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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. Associate 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 Poperty 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 Poperty 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

The additive inverse was not covered in the first video... watch this short video to understand and see examples of the additive inverse.

Name Change: Was S1 now R9

R.9 - Properties of addition and multiplication

 Lesson #1                                            Video                                           Assignment 

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