Solve: 1/4 × (1/3 + 1/2) Fraction Operation Problem

The order of operations (PEMDAS) requires parentheses first! If you multiply $\frac{1}{4}$ by each fraction separately, you're actually solving $\frac{1}{4} \times \frac{1}{3} + \frac{1}{4} \times \frac{1}{2}$, which is a completely different problem.

Find the Least Common Denominator (LCD)! For $\frac{1}{3} + \frac{1}{2}$, the LCD is 6. Convert: $\frac{1}{3} = \frac{2}{6}$ and $\frac{1}{2} = \frac{3}{6}$, then add to get $\frac{5}{6}$.

Multiply straight across! For $\frac{1}{4} \times \frac{5}{6}$, multiply numerators: 1 × 5 = 5, then denominators: 4 × 6 = 24. Result: $\frac{5}{24}$.

Work backwards! Start with $\frac{5}{24}$ and divide by $\frac{1}{4}$: $\frac{5}{24} ÷ \frac{1}{4} = \frac{5}{24} \times \frac{4}{1} = \frac{5}{6}$. This should equal your parentheses result!

Remember, you're multiplying by $\frac{1}{4}$, which makes the result smaller! Since $\frac{5}{6}$ from the parentheses gets multiplied by a fraction less than 1, the final answer $\frac{5}{24}$ must be smaller than $\frac{5}{6}$.