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Real Number system
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Question | Answer |
---|---|
N | Natural |
W | Whole |
Z | Integers |
Q | Rational |
I | Irrational |
R | Real |
This applies to addition and multiplication, stating that the order of numbers doesn't change the result. For example, a+b=b+a and a×b=b×a | Commutative Property: |
This also applies to addition and multiplication, indicating that how numbers are grouped in parentheses doesn't affect the outcome. For example, (a+b)+c=a+(b+c) and (a×b)×c=a×(b×c) | Associative Property: |
This bridges addition and multiplication, showing that multiplying a number by a sum is the same as multiplying each addend individually and then adding the products. For example, a×(b+c)=(a×b)+(a×c) | Distributive Property: |
This describes the identity elements for addition and multiplication. For addition, the identity is 0, because any number plus 0 remains unchanged (a+0=a). For multiplication, the identity is 1, because any number times 1 remains unchanged (a×1=a) | Identity Property: |
This involves the additive and multiplicative inverses. The additive inverse is the number that, when added, results in zero (a+(−a)=0). The multiplicative inverse is the number that, when multiplied, results in one (a×1a=1, assuming a≠0) | Inverse Property: |
This property states that if the product of two numbers is zero, then at least one of the factors must be zero. In other words, for any numbers a and b, if a×b=0, then either a=0, b=0, or both. | Zero Property (also called the Zero Product Property): |