To simplify the expression (\frac{2}{3} + \frac{2}{2}), we first need to find a common denominator.
The fractions are:
[
\frac{2}{3} \quad \text{and} \quad \frac{2}{2}
]
The least common denominator (LCD) of 3 and 2 is 6.
Now, we will convert each fraction to have this common denominator.
- Convert (\frac{2}{3}):
[
\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}
]
- Convert (\frac{2}{2}):
[
\frac{2}{2} = \frac{2 \times 3}{2 \times 3} = \frac{6}{6}
]
Now we can add the fractions:
[
\frac{4}{6} + \frac{6}{6} = \frac{4 + 6}{6} = \frac{10}{6}
]
Next, we simplify (\frac{10}{6}):
[
\frac{10}{6} = \frac{5}{3}
]
Thus, the final result is:
[
\frac{5}{3}
]
Alternatively, this result can also be expressed as a mixed number:
[
1 \frac{2}{3}
]
So the final simplified answer is (\frac{5}{3}) or (1 \frac{2}{3}).
