Properties of Real numbers( integers and non integers)

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1. PROPERTIES OF REAL NUMBERS Prepared by: Mr. Erick Concepcion

2. CLOSURE PROPERTY OF ADDITION The sum of any two real number is a real number. Where a + b is a real number

3. EXAMPLE: 2 is a real number and 3.5 is a real number so 2 + 3.5 or 5.5 is a real number

4. CLOSURE PROPERTY OF MULTIPLICATION The product of any two real numbers is a real number. Where ab is a real number.

5. EXAMPLE: 12 is a real number and is a real number, so or 4 is a real number.  

6. COMMUTATIVE PROPERTY OF ADDITION Two real numbers can be added in any order. Where  

7. EXAMPLE:  

8. ASSOCIATIVE PROPERTY OF ADDITION If three real numbers are added, it makes no difference which two are added first. Where  

9. EXAMPLE: 19 24 24  

10. ASSOCIATIVE PROPERTY OF MULTIPLICATION If three real numbers are multiplied, it makes no difference which two are multiplied first. Where  

11. EXAMPLE: 420 420  

12. DISTRIBUTIVE PROPERTY OF MULTIPLICATION OVER ADDITION/SUBTRACTION Multiplication distributes over addition/subtraction Where  

13. EXAMPLE: 14  

14. IDENTITY PROPERTY OF ADDITION Any number added to the identity element will remain unchanged. is the identity element of addition.  

15. IDENTITY PROPERTY OF MULTIPLICATION Any number multiplied to the identity element 1 will remain unchanged. 1 is the identity element of multiplication.  

16. INVERSE PROPERTY OF ADDITION The sum of a number and its additive inverse (opposite) is the identity element . a and –a are additive inverses.  

17. INVERSE PROPERTY OF MULTIPLICATION The product of a number and its multiplicative inverse (reciprocal) is the identity element 1 . and are multiplicative inverses. Where  

18. SEATWORK # 2

19. Identify the axiom or real number property that justifies each statement. Write your answer before the number . 31+ x = x + 31 5(x – 4) = 5x – 20 4( xy ) = 4x(y) 9+(-9) = 0 1,001 (1) = 1,001 ax + x = x(a+1) (1 )(10)=1