Question

compare \\(\frac{2}{5}\\) and \\(\frac{4}{6}\\). \\(\frac{2}{5}\\) \\(\square\\) \\(\frac{4}{6}\\) options: =, <, >

Explanation:

Step1: Find a common denominator

To compare \(\frac{2}{5}\) and \(\frac{4}{6}\), we first find a common denominator. The least common multiple of 5 and 6 is \(5\times6 = 30\).

Step2: Convert the fractions

Convert \(\frac{2}{5}\) to a fraction with denominator 30: \(\frac{2}{5}=\frac{2\times6}{5\times6}=\frac{12}{30}\).
Convert \(\frac{4}{6}\) to a fraction with denominator 30: \(\frac{4}{6}=\frac{4\times5}{6\times5}=\frac{20}{30}\).

Step3: Compare the numerators

Since \(12 < 20\), we have \(\frac{12}{30}<\frac{20}{30}\), so \(\frac{2}{5}<\frac{4}{6}\).

Answer:

\(\frac{2}{5}<\frac{4}{6}\) (so the symbol to fill in the box is \( < \))