Should moldy food go straight into the trash, or can you still eat the parts that aren't moldy?
You can still eat hard cheese. Cut the moldy piece generously out of the cheese and the rest is still edible. Make sure you don't touch the mold with your knife before cutting the rest of the cheese.
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With bread it's a different story. Bread is moister, which makes it easier for mold to spread. Even if you don't see any of it, that may be the case. So throw it away immediately, a moldy bread.
In general, the sturdier and more solid a product is, the more difficult it is for mold to penetrate. With a carrot or a sweet potato, for example, you can cut away the moldy piece, the rest of the vegetables are still edible. You can dispose of soft products, such as raspberries.