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Question Take any 4 consecutive numbers. For example, 3, 4, 5, and 6. Place ‘+’ and signs in between the numbers. How many different possibilities exist? Write all of them.
Evaluate each expression and write the result next to it. Do you notice anything interesting? (Page 112)
When four consecutive numbers are used with all possible combinations of ‘+’ and signs, the results will always be even. This is because, regardless of the sign placement, the sum will always involve adding and subtracting an equal number of consecutive numbers. Specifically, the sum of four consecutive numbers is always even, and the differences between them also result in even numbers when combined with plus and minus signs. Example with 3, 4, 5, 6: 3 + 4 + 5 + 6 = 18 3 + 4 + 5 – 6 = 6 3 + 4 – 5 + 6 = 8 3 + 4 – 5 – 6 = -4 3 – 4 + 5 + 6 = 10 3 – 4 + 5 – 6 = -2 3 – 4 – 5 + 6 = 0 3 – 4 – 5 – 6 = -12 Observations: All results are even numbers. There are only eight possible combinations. The results can be positive, negative, or zero.