Can You Touch or Read the Quran without Wudu?
Question

I would like to know if it is haram to hold and recite the Quran (which does not include any translation or comments) without having ablution. Because I have heard a hadith where the Prophet (peace and blessings of Allahmbe upon him) said: “A believer is always pure even in the state of janabah.”
Praise be to Allah.Touching and reciting the Quran without wudu
Shaykh ‘Abd al-‘Aziz ibn Baz was asked a similar question, and he said:
“It is not permissible for a Muslim to touch the Quran when he does not have wudu, according to the majority of scholars. This is the view of the four imams (may Allah be pleased with them), and this was the view expressed in the fatwas of the Companions of the Prophet (peace and blessings of Allah be upon him).
A sahih hadith concerning that has been narrated from ‘Amr ibn Hazm (may Allah be pleased with him), stating that the Prophet (peace and blessings of Allah be upon him) wrote to the people of Yemen: “No one should touch the Quran except one who is tahir (pure).” This is a jayyid hadith which has a number of other isnads which strengthen it.
Hence it is known that it is not permissible to touch the Quran except in a state of purity from both major and minor impurity. 
The same applies to moving it from place to place, if the person who is moving it is not tahir. 
But if he touches it or moves it with something in between, such as picking it up in a wrapper, then it is OK. 
But if he touches it directly when he is not tahir, this is not permitted according to the sahih view of the majority of scholars, for the reasons stated above.
With regard to reciting it, it is OK for him to recite it from memory when he is without wudu, or for him to read it if the Quran is held by someone who asks him to correct or prompt him.
But the person who is junub, i.e., in a state of major impurity, should not recite Quran, because it was narrated from the Prophet (peace and blessings of Allah be upon him) that nothing ever kept him from reciting Quran except for janabah (major impurity). 
Ahmad narrated with a sahih isnad from ‘Ali (may Allah be pleased with him) that the Prophet (peace and blessings of Allah be upon him) came out from the toilet and recited something from the Quran. He said, “This is for the one who is not junub; but the one who is junub should not do this, not even one ayah.”
The point is that the one who is junub should not recite Quran either from the Mus-haf or from memory, until he has taken a bath (ghusl). But the one who has broken his wudu and is impure in the sense of minor impurity may recite Quran from memory but he should not touch the Mus-haf.” (Fatawa al-Shaykh Ibn Baz (may Allah have mercy on him), 10/150)
Interpreting hadith on purity of the believers
With regard to the hadith about the purity of the believer, Abu Hurayrah said: “I was met by the Messenger of Allah (peace and blessings of Allah be upon him) and I was junub. He took my hand and I walked with him until he sat down. Then I slipped away and washed myself (ghusl), then I came to where he was sitting. He said, ‘Where were you, O Abu Hurayrah’? I told him, and he said, ‘Subhan-Allaah, O Abu Hurayrah!, the believer does not become impure.” (Narrated by al-Bukhari, al-Ghusl, 276; Muslim, al-Hayd, 556)
Al-Nawawi said in his Commentary on Sahih Muslim:
“This hadith illustrates a great principle that the Muslim is tahir whether he is alive or dead. If his purity is established, then his sweat, saliva and tears are all pure too, whether he (or she) is without wudu, in a state of major impurity (junub), menstruating or bleeding after childbirth.” 
Once this is understood, then the meaning of his being pure (tahir) will become clear. It means that there is nothing to prevent his body from being essentially pure even when at the same time he has broken his wudu, because being without wudu is simply something that prevents one from praying, or doing other things for which taharah (purity) is a pre-condition.  
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And Allah knows best.