2*2+2:3

To solve the expression \(2 \times 2 + 2 : 3\), we need to follow the order of operations (often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

1. Multiplication: Calculate \(2 \times 2\): \[ 2 \times 2 = 4 \]

2. Division: Next, handle the division \(2 : 3\) (which can also be written as \(2 \div 3\)): \[ 2 : 3 = \frac{2}{3} \]

3. Addition: Combine the results: \[ 4 + \frac{2}{3} \]

To add these, convert \(4\) to a fraction: \[ 4 = \frac{12}{3} \]

Now add the fractions: \[ \frac{12}{3} + \frac{2}{3} = \frac{12 + 2}{3} = \frac{14}{3} \]

Thus, the final result is: \[ \frac{14}{3} \text{ or } 4\frac{2}{3} \text{ in mixed number form.} \]