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Algebraic Properties

Terms in this set (15)

Reflexive Property
Any quantity is equal to itself.
For any number a, a=a.
5=5 or 4+7 = 4+7
Symmetric Property
If one quantity equals a second quantity, then the second quantity equals the first.
For and numbers a and b, if a=b then b=a.
Transitive Property
If one quantity equals a second quantity and the second quantity equals a third quantity, then the first quantity equals the third quantity.
For any numbers a,b, and c, if a=b and b=c, then c=a
If 6+9 = 3+12 and 3+12 = 15, then 6+9 = 15
Substitution Property
A quantity may be substituted for its equal in any expression.
If a=b, then a may be replaces by b in any expression.
If n = 11 then 4n = 4x11
Additive Identity
For any number a, the sum of a and 0 is a.
a + 0 = 0 + a =a
2 + 0 = 2 or 0 + 2 = 2
Additive Inverse
A number and its opposite are additive inverses of each other.
a +(-a) = 0
3 + (-3) = 0 or 4-4 = 0
Multiplicative Identity
For any number a, the product of a and 1 is a.
ax1=a 1xa=a
1x14=14 14x1=14
Multiplicative Property of Zero
For any number a, the product of a and 0 is 0.
ax0=0 0xa=0
9x0=0 0x9=0
Multiplicative Inverse
For every number a/b, where a, b does not equal 0, there is exactly one number b/a such that the product of a/b and b/a is 1.
a/b x b/a=1 b/a x a/b=1
4/5 x 5/4=20/20 or 1
5/4 x 4/5=20/20 or 1
Communtative Property of Addition
The order in which you add numbers does not change their sum.
For any numbers a and b, a+b=b+a
4+8=8+4
Commutative Property of Multiplication
The order in which you multiply numbers does not change their product.
For any numbers a and b,
a x b=b x a
7 x 11=11 X 7
Associative Property of Addition
The way you group three or more numbers when adding does not change their sum.
For any numbers a, b and c,
(a+b)+c=a+(b+c)
(3+5)+7=3+(5+7)
Associative Property of Multiplication
The way you group three or more numbers when multiplying does not change their product.
For any numbers, a, b and c,
(ab)c=a(bc)
(2 x 6) x 9=2 x (6 x 9)
Distributive Property
a(b+c)=ab + ac and (b+c)a =ba+ca
a (b-c)=ab-ac
-a(b+c)=-ab-ac
No property
Mathematically untrue
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