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5. Affordances of Fractions and Decimals for Arithmetic

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   Rational numbers are represented by multiple notations: fractions, decimals, and percentages. Whereas previous studies have investigated affordances of these notations for representing different types of information (DeWolf, Bassok, & Holyoak, 2015; Tian, Braithwaite, & Siegler, 2020), the present study investigated their affordances for solving different types of arithmetic problems. We hypothesized that decimals afford addition better than fractions do and that fractions afford multiplication better than decimals do. This hypothesis was tested in two experiments with university students (Ns = 77 and 80). When solving fraction and decimal arithmetic problems, participants converted addition problems from fraction to decimal form more than vice versa, and converted multiplication problems from decimal to fraction form more than vice versa, thus revealing preferences favoring decimals for addition and fractions for multiplication. Accuracies paralleled these revealed preferences: Addition accuracy was higher with decimals than fractions, whereas multiplication accuracy was higher with fractions than decimals. Variations in notation preferences as a function of the types of operands involved (e.g., equal versus unequal denominator fractions) were more consistent with an explanation based on adaptive strategy choice (Siegler, 1996) than with one based on semantic interpretations associated with each notation. 

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