Question

now, compare \\(\frac{5}{8}\\) and \\(\frac{2}{7}\\). \\(\frac{5}{8}\\) ? \\(\frac{2}{7}\\)

Explanation:

Step1: Find a common denominator

To compare \(\frac{5}{8}\) and \(\frac{2}{7}\), we find the least common denominator (LCD) of 8 and 7. Since 8 and 7 are coprime, the LCD is \(8\times7 = 56\).

Step2: Convert fractions to equivalent forms

Convert \(\frac{5}{8}\) to a fraction with denominator 56: \(\frac{5}{8}=\frac{5\times7}{8\times7}=\frac{35}{56}\).
Convert \(\frac{2}{7}\) to a fraction with denominator 56: \(\frac{2}{7}=\frac{2\times8}{7\times8}=\frac{16}{56}\).

Step3: Compare the numerators

Since \(35>16\), we have \(\frac{35}{56}>\frac{16}{56}\), which means \(\frac{5}{8}>\frac{2}{7}\).

Answer:

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