Half cheaper than, please help me

  1. New pencil case is half cheaper than the new one.
  2. Ater my birthday, my sister is the only person to clean the house.

Are the two sentence right, please help me to correct them.
Many thanks

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The new pencil case is half the price of the new one.

After my birthday party my sister is the only one who is going to clean up the house.

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