Yes, it is permissible to recite part of a long soorah in prayer, instead of reciting a complete short soorah, But it is better to recite a complete soorah in each rak’ah. This is what the Prophet (peace and blessings of Allaah be upon him) usually did. Al-Bukhaari (762) and Muslim (451) narrated that Abu Qutaadah said: “The Prophet (peace and blessings of Allaah be upon him) used to recite al-Faatihah and another soorah in the first two rak’ahs of Zuhr and ‘Asr.” This hadeeth indicates that “reciting a short soorah in full is better than reciting an equal part of a longer soorah.” (Sharh Muslim by al-Nawawi (4/174). The words of Abu Qutaadah - “The Prophet (peace and blessings of Allaah be upon him) used to recite…” indicate that the Prophet (peace and blessings of Allaah be upon him) persisted in doing that, or that this is what he usually did. Fath al-Baari, 2/244. 

It was narrated that the Prophet (peace and blessings of Allaah be upon him) recited certain soorahs in certain prayers. Muslim (727) narrated that Ibn ‘Abbaas said: “The Messenger of Allaah (peace and blessings of Allaah be upon him) used to recite ‘Say (O Muslims): “We believe in Allaah and that which has been sent down to us…’ [al-Baqarah 2:136 – interpretation of the meaning] and ‘Come to a word that is just between us and you…’ [Aal ‘Imraan 3:64 – interpretation of the meaning] in the two rak’ahs of Fajr prayer.” This hadeeth indicates that it is permissible to recite part of a soorah in a rak’ah. Nayl al-Awtaar, 2/255 

Ibn al-Qayyim (may Allaah have mercy on him) said: “The Prophet (peace and blessings of Allaah be upon him) taught us to recite a complete soorah, and sometimes he would recite a complete soorah over the two rak’ahs; or he would recite the first part of a soorah. As for reciting the last part of a soorah, or the middle part of a soorah, it was not narrated that he did that; and as for reciting two soorahs in one rak’ah, he would do that in naafil prayers, but it was not narrated that he did that in fard prayers.  The hadeeth of Ibn Mas’ood (may Allaah be pleased with him), “I know the pairs of soorahs that the Messenger of Allaah (peace and blessings of Allaah be upon him) would recite in one rak’ah. He would recite Soorat al-Rahmaan and Soorat al-Najm in one rak’ah, or Soorat al-Qamar and Soorat al-Haaqqah in one rak’ah, or Soorat al-Toor and Soorat al-Dhaariyaat in one rak’ah, or Soorat al-Waaqi’ah and Soorat al-Qalam in one rak’ah.” This hadeeth indicates that the Prophet (peace and blessings of Allaah be upon him) did that, but it does not specify whether he did it in fard (obligatory) prayers or naafil (supererogatory) prayers. The hadeeth may mean either. As for reciting one soorah in two rak’ahs, he used to do that rarely. Abu Dawood narrated from a man from Juhaynah that he heard the Messenger of Allaah (peace and blessings of Allaah be upon him) reciting Soorat al-Zalzalah in two rak’ahs of Fajr prayer, and he said: “I do not know whether the Messenger of Allaah (peace and blessings of Allaah be upon him) forgot or did he do that deliberately?” (Zaad al-Ma’aad, 1/214-215). 

Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said: “There is nothing wrong with a man reciting one verse from a soorah in an obligatory prayer or in a naafil prayer. This may be understood from the aayah (interpretation of the meaning): 

‘So, recite you of the Qur’aan as much as may be easy for you’

[al-Muzzammil 73:20]

But the Sunnah – which is preferable – is to recite a soorah, and the best is to recite one soorah in each rak’ah. If that is too difficult then it is acceptable to divide the soorah between the two rak’ahs.” (al-Sharh al-Mumti’, 3/104). 

May Allaah help us all to acquire useful knowledge and to do righteous deeds. 

And Allaah knows best. May Allaah bless our Prophet Muhammad.