Question

lets compare \\(\frac{8}{9}\\) and \\(\frac{5}{6}\\).
(a) first, write the fractions with the same denominator.
\\(\frac{8}{9} = \frac{\square}{\square}\\) \\(\frac{5}{6} = \frac{\square}{\square}\\)
(b) then, use <, =, or > to compare the fractions.
\\(\frac{8}{9} \square \frac{5}{6}\\)

Explanation:

Step1: Find LCM of denominators

Denominators are 9 and 6. Prime factors: \(9 = 3^2\), \(6 = 2\times3\). LCM is \(2\times3^2 = 18\).

Step2: Convert \(\frac{8}{9}\) to denominator 18

Multiply numerator and denominator by 2: \(\frac{8\times2}{9\times2}=\frac{16}{18}\).

Step3: Convert \(\frac{5}{6}\) to denominator 18

Multiply numerator and denominator by 3: \(\frac{5\times3}{6\times3}=\frac{15}{18}\).

Step4: Compare the fractions

Since \(16 > 15\), \(\frac{16}{18}>\frac{15}{18}\), so \(\frac{8}{9}>\frac{5}{6}\).

Answer:

(a) \(\frac{8}{9}=\frac{16}{18}\), \(\frac{5}{6}=\frac{15}{18}\)
(b) \(\frac{8}{9}>\frac{5}{6}\)