Question

subtraction has no commutative property justify​

Answer 1

Answer:

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Answer 2

Answer:

❝I am less than satisfied with answers to “why” that reduce to “because it it so”. It is true that subtraction does not have a commutative property. The order of the quantities either side of the operator do matter.❞

☛Just one example,

3−2≠2−3

⫸The reason why, which extends also to division, is that subtraction is defined as an inverse function for addition. This allows us to re-use our prior knowledge about addition, applying it to a further domain. Think back to elementary school and the grid that was the addition table you needed to memorize. When it came time for learning subtraction, we used the same addition table, but in a different sequence. Where, in addition we would find the intersection of the row and column matching our addends, in subtraction we started at the row for the number which we wanted to subtract, then scanned in the body of the table for the number from which we wanted to subtract it. We then looked up to the column heading to find that, say,

⫸What we avoided doing, this way, was memorization of a separate addition table that had negative values in the rows and columns.

. And this is commutative, i.e.,

⫸Our shortcut, inventing subtraction, comes at the cost of loss of the commutative property.

⫸With division, a moment’s reflection brings awareness that we re-used the multiplication table. As with subtraction, we find the row with the divisor, scan across for the dividend, and then look up that column heading to find the quotient.

⫸The shortcut of re-using multiplication knowledge saved us from learning the multiplication by reciprocals, at the cost of loss of the commutative property.