2 3 — + — 2. 2
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 \(1 \frac{2}{3}\).
