Solve: 2(3 + ½×8) - Order of Operations with Mixed Numbers

$2\cdot(3+\frac{1}{2}\cdot8)=$

Let's simplify this expression while following the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses come before all of these,

We will start by simplifying the expression in parentheses, since multiplication comes before addition, we will first perform the multiplication in the expression, while remembering that multiplying by a fraction means multiplying by the fraction's numerator, then we will perform the division of the fraction (by reducing it), we will complete simplifying the expression in parentheses by performing the addition within them:

$2\cdot(3+\frac{1}{2}\cdot8)= \\ 2\cdot(3+\frac{1\cdot8}{2})= \\ 2\cdot(3+\frac{\not{8}}{\not{2}})= \\ 2\cdot(3+4)= \\ 2\cdot7 \\$We will finish simplifying the given expression and perform the remaining multiplication:

$2\cdot7= \\ 14$Therefore the correct answer is answer C.