1. 1.2 Properties of Real Numbers Activity
11 Properties Stations
3 minutes per station
Match the correct Property with the examples given in your worksheet and explain how you figured out the answer

2. Example
The Closure Property says when you add two real numbers the sum is also a real number.
For any real numbers a and b,
a + b is a real number and a • b is a real number
Which example matches this property best?
a) = 3 + 4
5(2 + 6) =
5 + 9 = 14

3. The Commutative Property says the order in which two numbers are added or multiplied does not affect the answer.
a • b = b • a
x + (y + z) = (y + z) + x

4. The Associative Property says the sum or product of any three numbers is the same, no matter how they are grouped using parentheses and the order of the numbers always stays the same.
(a + b) + c = a + (b + c)
x • (y • z) = (x • y) • z

5. The Inverse Property of Addition says the sum of a number and its opposite equals 0.
a + (-a) = 0
-x + x = 0

6. The Inverse Property of Multiplication says any number multiplied by its reciprocal equals 1.

7. The Additive Identity: 0 added to any number will always equal the same number.
a + 0 = a
0 + x = x

8. The Multiplicative Identity: any number multiplied by 1 will always equal the same number.
a • 1 = a
1 • x = x

9. (a + b)(x + y) = ax + ay + bx + by
The Distributive Property multiplies the expression outside parentheses to the expression inside.
a(x + y) = ax + ay
(a + b)(x + y) = ax + ay + bx + by

10. Rational Numbers can be expressed as a fraction, terminating, and repeating decimals.

11. Irrational Numbers cannot be written as fraction, they are not terminating or repeating decimals.

12. Integers are positive and negative whole numbers.

13. Whole numbers are positive numbers, including zero, that are not fractions nor decimals.

14. Natural Numbers are positive whole numbers, excluding 0.