To solve the problem of adding [tex]\(\frac{8}{9} + \frac{4}{9}\)[/tex], follow these steps:
1. Ensure Common Denominators:
Both fractions, [tex]\(\frac{8}{9}\)[/tex] and [tex]\(\frac{4}{9}\)[/tex], already have the same denominator, which is 9. Therefore, we can directly add the numerators while keeping the denominator the same.
2. Add the Numerators:
Add the numerators of the two fractions:
[tex]\[
8 + 4 = 12
\][/tex]
So, the sum of the fractions is:
[tex]\[
\frac{12}{9}
\][/tex]
3. Simplify the Fraction:
If possible, simplify the fraction. [tex]\(\frac{12}{9}\)[/tex] can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is 3:
[tex]\[
\frac{12 \div 3}{9 \div 3} = \frac{4}{3}
\][/tex]
4. Express as a Mixed Number:
Convert the improper fraction [tex]\(\frac{4}{3}\)[/tex] to a mixed number. We do this by dividing the numerator by the denominator to find the whole number part:
[tex]\[
4 \div 3 = 1 \text{ remainder } 1
\][/tex]
This means that:
[tex]\[
\frac{4}{3} = 1 \frac{1}{3}
\][/tex]
Hence, the sum [tex]\(\frac{8}{9} + \frac{4}{9}\)[/tex] simplifies to the mixed number [tex]\(1 \frac{1}{3}\)[/tex].
The answer is:
[tex]\[
1 \frac{1}{3}
\][/tex]
