According to the Al-Arabiya broadcaster, the attacks were carried out late on Sunday.
One of the explosions took place in the northern part of the city, in the vicinity of the Aden square, while three others hit the eastern area of Baghdad, and another one hit the south of the city.
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Last year, a blast of a mine-studded car in the southwest of Iraqi capital, Baghdad, killed 55 people. The Daesh* terrorist group reportedly claimed responsibility for the attack.
*Daesh (also known as ISIS/ISIL/IS) is a terrorist group banned in Russia and many other countries.