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Properties of Rational numbers

All the properties of rational numbers with examples.
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order of numbers can change (addition and multiplication)
Commutative property
grouping of numbers can change (addition and multiplication)
associative property
commutative property
a+b = b+a
associative property
(a+b)+c = a+(b+c)
when added to a number, the number stays the same (0)
additive identity
additive identity
a+0 = a
when multiplied by a number, the number stays the same (1)
multiplicative identity
multiplicative identity
a(1)= a
when added to a number, sum = 0
additive inverse
additive inverse
2+(-2)= 0
when multiplied by a number, product = 1
multiplicative inverse
multiplicative inverse
a(1/a)=1
any number multiplied by 0 = 0
multiplication property of zero
multiplication property of zero
a(0)=0
distributive property
a(b+c) = ab + ac