Question

add.
\\(\frac{8}{9} + \frac{3}{4}\\)
write your answer as a fraction in simplest form.

Explanation:

Step1: Find a common denominator

The denominators are 9 and 4. The least common denominator (LCD) of 9 and 4 is \( 9\times4 = 36 \) since 9 and 4 are coprime (their greatest common divisor is 1).

Step2: Rewrite the fractions with the common denominator

For \( \frac{8}{9} \), multiply numerator and denominator by 4: \( \frac{8\times4}{9\times4}=\frac{32}{36} \)
For \( \frac{3}{4} \), multiply numerator and denominator by 9: \( \frac{3\times9}{4\times9}=\frac{27}{36} \)

Step3: Add the fractions

Now that the fractions have the same denominator, add the numerators: \( \frac{32}{36}+\frac{27}{36}=\frac{32 + 27}{36}=\frac{59}{36} \)

Step4: Check if the fraction is in simplest form

The greatest common divisor of 59 and 36 is 1 (since 59 is a prime number and does not divide 36), so \( \frac{59}{36} \) is in simplest form.

Answer:

\( \frac{59}{36} \)