1. 1)12 (–28) 2) –23 + (–15) 3) 28 ÷ ( –12) 4) 0.314, 0.0978, 0.309, 0.3131 1.1 Warm-Up Simplify. Order the numbers from least to greatest. -336-38 7 3 0.0978,0.309,0.3131,0.314

2. Alg2 Lesson 1-1 Properties of Real Numbers Objectives: 1.Identify the subsets of real numbers. 2.Identify the properties of real numbers. 3.Find the opposite and reciprocal of a number. 4.Order real numbers and graph on a number line.

3. SUBSETS OF THE REAL NUMBERS WHOLE NUMBERS: 0, 1, 2, 3, ……………. INTEGERS: ……., -3, -2, -1, 0, 1, 2, 3, …………. RATIONAL NUMBERS: A ratio of two integers (3/4, 1/3, -4/1, ….) when written as decimals, rational numbers terminate or repeat. (3/4 = 0.75, or 1/3 = 0.3333….) IRRATIONAL NUMBERS: They neither terminate or repeat. (л, 2, etc.) NATURAL NUMBERS: 1, 2, 3, …………….

5. Example 1 Graph the real numbers, 3, and – 1.8 5 2 –5–4–3–2–112543 0 Where is the origin? –5–4 –3–2–112543 0

6. Properties of Real Numbers Opposite or Additive Inverse of any number a is –a –The sum of any two opposites is 0 The Reciprocal or Multiplicative Inverse of any nonzero number a is 1/a –The product of reciprocals is 1

7. Example 4 Find the opposite and the reciprocal of each number a) -3b) Opposite: Reciprocal:

8. PROPERTIES OF ADDITION AND MULT. ASSOCIATIVE: (a + b) + c = a + (b + c) & (ab)c = a(bc) COMMUTATIVE: a + b = b + a & ab = ba DISTRIBUTIVE: a(b + c) = ab + ac IDENTITY: a + 0 = a & a 1 = a INVERSE: a + (-a) = 0 & a = 1 1 a CLOSURE: a + b is a real number & ab is a real number

9. Example 2 Identify the property shown. a. 14 + 7 = 7 + 14b. 5 = 1 Commutative property of addition Inverse Property of multiplication 1 5

10. Operations with Real Numbers. Example 3 a.The difference of -3 and -15 is: b.The Quotient of -18 and 1/6 is: Sum + Difference – Product x ÷ Quotient -3 – -15 18 -3 + 15 = 12 1 6 6 1 6 1 -18 6 =-108

11. The Absolute Value of a real number is its distance from zero on the number line Example 5 Find the absolute value of: a)|-4| b)|0| c)|-1 (-2)| 4 0 2

12. HOMEWORK Due Wednesday: Pg. 8 – 9 12 – 24, 34 – 36, 42 – 62 even