A 2-cup mixture is 1/3 flour and 2/3 cornmeal. If 1 cup of flour is added to the 2-cup mixture, what fraction of the new 3-cup mixture is flour? Express your answer as a common fraction.

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Let's do everything in terms of "thirds of a cup"
The original 2 cup mixture was one third flour.
Therefore the original mixture contained 2/3 of a cup of flour.
Like wise, the original mixture contained 4/3 of a cup of cornmeal.
Now we are adding three thirds (note how we express everything in thirds of a cup) of a cup of flour.
There are now THREE cups of mixed flour+cornmeal - or in other words there are NINE THIRDS of a cup.
Of those nine thirds, FIVE of them (the original 2 plus the extra 3) are made up of flour
So the fraction of the final mixture made up of flour is 5/9

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