Which of the following are procedures by which the U.S. Constitution can be formally changed?

The U.S. Constitution can be formally changed through a process called constitutional amendment. There are two primary procedures established by the Constitution for proposing and ratifying amendments:

1. Proposal:
- The first method is through a two-thirds (⅔) majority vote in both chambers of the U.S. Congress (the House of Representatives and the Senate). This means that both the House and the Senate must agree by a two-thirds majority to propose an amendment.
- The second method is through a constitutional convention requested by at least two-thirds of the state legislatures. Once the convention is called, delegates from each state would meet to propose amendments. However, to date, all amendments have been proposed by Congress, and this method has never been used.

2. Ratification:
- Once an amendment is proposed, it must be ratified by three-fourths (¾) of the states. This can be achieved through the state legislatures, where the proposed amendment must be approved by the legislatures of three-fourths of the states.
- Alternatively, a constitutional amendment can be ratified through special state conventions. In this case, the proposed amendment needs to be approved by three-fourths of the state conventions called specifically for this purpose. However, this method has only been used once, for the ratification of the 21st Amendment, which repealed Prohibition.

Therefore, to formally change the U.S. Constitution, an amendment must be proposed by a two-thirds majority in Congress or through a constitutional convention requested by two-thirds of the state legislatures. Following the proposal, the amendment must be ratified by three-fourths of the states either through their legislatures or through special state conventions.

None of the above.