She died and left behind a daughter and a brother

Praise be to Allah.

The daughter gets half, because Allaah says (interpretation of the meaning): 

“Allaah commands you as regards your children’s (inheritance): to the male, a portion equal to that of two females; if (there are) only daughters, two or more, their share is two-thirds of the inheritance; if only one, her share is a half”

[al-Nisa’ 4:11]

The questioner does not describe the brother’s situation. Is he a full brother or a brother through the father only or through the mother only? If he is a full brother or a brother through the father only, then he gets the rest of the estate after the daughter takes her share (half). That is because the Messenger (peace and blessings of Allaah be upon him) said: “Give the shares of inheritance to those who are entitled to them, and whatever is left, it should go to the closest male relative (on the father’s side).” Narrated by al-Bukhaari (6773), Muslim (1615). 

This brother is the closest male relative to her, so he gets the rest after the daughter takes her share. 

But if this brother is a brother through the mother only, then the division of the estate is different.  

The daughter gets half, as stated above, and this brother through the mother does not get a share, as he is not entitled to anything of the estate, because a brother through the mother does not inherit anything if there are any children (whether male or female), because Allaah says (interpretation of the meaning): 

“If the man or woman whose inheritance is in question has left neither ascendants nor descendants, but has left a brother or a sister,” – i.e., on the mother’s side – “ each one of the two gets a sixth”

[al-Nisa’ 4:12]

So the brother on the mother’s side does not inherit anything unless the deceased left neither ascendants nor descendants (kalaalah). 

Kalaalah means the one who has no father or son, i.e., he has no father or grandfather, and no son or daughter. 

The scholars are unanimously agreed that brothers on the mother’s side do not inherit anything if there is one of the children of the deceased (whether male of female). This was quoted by Ibn Qudaamah in al-Mughni (9/7). 

Based on this, the daughter gets half, as mentioned above, then if there are any male relatives such as paternal uncles and their sons, after the daughter takes her share, the rest is given to the closest man among them. If there is no one, then this wealth should be given to the daughter, who takes the whole estate.