g. spelling, punctuation and grammar) " - the Centre for Academic Writing at Coventry University

"Other students require specific assistance with the mechanics of writing." - Royal Literary Fund

The reason we don't hear much about it is that we don't have the same tradition of university writing schools that America has. That's partly why the MA course in Creative Writing at UEA, set up in 1970 and led by Malcolm Bradbury and Angus Wilson, was so revolutionary. It was only really in the nineties that British universities started to introduce writing schools.

American university writing school websites, such as the OWL at Purdue University, currently celebrating its 2oth anniversary, can be a great resource for anyone wanting to do any kind of writing, not just creative writing, or to check grammar, punctuation rules etc.

http://owl.english.purdue.edu/owl/section/1/

@Dyske - some five years later I bet your daughter has got them sorted now. At the age of four, children are still mastering the basic rules, and the whole beauty of language acquisition is that they do indeed learn logical patterns, not in a piecemeal way - see Stephen Pinker's 'The Language Instinct'.

At that age this is nothing to worry about as by about the age of eight most of then have sorted out the most common irregularities.

It's different for ESL students, incidentally, as they learn the irregular forms at the same time as learning the rules for regular forms.

An infinitive without "to", also known as the bare infinitive, is used after modal auxiliary verbs (amongst others), for example:

"can do, will do, must do" etc

The verb "need" is a semi-modal, which means it can be used like a modal auxiliary verb or an ordinary verb:

"He need not wait." - modal with bare infinitive
"He doesn't need to wait." - normal verb with "to"-infinitive

The modal use "need" really only occurs in negatives an questions "Need I do it right now?", and normal verb use is probably becoming more common, and the modal use .

As far as I'm concerned "He needs not wait."is ungrammatical: it is neither modal nor normal verb use, but is trying to mix the two. At Oxford Online they say "he need not worry, not he needs not worry":

http://www.oxforddictionaries.com/definition/english/need (see Usage Note)

I'd never heard of mechanics being used in this way before (I think it's mainly American - actually the whole idea of writing schools is pretty American). But a quick look around suggests that some good writing websites, such as Grammarly.com, Grammar.ccc.net and The Owl at Purdue University do indeed distinguish between the two. For them, mechanics seems to refer to things like like sentence structure, spelling and capitalization, the use of numerals and other symbols such as italics, etc. Incidentally, apostrophes and hyphens seem to belong to mechanics rather than punctuation in this definition.

http://www.grammarly.com/handbook/mechanics/
http://owl.english.purdue.edu/owl/section/1/4/

Other websites, however, such as Grammar.about.com, Time4Writing.com and the University of Minnesota, include punctuation under mechanics.

You pays your money and you takes your choice!

Seinfeld may well have popularised it, but it was around well before that. Earliest example at Google Books is from a comedy from 1924, but it really seems to have taken off in the 1960s. This is from "Sex and the Office", by Helen Gurley Brown, from 1964 - "He helped out in the rose garden at home — not that there's anything wrong with that", and this is from 1967 - "... question of tolerance, disgust, hate, nor anything else, but lechery (not that there's anything wrong with that). " ("Anything goes", by Bine Strange Petersen, 1967)

Looking again at the original question, I've noticed that, apart from the fact that strict grammarians wouldn't allow "her" as the subject, there is an inconsistency here, in that "her" is objective and "I" subjective.

In neutral to formal English, we would indeed say "She and I travelled to Kansas together", but in Britain, at least, in informal conversation it's becoming quite common to use objective pronouns when there is a compound subject as in this example (but never with a single subject) - and in this case the "stand alone" rule doesn't apply. But when this happens, in the majority of cases "me" comes first, so "Me and her travelled to Kansas together" is probably more idiomatic than "Her and me travelled ...". But I stress, this only happens in informal, conversational English.