1) 12 • (–28) 2) –23 + (–15) 3) 28 ÷ ( –12)

4) 0.314, 0.0978, 0.309, 0.3131

1.1 Warm-UpSimplify.

Order the numbers from least to greatest.

-336 -38 7

3

0.0978, 0.309, 0.3131, 0.314

Alg2 Lesson 1-1Properties 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.

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, …………….

Example 1

Graph the real numbers , 3, and – 1.8 5 2

–5 –4 –3 –2 –1 1 2 5430

Where is the origin?

–5 –4 –3 –2 –1 1 2 5430

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

• Example 4

Find the opposite and the reciprocal of each number

a) -3 b)

Opposite: Opposite:

Reciprocal: Reciprocal:

3

5

5

3

1

3

3

5

3

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

Example 2

Identify the property shown.

a. 14 + 7 = 7 + 14 b. 5 • = 1

Commutative property of addition

Inverse Property of multiplication

1 5

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

• 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

HOMEWORKDue Wednesday:

Pg. 8 – 9

12 – 24, 34 – 36, 42 – 62 even