Simplify the expression $2 \cdot 3+6 / 2$.
To simplify the expression \(2 \cdot 3 + \frac{6}{2}\), we need to follow the standard order of operations, often referred to as PEMDAS or BODMAS. This rule states that we should perform multiplication and division (from left to right) before addition and subtraction.
First, we handle the multiplication and division.
The multiplication is \(2 \cdot 3 = 6\).
The division is \(\frac{6}{2} = 3\).
Substituting these values back into the expression, we get \(6 + 3\).
Now, we perform the final addition operation: \(6 + 3 = 9\). Thus, the simplified value of the expression is \(\boxed{9}\).
Order of operations is fundamental in everyday calculations. For example, if you buy 2 bags of apples at \$3 each and split a \$6 shipping fee between yourself and a friend (\(\frac{\$6}{2}\)), you can calculate your total cost as \(2 \times 3 + \frac{6}{2} = 6 + 3 = \$9\). Understanding this sequence ensures that financial, scientific, and engineering calculations are performed accurately.