Multiplicative Reasoning: Compare Rational Numbers . Multiplicative reasoning is a vital part of the progression of mathematical understanding. To reason multiplicatively, students need to be able to understand relationships between quantities including parts and wholes. . Early multiplicative reasoning requires students to work with ‘composite units’ (Siemon et al, 2011) where they need to distinguish not only ‘how many’ as they would when using additive thinking but also ‘how much’. Fractions