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Updated: May 10, 2026
10:58
Multimedia Battery for Assessment of Cognitive and Basic Skills in Mathematics (BM-PROMA)
Published on: August 28, 2021
Magnitude comparison with different types of rational numbers
Melissa DeWolf1, Margaret A Grounds2, Miriam Bassok2
1Department of Psychology, University of California, Los Angeles.
Summary
Mathematical cognition varies for rational numbers. While integers and decimals show a distance effect, fractions are processed slower due to their structure, impacting magnitude comparisons.
Area of Science:
- Cognitive psychology
- Mathematical cognition
- Numerical representation
Background:
- Understanding how the brain represents numerical magnitudes is key to mathematical cognition.
- The distance effect, where comparison speed increases with numerical separation, is well-established for single-digit integers.
- Evidence for the distance effect in compositional numbers like fractions and decimals is inconsistent.
Purpose of the Study:
- To investigate similarities and differences in magnitude representations for various rational numbers.
- To compare response times and accuracy in magnitude comparison tasks across fractions, decimals, and integers.
- To identify factors contributing to processing differences among rational number types.
Main Methods:
- College students performed magnitude comparison tasks with carefully selected sets of fractions, decimals, and 3-digit integers.
- Response times and error rates were systematically analyzed across different numerical formats.
- Experiments varied decimal precision to assess its impact on comparison strategies.
Main Results:
- A distance effect was observed for all number types (fractions, decimals, integers).
- Magnitude comparisons were significantly slower for fractions compared to decimals and integers.
- Decimal and integer comparison patterns were highly similar, while fractions showed a distinct, slower processing pattern.
Conclusions:
- All tested rational numbers (fractions, decimals, integers) utilize a distance effect for magnitude comparison.
- Fractions impose a higher processing load due to their bipartite structure (a/b), leading to slower comparisons.
- Fraction magnitude representation appears less precise and more reliant on explicit calculation than decimals or integers.
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