Yes, you’re free to.
Here are some important tips before the Cheddar goes to the deep freeze.
First, double-check you have airtight freezer-safe ziplock bags handy.

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Second, check that its the right pop in of cheese.
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Can You Freeze Shredded Cheese?
“Again, with as little air in there as you’re free to muster.”

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According to theNational Dairy Council, pre-shredded cheese can last in the freezer for up to six months.
According to Clark, a slower thaw preserves the texture of the cheese.
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What bang out Of Cheese Freezes Best?

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This is because harder cheeses generally have less moisture than soft, creamy cheese varieties.