Let's solve the problem step-by-step to add the fractions [tex]\(\frac{8}{9}\)[/tex] and [tex]\(\frac{1}{6}\)[/tex].
1. Find a common denominator:
To add two fractions, we need a common denominator. The denominators we have are 9 and 6. We need to find the least common multiple (LCM) of 9 and 6. The LCM of 9 and 6 is 18.
2. Convert each fraction to have the common denominator:
- For [tex]\(\frac{8}{9}\)[/tex]:
[tex]\[
\frac{8}{9} = \frac{8 \times 2}{9 \times 2} = \frac{16}{18}
\][/tex]
- For [tex]\(\frac{1}{6}\)[/tex]:
[tex]\[
\frac{1}{6} = \frac{1 \times 3}{6 \times 3} = \frac{3}{18}
\][/tex]
3. Add the two fractions:
[tex]\[
\frac{16}{18} + \frac{3}{18} = \frac{16 + 3}{18} = \frac{19}{18}
\][/tex]
4. Convert the improper fraction to a mixed number:
[tex]\[
\frac{19}{18} = 1 \frac{1}{18}
\][/tex]
This mixed number consists of a whole number part and a fractional part:
- The whole number part is 1.
- The fractional part is [tex]\(\frac{1}{18}\)[/tex].
Therefore, after adding [tex]\(\frac{8}{9}\)[/tex] and [tex]\(\frac{1}{6}\)[/tex], we get the result:
[tex]\[
1 \frac{1}{18}
\][/tex]
