1. Lesson 1-4 Identity and Equality Properties Miss Simpson 1-11-08

2. ADDITIVE IDENTITY Definition: Any number plus zero equals that number. a+ 0 = a 3+ 0 = 3 1600 + 0 = 1600 n + 0 = 18 What is the value of n?

3. MULTIPLICATIVE IDENTITY Definition: Any number multiplied by one equals that number. a· 1 = a 8· 1 = 8 19 · 1 = 19 n · 1 = 58 What is the value of n?

4. MULTIPLICATIVE PROPERTY OF ZERO Definition: Any number multiplied by zero equals zero. a· 0 = 0 4.53· 0 = 0 31 · 0 = 0 n · 15 = 0 What is the value of n?

5. MULTIPLICATIVE INVERSE Definition: Any number multiplied by its reciprocal equals one. Which brings up the question: What is reciprocal?

6. WHAT IS RECIPROCAL?  Two numbers whose product is one. “FLIP “ a number. What is the reciprocal of: 1.8 2. 13. 74. - 6 9 25 9 8 2 = 2 1 7 5 -6

7. a· b = 1 b a 7 · 9 = 1 9 7 5· 1 = 1 n What is the value of n?

8. REFLEXIVE PROPERTY Definition: Any quantity equals itself. a = a 9 = 9 2 + 6 = 2 + 6 2 + 3 = 2 + n What is the value of n?

9. SYMEMETRIC PROPERTY Definition: If one quantity equals a second quantity, then the second quantity equals the first. If a = b, then b = a. If 4 + 5 = 9, then 9 = 4 + 5. If 8 = 4· 2, then 4· 2 = 8. If 2a = 10, then 10 = 2a.

10. TRANSITIVE PROPERTY Definition: If one quantity equals a second and a second quantity equals a third, then the first equals the third. If a = b and b = c, then a = c. If 2 + 3 = 5 and 5 = 4 + 1, then 2 + 3 = 4 + 1. If 5(6) = 3(10) and 3(10) = 30, then...

11. SUBSTITUTION (“SOLVE”) PROPERTY Definition: A quantity may be substituted for its equal. If a = b, then a can be replaced by b. If n = 15, then 3n = 3(15) 5(9-7) = 5(?) 25 ÷ 5 = ?

12. NAME THAT PROPERTY. n + 0 = 19

13. NAME THAT PROPERTY. 28· a = 0

14. NAME THAT PROPERTY. 9 + 6 = f + 6

15. NAME THAT PROPERTY. 1 · b = 23

16. NAME THAT PROPERTY. 1 · x = 1 4

17. NAME THAT PROPERTY. 2(9 – 3) = 2(m)

18. NAME THAT PROPERTY. 24 ÷ 4 = y

19. NAME THAT PROPERTY. n· 9 = 9

20. NAME THAT PROPERTY. If 8 + 4 = 12, then 12 = 8 + 4

21. NAME THAT PROPERTY. If 8(3) = 24 and 24 = 12(2), then 8(3) = c.

22. NAME THAT PROPERTY. 7 + z = 7

23. NAME THAT PROPERTY. (8+ 7)(4) = r(4)

24. EVALUATE. NAME PROPERTY. 7 + (16 ÷ 4²) 7 (16 ÷ 16) - SUBSTITUTION 7 (1) - SUBSTITUTION 7 – MULT. IDENTITY

25. EVALUATE. NAME PROPERTY. 2(3· 5· 1 – 14) – 4 · ¼ 2(15 · 1 – 14) - 4 ·¼ - SUBSTITUTION 2(15 – 14) - 4 ·¼ - MULT. IDENTITY 2(1) - 4 ·¼ – SUBSTITUTION 2 - 4 ·¼ – MULT. IDENTITIY 2 - 1 – MULT. INVERSE 1– SUBSTITUTION

26. EVALUATE. NAME PROPERTY. 2[5 – (15 ÷ 3)] 2[5 – 5] - SUBSTITUTION 2[0] - SUBSTITUTION 0- MULT. PROPERTY OF ZERO

27. EVALUATE. NAME PROPERTY. 3(5 – 5·1²) + 21 ÷ 7 3(5 - 5· 1) + 21 ÷ 7 - SUBSTITUTION 3(5 – 5) + 21 ÷ 7 - MULT. IDENTITY 3(0) + 21 ÷ 7 – SUBSTITUTION 0 + 21 ÷ 7 – MULT. PROP. OF ZERO 0 + 3 – SUBSTITUION 3 – ADDITIVE IDENTITY

28. EVALUATE. NAME PROPERTY. 4 – 3[7 – (2· 3)] 4 – 3[7 – 6] - SUBSTITUTION 4 – 3[1] - SUBSTITUTION 4 – 3 - MULT. IDENTITY 1- SUBSTITUTION