Question

add.
\\(\frac{8}{9} + \frac{11}{12}\\)
write your answer as a fraction in simplest form.

Explanation:

Step1: Find the least common denominator (LCD) of 9 and 12.

The prime factorization of 9 is $3^2$ and of 12 is $2^2\times3$. So the LCD is $2^2\times3^2 = 36$.

Step2: Rewrite the fractions with the LCD.

For $\frac{8}{9}$, multiply numerator and denominator by 4: $\frac{8\times4}{9\times4}=\frac{32}{36}$.
For $\frac{11}{12}$, multiply numerator and denominator by 3: $\frac{11\times3}{12\times3}=\frac{33}{36}$.

Step3: Add the numerators.

$\frac{32}{36}+\frac{33}{36}=\frac{32 + 33}{36}=\frac{65}{36}$.

Answer:

$\frac{65}{36}$