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Literal representation of the properties of addition and subtraction

Properties of addition and subtraction are easier to write with letters so one rule works for any numbers. Commutative property of addition: a+b=b+aa+b=b+a. Associative property of addition: (a+b)+c=a+(b+c)(a+b)+c=a+(b+c) — the sum does not depend on how you place parentheses. Zero: a+0=0+a=aa+0=0+a=a; subtracting zero: a0=aa-0=a. Link between addition and subtraction: if a+b=ca+b=c, then ca=bc-a=b and cb=ac-b=a; from ax=ba-x=b it follows that a=b+xa=b+x. Check subtraction: add the subtrahend to the difference — you should get the minuend.
a+b=b+aa+b=b+a — order of addends
(a+b)+c=a+(b+c)(a+b)+c=a+(b+c) — parentheses in addition
a+0=aa+0=a, a0=aa-0=a
From a+b=ca+b=c follows ca=bc-a=b
Commutative property: the same sum
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