English is full of little phrases that you hear a lot when people speak- but, these phrases aren't usually taught in textbooks.
Here are a few with "Half". When you use them, you'll sound more natural and more like a native speaker.
If you are "half-way there" it means that you are on the right path for solving a problem or achieving a goal.
"Once you've got your National Insurance number, you're half-way there."
given half the chance
You would so something very happily if you were given half the chance.
"I'd go and work abroad, given half the chance."
Often we use it to mean that someone would do something bad or wrong if they had the opportunity.
"Oh, he'd have the shirt off your back given half the chance!"
glass half empty
The full expression is "do you see the glass as half-empty or half-full?" but we often say things like "he's a glass half-empty person". It means you're pessimistic (glass half-empty) or optimistic (half-full).
cheap at half the price
If something is cheap at half the price, it's a great bargain.
"That sofa would be cheap at half the price. You should buy it!"
my better half
Your better half is your spouse (husband or wife.) It's often used ironically.
"I don't know what we're up to this weekend. I'll ask my better half."
six of one, half a dozen of another
This means that two alternatives will lead to the same result.
"You can get the train from London Bridge or Charing Cross. It's six of one, half a dozen of the other."
be too clever by half
If you are too clever by half, you are too confident that you're clever, and it annoys other people.
"I've got one of those kids in my class who's always trying to correct my English accent. He's too clever by half."
have half a mind to..
If you have half a mind to do something, you say you want to do something (because you're angry), but you probably won't.
"I've half a mind to write to the school to complain."
how the other half lives
The "other half" are rich people, and we often use the expression "see how the other half lives" to compare a rich lifestyle with our own.
"I took some photos of their house to show you how the other half lives!"
"They've got a cleaner and a gardener!"
"Ooh, how the other half lives!"
listen with half an ear
"If you listen with half an ear, you aren't really paying attention.
"She was telling me all about her holiday, but I was just listening with half an ear."
you don't know the half of it!
If we say "you don't know the half of it", we mean that you don't know the whole story - and that the part you don't know is even worse.
"I can't believe you had all those problems with the car-hire company."
"Oh, you don't know the half of it!"
time and a half
When you are paid "time and a half" it means that you earn half as much again because you're working at the weekend or in the evening, or on a public holiday.
"You get time and a half if you work on a Sunday."