Definition
Partition
A partition splits a whole or set into parts that do not overlap and together use everything exactly once.
Continue from this idea into connected AXIO math.
What it means
Give every item or piece one home. Nothing is left outside, and nothing belongs to two homes at once. When all the homes together make the original whole or set, you have a partition. The homes can be different sizes unless the task asks for equal parts.
Remember it
One home each: nothing missing, nothing counted twice.
Example
Lay out 10 counters. Put counters 1–4 in one hoop and counters 5–10 in another. Every counter is in exactly one hoop, and 4 + 6 = 10, so the two groups form a partition even though they are not equal in size.
Watch for
Groups of 4 and 5 do not partition a set of 10 counters if one counter is left out. Equal size is a separate rule unless the problem asks for equal shares.
Common mix-up
Partition does not always mean equal parts. Equal fractional shares must be equal, but an ordinary set partition may contain groups of different sizes.
Exact meaning
A partition divides a whole, region, or set into parts that cover or use the original exactly once. Set items belong to one part, and regions have no gaps or overlaps. The parts are equal only when the problem says so or when they represent equal fractional shares.