Appendix 1 – Rules of Arithmetic
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Commutative Rule of Addition: |
Commutative Rule of Multiplication: |
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For any numbers a and b, |
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a+b=b+a |
a∙b=b∙a |
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Associative Rule of Addition: |
Associative Rule of Multiplication: |
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For any numbers a, b, and c, |
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(a+b)+c=a+(b+c) |
a(a∙b)∙c=a∙(b∙c) |
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Identity Rule of Addition: |
Identity Rule of Multiplication: |
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For any number a, |
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0+a=a |
1∙a=a |
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Inverse Rule of Addition: |
Inverse Rule of Multiplication: |
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For any number a, |
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-a+a=0 |
1/a∙a=1 |
Distributive Rule:
For any numbers a, b, and c,
a∙(b+c)=a∙b+a∙c
Any Which Way Rule for Addition:
Given any list of numbers to be added, they may be ordered in any way, and grouped by parentheses in any way, without changing the answer. (This includes subtraction by thinking of subtraction of a number as being the same as adding its negative. When rearrangement is done with subtraction, the minus signs should move with the numbers they are in front of.)
Examples:
- ((((1 + 2) – 3) + 4) – 5) + 6 = (1 + 2) + (4 + 6) – 3 – 5
- x + (1 + x) = (x + x) + 1
- x + (x+ 1) + (x + 2) + (x + 3) = (x + x + x + x) + (1 + 2 + 3)
- (2x + 3) + (4x + 5) = (2x + 4x) + (3 + 5)
- 23 + 45 = (20 + 3) + (40 + 5) = (20 + 40) + (3 + 5) = 60 + 8 = 68
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