Attached to a verb stem, ~かける means an action has been started but not finished ('to begin to ~; to half-do ~'), and ~かけだ / ~かけの describes something in that half-finished state. It captures an action interrupted midway or on the verge of happening.
[Verb ます-stem] + かける / かけだ / かけの + [Noun]
テーブルに食べかけのケーキがある。
Teeburu ni tabekake no keeki ga aru.
There is a half-eaten cake on the table.
ます-stem 食べ + かけの + noun describes the cake in a half-eaten state.
彼は何か言いかけて、やめた。
Kare wa nanika iikakete, yameta.
He started to say something, then stopped.
言い + かけて shows an action begun but broken off midway.
この本はまだ読みかけだ。
Kono hon wa mada yomikake da.
I'm still only partway through this book.
読み + かけだ describes the book as left in a half-read state.
• Attaches to the verb ます-stem (食べ, 読み, 言い). • かける = the act of half-doing; かけだ/かけの = the resulting half-done state. • Can also mean 'on the verge of', e.g. 死にかける (nearly die).
The JLPT rarely asks whether you recognise a pattern — it asks which of several similar patterns fits. These are the ones ~かけだ/~かける is tested against.
~ている途中 neutrally states 'in the middle of doing'; ~かけ emphasizes that the action was started and left unfinished/interrupted.
~だす marks the sudden start of an action (降り出す = start raining); ~かける marks starting but not completing, with the unfinished state in focus.
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