Evaluate. $$ \frac{8}{9}+\frac{1}{3} \cdot \frac{5}{6} $$ Write your answer in simplest form. $$ \square $$

Question

UpStudy AI · Accepted Answer

We start by evaluating the multiplication:

$$
\frac{1}{3} \cdot \frac{5}{6} = \frac{1 \times 5}{3 \times 6} = \frac{5}{18}.
$$

Now, substitute back into the original expression:

$$
\frac{8}{9} + \frac{5}{18}.
$$

To add these fractions, we need a common denominator. The denominator $$ 9 $$ can be converted to $$ 18 $$ since $$ 9 \times 2 = 18 $$:

$$
\frac{8}{9} = \frac{8 \times 2}{9 \times 2} = \frac{16}{18}.
$$

So the sum becomes:

$$
\frac{16}{18} + \frac{5}{18} = \frac{16+5}{18} = \frac{21}{18}.
$$

Finally, simplify the fraction by dividing the numerator and denominator by their greatest common divisor $$ 3 $$:

$$
\frac{21}{18} = \frac{21 \div 3}{18 \div 3} = \frac{7}{6}.
$$

$$
\square \quad \frac{7}{6}
$$
$$ \frac{7}{6} $$

Evaluate.

Write your answer in simplest form.