# Resource 4: Number systems and their properties

Table R3.1 gives an overview of the properties of operations on numbers in the different number systems. You could also ask your students to fill in the ‘yes’ and ‘no’.

Table R3.1 Number systems and their properties.
Property of operations on numbers Number system
Natural Whole Integers Rational Irrational Real
Closed under addition: If a, b belong to a set, then a + b also belongs to the set. Yes Yes Yes Yes No Yes
Additive identity: For a belonging to a set, there is a number z in the set, such that a + z = a. No Yes Yes Yes No Yes
Additive inverse: For every number a in a set, there is another number –a in the set such that, a + (–a) = z. No No Yes Yes No Yes
Closed under multiplication: If a, b belong to a set, then a × b also belongs to the set. Yes Yes Yes Yes No Yes
Multiplicative identity: For a belonging to a set, there is a number u in the set, such that a × u = a. Yes Yes Yes Yes No Yes
Multiplicative inverse: For every number a in a set, there is another number a-1 in the set such that, a x a-1 = u No No No Yes No Yes

Resource 3: Activity 1 in ‘card’ format

Resource 5: Planning lessons