median
don steward
mathematics teaching 10 ~ 16

Sunday, 7 November 2010

five subtract negative three


(some) reasons why 5 - -3 = 8

(i) with subtraction you can add the same amount to both bits (the minuend and the subtrahend) and it doesn't change the result; so add 3 to both: 5 - -3 = 8 - 0

(ii) it's the gap from -3 up to 5 on a number line

(iii) extending a pattern:
5 - 3 = 2,
5 - 2 = 3,
5 - 1 = 4,
5 - 0 = 5
so 5 - -1 = 6,
5 - -2 = 7,
and so 5 - - 3 is 8

(iv) using a straight line graph rule: continuing the graph of y = 5 - x into the negative quadrants you can see that when x = -3, y = 8

(v) using inverses: 5 = 8 - 3 so 5 - -3 = 8

(vi) also using inverses: 8 + - 3 = 5 so 8 = 5 - -3

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