Sure! Let's work through the problem step-by-step:
### Step 1: Convert mixed fractions to improper fractions
1. First term: [tex]\( 8\frac{1}{4} \)[/tex]
- [tex]\( 8\frac{1}{4} \)[/tex] can be converted to an improper fraction.
- [tex]\( 8 \frac{1}{4} = 8 + \frac{1}{4} \)[/tex]
- [tex]\( 8 + \frac{1}{4} = 8.25 \)[/tex]
2. Second term: [tex]\( 2\frac{3}{4} \)[/tex]
- [tex]\( 2 \frac{3}{4} \)[/tex] can be converted to an improper fraction.
- [tex]\( 2 \frac{3}{4} = 2 + \frac{3}{4} \)[/tex]
- [tex]\( 2 + \frac{3}{4} = 2.75 \)[/tex]
3. Third term: [tex]\( 3\frac{1}{2} \)[/tex]
- [tex]\( 3 \frac{1}{2} \)[/tex] can be converted to an improper fraction.
- [tex]\( 3 \frac{1}{2} = 3 + \frac{1}{2} \)[/tex]
- [tex]\( 3 + \frac{1}{2} = 3.5 \)[/tex]
### Step 2: Calculate the sum within the parentheses
- Add the second term and the third term:
[tex]\[
2.75 + 3.5 = 6.25
\][/tex]
### Step 3: Calculate the result of the subtraction
- Subtract the sum within parentheses from the first term:
[tex]\[
8.25 - 6.25 = 2.0
\][/tex]
### Final Result:
The result of the expression [tex]\( 8\frac{1}{4} - \left(2\frac{3}{4} + 3\frac{1}{2}\right) \)[/tex] is [tex]\( 2.0 \)[/tex].
