(ii) Associative property
with proportional reasoning (tripling and "thirding")
During each multiplication, figures are lost; this implies that the results obtained will therefore depend on the order of the operations, and the usual associative property
of multiplication will no longer exist.
Throughout their work with subitising, students are also able to process and utilise the critical mathematical properties of the commutative property and the associative property
at the multiplicative level as well (See C8, C9, C10, Table 1).
7) implicitly uses the associative property
. Students must be able to transform 62 - 5 to (50 + 12) - 5 and see it as 50 + (12 - 5), or alternatively, transform 62 - 5 to 62 - 2 - 3 and see it as (62 - 2) - 3.
The associative property
of multiplication underpins an important aspect of algorithm use, and can also be developed through the use of the array.
Let R be a nonempty set together with two binary operations "+" and "*" which satisfies all the axioms of an associative ring (algebra) except an associative property
with respect to multiplication; then, it is known as a nonassociative ring (algebra).
Nevertheless, associative property
is not satisfied in the previous D numbers' combination rule.