When Addition Becomes Subtraction!

Addition can become subtraction! (Vice versa is possible, too!) How? Observe below:

A - B + C - D = (A + C) - (B + D)

In fact, more variables can be included!

A - B + C - D + E - F = (A + C + E) - (B + D + F)

A - B + C - D + E - F - G + H = (A + C + E + H) - (B + D + F + G)

The variables with pluses to their left go in the 1st group & the variables with minuses to their left go in the 2nd group! It has something to do the Plus-Minus Parentheses Rule!

Examples:

1 + 2 - 3 + 4 - 5 = (1 + 2 + 4) - (3 + 5) = 7 - 8 = -1

9 - 11 + 13 - 15 - 18 + 17 = (9 + 13 + 17) - (11 + 15 + 18) = 39 - 44 = -5

-7 + 8 - 9 + 10 = (8 + 10) - (7 + 9) = 18 - 16 = 2

23 - 25 + 2 + 4 + 6 + 8 - 1.5 = (23 + 2 + 4 + 6 + 8) - (25 + 1.5) = 43 - 26.5 = 16.5

If the 2nd group has the greater absolute value, then the sum will be negative. If the 1st addend (or augend) is negative, it'll have a minus to its left. (The 1st addend in an addition problem can also be called the augend.) Remember that the 1st group of addends are the positive ones & the 2nd group of addends are the negative ones. (Considering the parentheses in the formulae at the top of the Web page!) The negative addends have minuses to their left & the positive ones have pluses to their left. The augend is positive by default with no sign to its left!

Any kind of number can be used in this math trick, including imaginary numbers & complex numbers!

5i + 2 - 3i + π - √(2) = (5i + 2 + π) - (3i + √(2)) = (2 + π - √(2)) + (5 - 3)i = 2 + π - √(2) + 2i = 3.727379091... + 2i

In complex numbers, the real parts are put to the left & the imaginary parts are put to the right; that's just how it's done. I also show the irrational real part sum in decimal form.

Finally, as I conclude this Web page, when addition becomes subtraction or vice versa, pluses will sometimes turn into minuses & minuses will sometimes turn into pluses! But not every sign will change; only signs that get "multiplied" by a minus will change, so watch out!

(Danielle Lipstick here just gave you a clue about it!)

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