To evaluate the expression [tex]\(\frac{4}{3} + \frac{9}{2}\)[/tex], follow these steps:
1. Find a common denominator:
The first step in adding fractions is to make sure the denominators are the same. The least common multiple (LCM) of 3 and 2 is 6.
2. Convert each fraction to have the common denominator:
- For [tex]\(\frac{4}{3}\)[/tex], multiply both the numerator and the denominator by 2 to get [tex]\(\frac{8}{6}\)[/tex].
- For [tex]\(\frac{9}{2}\)[/tex], multiply both the numerator and the denominator by 3 to get [tex]\(\frac{27}{6}\)[/tex].
3. Add the fractions:
Now, with a common denominator, you can add the numerators together:
[tex]\[
\frac{8}{6} + \frac{27}{6} = \frac{8 + 27}{6} = \frac{35}{6}
\][/tex]
4. Simplify the fraction:
The fraction [tex]\(\frac{35}{6}\)[/tex] is already in its simplest form because 35 and 6 have no common factors other than 1.
So, the final answer is:
[tex]\[
\frac{35}{6}
\][/tex]
