A simple majority is required for a session of Congress. This is known as a quorum. Since the Senate has 100 members, 51 of them must be present. And since the House has 435 members, 218 must be present.
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with a two-thirds majority in each chamber
The Democrat Party has had the majority in Congress for the longest duration over the last 40 years. Out of the last 22 Congresses they have had the majority 12 times in the Senate and 14 times in the House.
To make it simple, a law begins as a bill, introduced by a member of one of the two houses of Congress. After discussion and possible amendments are proposed and voted up or down, the body votes on the amended bill. If it passes, it is sent to the other house and voted on. If it passes both houses, it is sent to the President. If he signs it or ignores it for ten days, it becomes a law. If he vetoes it, it goes back to the house where it first passed and if they pass it again with a 2/3 majority, it is sent to the other house. If they also pass it again with a 2/3 majority, it becomes law without the President's approval.
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The permanent committees of Congress are called a standing committee. The standing committees of each house are controlled by the majority leader.