When she and Kakeru were young, their mothers (they had the same father, but not the same mother) argued over whose child would become the heir to the family after their father's death. Machi's mother forced Machi to be perfect in everything - but in school all Machi could manage. Soon Machi's mother had a son and said that there was no need for Machi now. She also said that Machi was boring, even after Machi said that she was only listening to her mother's orders.
Kakeru explains to Yuki that is the reason Machi tends to destroy things that look nice or ruin something that is perfect. Ever since then, Machi has hated all forms of perfection, even walking around in circles dozens of times in clean, unblemished snow because it appeared too perfect.
She is very quiet and has a destructive tendency. She spends many hours each day spinning around and around. This destructive tendency came from her frustration at having to be completely perfect for her mother's sake, then being mocked and put down by the very person she worked so hard for.
Machi has brown hair that goes right above the middle of her back and has brown eyes. Machi usually has a blank expression on her face which is also due to her being so quiet, especially in the student council room among the other members. She's standing 5'5-5'6 (almost close to Yuki).
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When Yuki first sees her, she had trashed the student council room.
Yuki, after hearing Machi's and Kakeru shared past, promised to walk in the snow with her the next time it snowed, a promise Machi didn't think he'd keep. Over time, Yuki and Machi grew much closer.
Yuki called her, asking her to meet him at a certain spot. He was planning on telling her about the curse, but then his curse broke unexpectedly, so he instead told Machi that he loved her. Machi asked him if she could call him by his first name, to which Yuki consented.
In the last parts of the series, Yuki gave Machi the key to the apartment he will be staying in while he attends a university.
Since they are half-siblings, the two don't look at all alike. The two don't argue in school, but when he visits her house with Yuki, she is very hostile towards him. Kakeru sometimes uses her as an object of teasing, but usually she deals with it by threatening to strangle him. Despite his teasing nature, Kakeru cares for Machi, doing what he can to help her fit in (albeit in his own eccentric way).
Machi, despite her obvious irritation with his antics, proves to be far more open with Kakeru than anyone else, with the only possible exception being Yuki. She doesn't bother to hide her annoyance with him or hesitate to hit him when he makes her mad. Kakeru, in turn, allows her to do so and never gets mad at her, even when she physically abuses him.
Machi is one of the few who boldly proclaimed her distaste in Yuki, or at least disagrees with the Prince Yuki Fan Club. When Yuki was not chosen as Prince for the school play, Sorta Cinderella, Machi said that Yuki did not meet the requirements to be Prince. Later in the series she becomes attracted to Yuki as he tries to understand her.
Machi and Komaki seem to have a fairly good relationship. When visiting her and Kakeru, Machi made a point to bring something she knew Komaki would like. Komaki also seems to be fond of Machi, affectionately calling her "Chi-chan". They also seem to relate to one another in that they are both regular victims of Kakeru's teasing.
Kimi is likely the closest thing that Machi has to a "best friend". Unlike with Kakeru, Machi shows no signs of annoyance towards Kimi's enthusiastic personality and Kimi seems to enjoy Machi's company.
Kimi is also the only person Machi seems to listen to without objection, even going so far as to follow Kimi's advice on how to get Yuki to call her by name (although Yuki stopped her before she could go through with it). It should also be noted that Kimi never brought up the rumors about Machi, possibly suggesting that she either didn't believe them, or she simply didn't care. Machi seems to have some degree of respect for Kimi, possibly due to her honest and open personality.
- She doesn't appear in the anime.
all information on Kuragi Machi came from http://fruitsbasket.wikia.com/wiki/Machi_Kuragi