ABSTRACT
However, as we have already pointed out, the same fraction notation may be used to convey many different meanings. The fractions in this picture may be interpreted as ratios; ratio addition is different from addition with part-whole comparisons. If we interpret the first two pictures as “1 out of 2” then 1 out of 2 and another 1 out of 2 gives 2 out of 4. You can think about this in a baseball context. If you hit 1 ball out of 2 and later in the practice hit 1 ball out of 2, then for the day, you hit 2 out of 4 balls. But even if we limit the discussion to ratio situations, we still must take great care to make sure
that pictures correspond with interpretations. For example, we could write 1:2 or meaning a ratio of 1 shaded square to 2 nonshaded squares. For this interpretation, the pictures do not work.
