To determine the sum of [tex]\(\frac{2}{9}\)[/tex] and [tex]\(\frac{4}{9}\)[/tex] and simplify it, follow these steps:
1. Check for common denominators:
We have the fractions [tex]\(\frac{2}{9}\)[/tex] and [tex]\(\frac{4}{9}\)[/tex], both of which already have the same denominator (9).
2. Write the sum:
[tex]\[
\frac{2}{9} + \frac{4}{9}
\][/tex]
3. Add the numerators:
Since both fractions have a common denominator, we can add the numerators directly:
[tex]\[
\frac{2 + 4}{9} = \frac{6}{9}
\][/tex]
4. Simplify the fraction:
To simplify [tex]\(\frac{6}{9}\)[/tex], we need to find the greatest common divisor (GCD) of 6 and 9, which is 3.
Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{6 \div 3}{9 \div 3} = \frac{2}{3}
\][/tex]
Thus, the sum of [tex]\(\frac{2}{9}\)[/tex] and [tex]\(\frac{4}{9}\)[/tex] when simplified is [tex]\(\frac{2}{3}\)[/tex].
