$13\frac{1}{2} - \left[ 4\frac{1}{2} - \left\{ 3 - \left( 2 - \frac{1}{2} \right) \right\} \right]$ is equal to:

Q: $13\frac{1}{2} - \left[ 4\frac{1}{2} - \left\{ 3 - \left( 2 - \frac{1}{2} \right) \right\} \right]$ is equal to:

To solve the expression $13\frac{1}{2} - \left[ 4\frac{1}{2} - \left\{ 3 - \left( 2 - \frac{1}{2} \right) \right\} \right]$, we need to carefully evaluate it step by step, following the order of operations (parentheses, brackets, and then subtraction). 1. **Evaluate the innermost parentheses:** \[ 2 - \frac{1}{2} = \frac{4}{2} - \frac{1}{2} = \frac{3}{2} \] 2. **Substitute back into the expression:** \[ 3 - \frac{3}{2} = \frac{6}{2} - \frac{3}{2} = \frac{3}{2} \] 3. **Substitute back into the expression inside the brackets:** \[ 4\frac{1}{2} - \frac{3}{2} = \frac{9}{2} - \frac{3}{2} = \frac{6}{2} = 3 \] 4. **Substitute back into the original expression:** \[ 13\frac{1}{2} - 3 = \frac{27}{2} - \frac{6}{2} = \frac{21}{2} = 10\frac{1}{2} \] Thus, the expression evaluates to $10\frac{1}{2}$, which corresponds to Option 2. **Explanation for why each option is incorrect:** 1. **Option 1: $9\frac{1}{2}$** - This result is incorrect because it does not account for the correct subtraction of fractions and whole numbers as shown in the detailed calculation above. 2. **Option 3: $10\frac{3}{4}$** - This result is incorrect because the calculation of the expression does not yield a fraction with a denominator of 4. The correct calculation results in a fraction with a denominator of 2. 3. **Option 4: $13\frac{1}{2}$** - This result is incorrect because it suggests no subtraction took place, which contradicts the operations performed in the expression. The correct subtraction results in a reduced value. Therefore, the correct answer is Option 2: $10\frac{1}{2}$.

Question

Accepted Answer

To solve the expression $13\frac{1}{2} - \left[ 4\frac{1}{2} - \left\{ 3 - \left( 2 - \frac{1}{2} \right) \right\} \right]$, we need to carefully evaluate it step by step, following the order of operations (parentheses, brackets, and then subtraction).

1. **Evaluate the innermost parentheses:**
   $$
   2 - \frac{1}{2} = \frac{4}{2} - \frac{1}{2} = \frac{3}{2}
   $$

2. **Substitute back into the expression:**
   $$
   3 - \frac{3}{2} = \frac{6}{2} - \frac{3}{2} = \frac{3}{2}
   $$

3. **Substitute back into the expression inside the brackets:**
   $$
   4\frac{1}{2} - \frac{3}{2} = \frac{9}{2} - \frac{3}{2} = \frac{6}{2} = 3
   $$

4. **Substitute back into the original expression:**
   $$
   13\frac{1}{2} - 3 = \frac{27}{2} - \frac{6}{2} = \frac{21}{2} = 10\frac{1}{2}
   $$

Thus, the expression evaluates to $10\frac{1}{2}$, which corresponds to Option 2.

**Explanation for why each option is incorrect:**

1. **Option 1: $9\frac{1}{2}$**
   - This result is incorrect because it does not account for the correct subtraction of fractions and whole numbers as shown in the detailed calculation above.

2. **Option 3: $10\frac{3}{4}$**
   - This result is incorrect because the calculation of the expression does not yield a fraction with a denominator of 4. The correct calculation results in a fraction with a denominator of 2.

3. **Option 4: $13\frac{1}{2}$**
   - This result is incorrect because it suggests no subtraction took place, which contradicts the operations performed in the expression. The correct subtraction results in a reduced value.

Therefore, the correct answer is Option 2: $10\frac{1}{2}$.