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Rodrigo added [tex]\frac{2}{9}[/tex] and [tex]\frac{4}{9}[/tex] using these steps. What is the sum in simplest terms?

1. Check for common denominators:
[tex]\frac{2}{9}[/tex] and [tex]\frac{4}{9}[/tex]

2. Write the sum:
[tex]\frac{2}{9} + \frac{4}{9}[/tex]

3. Add the numerators:
[tex]\frac{2+4}{9} = \frac{6}{9}[/tex]

What is the sum in simplest terms?


Sagot :

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].
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