To solve the expression [tex]\(2 \frac{1}{4} + 1 \frac{1}{2} \times 2 \frac{2}{3}\)[/tex], we'll follow these steps:
1. Convert the mixed numbers to improper fractions:
- [tex]\(2 \frac{1}{4}\)[/tex] can be converted as follows:
- [tex]\(2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4}\)[/tex]
- [tex]\(1 \frac{1}{2}\)[/tex] can be converted as follows:
- [tex]\(1 \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}\)[/tex]
- [tex]\(2 \frac{2}{3}\)[/tex] can be converted as follows:
- [tex]\(2 \frac{2}{3} = 2 + \frac{2}{3} = \frac{6}{3} + \frac{2}{3} = \frac{8}{3}\)[/tex]
2. Multiply the second and third fractions:
- [tex]\(\left(\frac{3}{2}\right) \times \left(\frac{8}{3}\right) = \frac{3 \times 8}{2 \times 3} = \frac{24}{6} = 4\)[/tex]
3. Add the first fraction to the multiplication result:
- [tex]\(\frac{9}{4} + 4\)[/tex]
To add these, convert 4 to a fraction with a denominator of 4:
- [tex]\(4 = \frac{16}{4}\)[/tex]
- So, [tex]\(\frac{9}{4} + \frac{16}{4} = \frac{9 + 16}{4} = \frac{25}{4} = 6 \frac{1}{4}\)[/tex]
Therefore, the value of the expression [tex]\(2 \frac{1}{4} + 1 \frac{1}{2} \times 2 \frac{2}{3}\)[/tex] is [tex]\(6 \frac{1}{4}\)[/tex] or 6.25.
