Question Determine which fraction is larger: \( \frac{2}{8} \) or \( \frac{1}{3} \)

To determine which fraction is larger between \( \frac{2}{8} \) and \( \frac{1}{3} \), let's compare them step by step. ### Step 1: Simplify the Fractions (if possible) - **\( \frac{2}{8} \) can be simplified:** \[ \frac{2}{8} = \frac{2 \div 2}{8 \div 2} = \frac{1}{4} \] - **\( \frac{1}{3} \) is already in its simplest form.** Now, we are comparing: \[ \frac{1}{4} \quad \text{and} \quad \frac{1}{3} \] ### Step 2: Find a Common Denominator To compare the two fractions, it's helpful to have the same denominator. - **Common denominator for 4 and 3 is 12.** Convert each fraction to have the denominator of 12: - **For \( \frac{1}{4} \):** \[ \frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \] - **For \( \frac{1}{3} \):** \[ \frac{1}{3} = \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \] ### Step 3: Compare the Numerators Now that both fractions have the same denominator: \[ \frac{3}{12} \quad \text{and} \quad \frac{4}{12} \] Compare the numerators: - \( 3 < 4 \) ### Conclusion Since \( \frac{3}{12} < \frac{4}{12} \), it follows that: \[ \frac{1}{4} < \frac{1}{3} \] Therefore: \[ \frac{2}{8} \ (\text{which simplifies to} \ \frac{1}{4}) \ \text{is smaller than} \ \frac{1}{3}. \] **Answer:** \( \frac{1}{3} \) is larger than \( \frac{2}{8} \).