Question
Determine if the steps are in the correct order for simplifying the expression 12−4÷43+112−4÷43+1 (1 point) True False Step 1: 4÷434÷43 Step 2: 3+13+1 Step 3: 12−4
Answers
Answered by
GPT-4o mini
To simplify the expression \( 12 - 4 \div 4^3 + 1 \), let's follow the proper order of operations (PEMDAS/BODMAS):
1. **Calculate the exponent:** \( 4^3 = 64 \)
2. **Perform the division:** \( 4 \div 64 = \frac{4}{64} = \frac{1}{16} \)
3. **Substitute into the expression:** \( 12 - \frac{1}{16} + 1 \)
4. **Convert to a common denominator to simplify:** \( 12 = \frac{192}{16} \) and \( 1 = \frac{16}{16} \)
5. **Combine the fractions:** \( \frac{192}{16} - \frac{1}{16} + \frac{16}{16} = \frac{192 - 1 + 16}{16} = \frac{207}{16} \)
Now let's analyze the proposed steps:
1. **Step 1: \( 4 \div 4^3 \):** This should actually be \( 4 \div 64 \) after calculating \( 4^3 \). The notation \( 4 \div 434 \) seems incorrect.
2. **Step 2:** The result should actually involve the simplified term from Step 1.
3. **Step 3:** This step looks at \( 12 - 4 \), which does not correctly represent the previous steps.
Since Step 1 incorrectly represents the calculation and does not follow the correct order and operations, the sequence of the steps is **not in the correct order**.
So, the answer is **False**.
1. **Calculate the exponent:** \( 4^3 = 64 \)
2. **Perform the division:** \( 4 \div 64 = \frac{4}{64} = \frac{1}{16} \)
3. **Substitute into the expression:** \( 12 - \frac{1}{16} + 1 \)
4. **Convert to a common denominator to simplify:** \( 12 = \frac{192}{16} \) and \( 1 = \frac{16}{16} \)
5. **Combine the fractions:** \( \frac{192}{16} - \frac{1}{16} + \frac{16}{16} = \frac{192 - 1 + 16}{16} = \frac{207}{16} \)
Now let's analyze the proposed steps:
1. **Step 1: \( 4 \div 4^3 \):** This should actually be \( 4 \div 64 \) after calculating \( 4^3 \). The notation \( 4 \div 434 \) seems incorrect.
2. **Step 2:** The result should actually involve the simplified term from Step 1.
3. **Step 3:** This step looks at \( 12 - 4 \), which does not correctly represent the previous steps.
Since Step 1 incorrectly represents the calculation and does not follow the correct order and operations, the sequence of the steps is **not in the correct order**.
So, the answer is **False**.