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Balance of Halves

Age 7 to 11 Challenge Level:

Before you try this activity, you might like to have a go at Number Balance and Getting the Balance, if you haven't already.

Here is a balance, or equaliser, which you might like to investigate:

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Now, what about a balance that has halves on it?

balance with halves marked

Imagine we hung a weight on the number 7 on the left-hand side. Let's say we can only use the "halves" on the right. Which two numbers on the right-hand side could you hang weights from so that it would balance?

For example, you might have a weight on the $\frac{1}{2}$ and the $6\frac{1}{2}$.

Where else could you hang two weights on the right-hand side to make it balanced?

You can set yourselves all kinds of problems with this new set-up.
What about asking, "I wonder what would happen if I had quarters marked up as well?"
Or, "I wonder what it'd be like to have three weights balancing two using halves wherever we wanted?"

Let us know what you find out.