Let's solve the expression step by step: [tex]\( 7 \frac{1}{2} - \left( 2 \frac{1}{2} + 3 \right) \div \frac{23}{2} \)[/tex].
1. Convert the mixed numbers to improper fractions.
- [tex]\( 7 \frac{1}{2} = 7 + \frac{1}{2} = 7.5 \)[/tex]
- [tex]\( 2 \frac{1}{2} = 2 + \frac{1}{2} = 2.5 \)[/tex]
- Note: 3 remains the same as a whole number.
- [tex]\( \frac{23}{2} = 11.5 \)[/tex] when converted to decimal.
2. Perform the calculations inside the parentheses first.
- Evaluate [tex]\( 2.5 + 3 \)[/tex].
- [tex]\( 2.5 + 3 = 5.5 \)[/tex].
3. Now we need to divide this sum by [tex]\(\frac{23}{2}\)[/tex] or [tex]\(11.5\)[/tex].
- [tex]\( \frac{5.5}{11.5} = 0.4782608695652174 \)[/tex].
4. Subtract the division result from [tex]\(7.5\)[/tex]:
- [tex]\( 7.5 - 0.4782608695652174 = 7.021739130434782 \)[/tex].
So, the final result of the expression [tex]\( 7 \frac{1}{2} - \left( 2 \frac{1}{2} + 3 \right) \div \frac{23}{2} \)[/tex] is:
[tex]\[ 7.021739130434782. \][/tex]
