Question

lets find \\(\frac{5}{6} - \frac{1}{9}\\). first write the subtraction with a common denominator. then subtract. \\(\frac{5}{6} - \frac{1}{9} = \frac{\square}{\square} - \frac{\square}{\square} = \frac{\square}{\square}\\)

Explanation:

Step1: Find the least common denominator (LCD) of 6 and 9.

The prime factorization of 6 is \(2\times3\) and of 9 is \(3\times3\). So, the LCD is \(2\times3\times3 = 18\).

Step2: Rewrite the fractions with the LCD as the denominator.

For \(\frac{5}{6}\), multiply numerator and denominator by 3: \(\frac{5\times3}{6\times3}=\frac{15}{18}\).
For \(\frac{1}{9}\), multiply numerator and denominator by 2: \(\frac{1\times2}{9\times2}=\frac{2}{18}\).

Step3: Subtract the numerators.

\(\frac{15}{18}-\frac{2}{18}=\frac{15 - 2}{18}=\frac{13}{18}\).

Answer:

\(\frac{5}{6}-\frac{1}{9}=\frac{15}{18}-\frac{2}{18}=\frac{13}{18}\)