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Consecutive Negative Numbers

Age 11 to 14 Challenge Level:

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Take, for example, four consecutive negative numbers, say $$-7, -6, -5, -4$$ Now place $+$ and/or $-$ signs between them.


There are many more possibilities. Try to list all of them.

Now work out the solutions to the various calculations.


Choose a different set of four consecutive negative numbers and repeat the process.

Take a look at both sets of solutions. Notice anything?
Can you explain any similarities?

Can you predict some of the solutions you will get when you start with a different set of four consecutive negative numbers?
Test out any conjectures you may have.

Can you explain and justify your findings?