Two equal shares
What Does Half Mean?
Half is not just a piece. It is one of exactly two equal pieces.
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Step 1 of 5
Sharing between two means splitting evenly.
Which is why the bigger half is a joke rather than a size. If you and a friend split a biscuit and you take three quarters, nobody would call that halves. Half only means anything if the pieces match.
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Step 2 of 5
Two halves make one whole.
Put the two pieces back together and you have exactly what you started with. Nothing is lost and nothing is added.
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Step 3 of 5
Half of a number is that number shared out twice.
Half of ten is five, because five and five make ten. Halving and doubling are the same journey in opposite directions.
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Step 4 of 5
The shape of a half can vary wildly.
Cut a cake straight across, or in a wiggly line, or take alternating stripes. As long as the amount matches, it is still a half.
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Step 5 of 5
Halving again gives quarters.
Take a half and halve it and you get a quarter. Keep going and you get eighths, sixteenths — smaller and smaller, but never quite nothing.
Half is the first fraction almost every child learns, and it is the only one most people use daily.
The short version
Equal is the whole of it: three quarters and one quarter are not halves, whatever anyone calls them. The shape can be anything — straight, wiggly, alternating stripes — as long as the amount matches, and halving is only doubling walked backwards.
Try it yourself
Fold a sheet of paper in half and tear along the fold. Stack the pieces to check they match exactly.