Problem 66
Question
. The U.S. Constitution states that a constitutional amendment requires approval by \(\frac{3}{4}\) of the state legislatures. There are 50 states. Find the number of legislatures that must approve a constitutional amendment. Round to the nearest whole number.
Step-by-Step Solution
Verified Answer
38
1Step 1: Understand the given values
There are 50 states in total. To approve an amendment, \(\frac{3}{4}\) of the state legislatures need to agree.
2Step 2: Set up the equation
The problem states that \(\frac{3}{4}\) of all state legislatures need to approve the amendment. Therefore, set up the equation as \(\frac{3}{4} \times 50\).
3Step 3: Perform the multiplication
Multiply \(\frac{3}{4}\) by 50 to find the number of legislatures required. This gives \(\frac{3}{4} \times 50 = 37.5\).
4Step 4: Round the result
Since you can't have a fraction of a legislature, round the result to the nearest whole number. \(37.5\) rounds to \(38\).
Key Concepts
U.S. ConstitutionMultiplication of FractionsRounding NumbersConstitutional Amendment Approval
U.S. Constitution
The U.S. Constitution is the supreme law of the United States. It outlines the national framework of government and includes key principles like the separation of powers and checks and balances. One important aspect is the process for amending the Constitution. This process ensures that any changes reflect a broad consensus. To amend the Constitution, three-fourths of the state legislatures must approve the proposed amendment. Let's break that down in the context of today’s topic.
Multiplication of Fractions
Multiplying fractions involves straightforward arithmetic once you understand the basic principles. In the problem given, you need to multiply \( \frac{3}{4} \) by 50 to find the number of state legislatures required to approve a constitutional amendment. Here’s a reminder on how to multiply fractions:
1. Multiply the numerator (top number of the fraction) by the whole number: \(3 \times 50 = 150\).
2. Divide the result by the denominator (bottom number of the fraction): \( \frac{150}{4} = 37.5\).
This tells you that 37.5 state legislatures are needed. But since you can't have half a legislature, we'll need to round that number.
1. Multiply the numerator (top number of the fraction) by the whole number: \(3 \times 50 = 150\).
2. Divide the result by the denominator (bottom number of the fraction): \( \frac{150}{4} = 37.5\).
This tells you that 37.5 state legislatures are needed. But since you can't have half a legislature, we'll need to round that number.
Rounding Numbers
Rounding numbers is the process of adjusting a number to its nearest whole value. This is especially useful in real-world applications where fractional values are impractical. For example, let’s look at 37.5. Here, the fractional part is 0.5 or higher, so you round up to the next whole number, which is 38. The rule of thumb for rounding is:
- If the decimal is 0.5 or higher, round up.
- If the decimal is less than 0.5, round down.
This is why in our problem, 37.5 was rounded up to 38.
- If the decimal is 0.5 or higher, round up.
- If the decimal is less than 0.5, round down.
This is why in our problem, 37.5 was rounded up to 38.
Constitutional Amendment Approval
Approving a constitutional amendment in the U.S. involves a rigorous process to ensure that any changes have widespread support. According to the Constitution, an amendment must be approved by three-fourths (\( \( \frac{3}{4} \) \)) of the 50 state legislatures.
1. Start by calculating \( \( \frac{3}{4} \) \) of 50 states: \( \frac{3}{4} \times 50\).
2. This equals 37.5. Since a legislature can't be divided, round to the nearest whole number.
3. Therefore, 38 state legislatures must approve the amendment for it to pass.
This process ensures that any amendment to the Constitution has substantial support from the states, maintaining the integrity and stability of the nation’s supreme legal document.
1. Start by calculating \( \( \frac{3}{4} \) \) of 50 states: \( \frac{3}{4} \times 50\).
2. This equals 37.5. Since a legislature can't be divided, round to the nearest whole number.
3. Therefore, 38 state legislatures must approve the amendment for it to pass.
This process ensures that any amendment to the Constitution has substantial support from the states, maintaining the integrity and stability of the nation’s supreme legal document.