Modeling Relational Priming and Multiplicative Reasoning with Rational Numbers

Previous research on multiplicative reasoning has shown that for whole numbers, understanding of division is intimately linked to multiplication, as retrieval of division facts is often accomplished through reverse multiplication. We recently extended this research to rational numbers, and found that inverse multiplication problems can serve as primes for one another (e.g., a × b/a = a primes b × a/b = b) when the second multiplier is expressed as a fraction, but not when it is expressed as a decimal. In the current paper we propose a process model of how such relational priming takes place, and report two experiments that test the limits of this priming effect. The first varies the format of the equations as fractions or a total division equation, and shows that priming is only observed using the fraction format; the second varies the multiplicative complexity of the factors in the equations, and shows that priming requires a common factor linking the successive problems.