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The conjugation paradigm for te-forms is complex, as we need to learn separate rules for ru-, u-, and irregular verbs. Furthermore, the rule for u-verbs is divided into five subrules. Read Grammar 1 in Lesson 6 (Genki I: p.150-151), then practice the conjugation rules for te-forms below.
The rule for ru-verbs is very simple: Take る off and add _____.
て（食べる 食べて）
って（食べる 食べって）
んで（食べる 食べんで）
u-verbs that end with う, つ, and る have their final syllable replaced by _____.
いて（待つ 待いて）
んで（待つ 待んで）
って（待つ 待って）
As discussed in Grammar 1 of Lesson 3 (Genki I: p.86-88), some verbs that end with る are ru-verbs and some others are u-verbs. Review the discussion on how the vowel before the final る syllable determines which verb belongs to which class. As far as te-forms are concerned, we observe that u-verbs that end with る will have a small っ, ru-verbs that end with る do not.
NEXT
u-verbs that end with む, ぶ, and ぬ have their final syllable replaced by _____.
んで（読む 読んで）
いで（読む 読いで）
して（読む 読して）
u-verbs that end with く have their final syllable replaced by _____.
って（書く 書って）
いで（書く 書いで）
いて（書く 書いて）
There is an important exception in the ～く class:
行く 行いて
行く 行って
行く 行いで
u-verbs that end with ぐ have their final syllable replaced by _____.
て（泳ぐ 泳て）
いで（泳ぐ 泳いで）
いて（泳ぐ 泳いて）
u-verbs that end with す have their final syllable replaced by _____.
って（話す 話って）
して（話す 話して）
んで（話す 話んで）
The irregular verbs する and くる, and compound verbs built with them, conjugate as follows.