# Computing with rational numbers: Not easy even for college students

- Jennifer Jacobs,
*Rutgers University- New Brunswick*
- Rochel Gelman,
*Rutgers University- New Brunswick*

## Abstract

Many individuals, including school children and adults, struggle
with rational numbers, especially in fractional and decimal format (Hartnett &
Gelman, 1998; Humberstone & Reeve, 2007; Jacobs & Gelman, 2010). A preliminary
study with undergraduates revealed difficulty with problems where a price
increase of x% is followed by a decrease of the same percent, for example,
“x increases by 50% and then decreases by 50%”. More than 75% of these
problems were answered incorrectly (Jacobs, 2010). A second study, where N =
1629, presented percentage problems in either an algebraic or numerical format.
The focus was on analyses of trends between and within subjects, including
systematic error patterns, the effect of problem-solving representational
formats, and problems that were easy. These data highlight the fact that even
undergraduates can have persistent problems with rational number concepts and
notations.

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