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It’s the Commutative Law!

October15

Yes, we mathematicians also have to keep the law and the Commutative Law is a big one for us! A commuter is someone who travels to work each day and then home again.They might look something like this;
commutersTheir travel route and distance is the same in both directions, so we call them a “Commuter”. In Math, the Commutative Law means that the answer is the same, even if the numbers on each side of the operator are reversed. Of course, this works well for addition and multiplication but don’t try this at home with either division or subtraction! For example, 2×3 = 3×2, but 2-3 does not equal 3-2!
commutative3

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NCEA Level 2 Algebra Problem. Using the information given, the shaded area = 9, that is:
y(y-8) = 9 –> y.y – 8y – 9 =0
–> (y-9)(y+1) = 0, therefore y = 9 (can’t have a distance of – 1 for the other solution for y)
Using the top and bottom of the rectangle,
x = (y-8)(y+2) = (9-8)(9+2) = 11
but, the left side = (x-4) = 11-4 = 7, but rhs = y+? = 9+?, which is greater than the value of the opp. side??
[I think that the left had side was a mistake and should have read (x+4)?]

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