Chapter 3.6 - Mathematical Properties
Mathematical Properties are 'rules' or 'truths' that will help us solve algebra problems.
1. Associative Property of Addition
You can change the grouping of an addition problem without changing the answer: (3+2)+4 = 3 +(2+4), a + (b+c) = (a+b)+c
2. Associative Property of Multiplication
You can change the grouping of a multiplication problem without changing the answer: (2X4)X5 = 2X(4X5), aX(bXc) = (aXb)Xc
3. Commutative Property of Addition
In an addition problem, you can change the order of the addends without changing the answer: 4 + 5 = 5 + 4, a + b = b + a
4. Commutative Property of Multiplication
In a multiplication problem, you can change the order without changing the answer:
4 X 6 = 6 X 4, a X b = b X a
5. Identity Property of Addition
When you add zero to a number, the answer is the number: 3 + 0 = 3, a + 0 = a
6. Identity Property of Multiplication
When you multiply a number by 1, the answer is the number: 5 X 1 = 5, a X 1 = a
7. Zero Property of Multiplilcation
Any number multiplied by zero equals zero. 8 X 0 = 0, a X 0 = 0
8. Additive Inverse
a number and its additive inverse (opposite) when added, equal zero: 3 + -3 = 0, a + -a = 0
9. Distributive property
To multiply a sum (or difference) by a number, multiply each addend by the number outside the parentheses: 3(4 + 2)= 3(4) + 3(2), a(b+c)= ab + ac, 5(6 - 2) = 5(6) - 5(2)
10. Transitive Property
states for any real numbers, a, b, and c: If a = b and b = c, then a = c