Did you ever have a goldfish that died? When they do, they "go belly up". When we talk about a business going belly up, it means that it closes or goes bankrupt.
Here are some examples:
- Lehman Brothers went belly up in 2008.
- In this recession, many small businesses are going belly up.
- What happened to that café that was here? Has it gone belly up?
- It is not the first business that’s gone belly up because of the cost of electricity.
It can also mean "fail" or "go badly".
Here's a sports example:
- After a promising start in a 0-0 draw against Manchester City the club's defending has gone belly-up again, and they have lost their last two games 4-0 and 3-2.
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Note: You can spell "belly up" with a hyphen too: "belly-up" is okay! It just depends on which dictionary you look at.