Solve: 1/4 × (1/3 + 1/2) - Mixed Fraction Operations

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,

In the given expression there is a term in parentheses that needs to be multiplied, so we'll start by simplifying the expression within these parentheses, meaning - we'll perform the addition of fractions within this expression, which we'll do by expanding the fractions to their minimal common denominator which is 6 (since it's the minimal common multiple of both fraction denominators in the expression - both 2 and 3), and performing the addition operation in the fraction's numerator, remembering that we know by how much to multiply each of the fraction's numerators when expanding the fractions by answering the question "by how much did we multiply the current denominator to get the common denominator?", then we'll simplify the expression in the fraction's numerator:

$\frac{1}{4}\cdot\big(\frac{1}{3}+\frac{1}{2}\big)= \\ \frac{1}{4}\cdot\frac{1\cdot2+1\cdot3}{6}= \\ \frac{1}{4}\cdot\frac{2+3}{6}= \\ \frac{1}{4}\cdot\frac{5}{6} \\$When simplifying the expression we got in the fraction's numerator, we remembered that according to the order of operations mentioned above, multiplication comes before addition,

We'll continue and perform the multiplication of fractions in the expression we got in the last step, remembering that multiplication of fractions is performed by multiplying numerator by numerator and denominator by denominator while keeping the original fraction line:

$\frac{1}{4}\cdot\frac{5}{6}= \\ \frac{1\cdot5}{4\cdot6}= \\ \frac{5}{24}$

Let's summarize the steps of simplifying the given expression, we got that:

$\frac{1}{4}\cdot\big(\frac{1}{3}+\frac{1}{2}\big)= \\ \frac{1}{4}\cdot\frac{5}{6} = \\ \frac{5}{24}$

Therefore the correct answer is answer C.