To solve the given expression [tex]\( 25 \times \left(2 \frac{1}{2} + \frac{1}{2} \right) \)[/tex], we can follow these steps:
1. Convert the mixed number to an improper fraction:
- [tex]\(2 \frac{1}{2}\)[/tex] can be written as [tex]\(2 + \frac{1}{2}\)[/tex].
- To add these, convert [tex]\(2\)[/tex] into a fraction with the same denominator as [tex]\(\frac{1}{2}\)[/tex], which gives [tex]\(\frac{4}{2}\)[/tex].
- Adding these together, [tex]\(\frac{4}{2} + \frac{1}{2} = \frac{5}{2}\)[/tex].
2. Convert the fraction to a number:
- [tex]\(\frac{5}{2}\)[/tex] is equivalent to [tex]\(2.5\)[/tex].
3. Add the two fractions:
- Now add [tex]\(2.5\)[/tex] and [tex]\(\frac{1}{2}\)[/tex].
- Convert [tex]\(\frac{1}{2}\)[/tex] to a decimal, which is [tex]\(0.5\)[/tex].
- Hence, [tex]\(2.5 + 0.5 = 3.0\)[/tex].
4. Multiply the result by 25:
- The sum of [tex]\(2 \frac{1}{2} + \frac{1}{2}\)[/tex] is [tex]\(3.0\)[/tex].
- Now, multiply [tex]\(25\)[/tex] by this sum, [tex]\(25 \times 3.0 = 75.0\)[/tex].
Therefore, the final result of the expression [tex]\( 25 \times \left(2 \frac{1}{2} + \frac{1}{2} \right) \)[/tex] is:
[tex]\[ 75.0 \][/tex]
