Question

Add, answer as a mixed number in simplest form.
2 1/3 + 8/9
[__] [__]/[__]

Answer 1

To add the mixed number \( 2 \frac{1}{3} \) and the fraction \( \frac{8}{9} \), we first convert the mixed number into an improper fraction.

1. Convert \( 2 \frac{1}{3} \) to an improper fraction:
\[
2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3}
\]

2. Now we need to add \( \frac{7}{3} \) and \( \frac{8}{9} \). To do this, we need a common denominator. The least common denominator (LCD) of 3 and 9 is 9.

3. Convert \( \frac{7}{3} \) to have a denominator of 9:
\[
\frac{7}{3} = \frac{7 \times 3}{3 \times 3} = \frac{21}{9}
\]

4. Now we can add the two fractions:
\[
\frac{21}{9} + \frac{8}{9} = \frac{21 + 8}{9} = \frac{29}{9}
\]

5. Convert \( \frac{29}{9} \) back to a mixed number:
- Divide 29 by 9, which equals 3 with a remainder of 2.
- Thus, \( \frac{29}{9} = 3 \frac{2}{9} \).

The final answer in mixed number form is:
\[
3 \frac{2}{9}
\]

To fill in your format:
[3] [2]/[9]