1. Warm-Up #1 1. 18 + (–25) = ? 2. 1 2 – 4 3 = ? ANSWER –7 2 3 ANSWER
(–25) = ? 2. 1 2 – 4 3 = ?
ANSWER –7 2 3
ANSWER
3. What is the difference between a daily low temperature of –5º F and a daily high temperature of 18º F ?
ANSWER
23º F

3. Real Numbers Real Numbers Natural (Counting) numbers: N = {1, 2, 3, …}
Whole numbers: W = {0, 1, 2, 3, …}
Integers: Z = {0, 1, 2, 3, …}
Rational Numbers: Any number that can be written as a fraction where the numerator and denominator are both integers and the denominator doesn’t equal zero
Irrational Numbers: Any number that isn’t a rational number
Real Numbers
Rational Numbers
Irrational Numbers
Integers
Whole Numbers
Natural Numbers

4. Graph real numbers on a number line
EXAMPLE 1
Graph real numbers on a number line
Graph the real numbers – and 3 on a number line. 5 4
SOLUTION
Note that – = –1.25. Use a calculator to approximate
3 to the nearest tenth: 5 4
(The symbol means is approximately equal to.)
So, graph – between –2 and –1, and graph 3 between
1 and 2, as shown on the number line below. 5 4

5. EXAMPLE 3
Identify properties of real numbers
Identify the property that the statement illustrates.
7 + 4 = 4 + 7
SOLUTION
Commutative property of addition
= 1 1 13
SOLUTION
Inverse property of multiplication

6. GUIDED PRACTICE
for Examples 3 and 4
Identify the property that the statement illustrates.
(2 3) 9 = 2 (3 9)
SOLUTION
Associative property of multiplication.
= 15
SOLUTION
Identity property of addition.

7. GUIDED PRACTICE
for Examples 3 and 4
Identify the property that the statement illustrates.
4(5 + 25) = 4(5) + 4(25)
SOLUTION
Distributive property.
= 500
SOLUTION
Identity property of multiplication.

10. EXAMPLE 1
Evaluate powers
(–5)4
= (–5) (–5) (–5) (–5)
= 625
–54
= –( )
= –625

11. Evaluate an algebraic expression Evaluate –4x2 – 6x + 11 when x = –3.
EXAMPLE 2
Evaluate an algebraic expression
Evaluate –4x2 – 6x + 11 when x = –3.
–4x2 – 6x + 11
= –4(–3)2 – 6(–3) + 11
Substitute –3 for x.
= –4(9) – 6(–3) + 11
Evaluate power.
= –
Multiply.
= –7
Add.

12. Evaluate the expression.
GUIDED PRACTICE
for Examples 1, 2, and 3
Evaluate the expression. 63
SOLUTION
216
–26
SOLUTION
–64

13. GUIDED PRACTICE
for Examples 1, 2, and 3
(–2)6
SOLUTION 64
5x(x – 2) when x = 6
SOLUTION
120

14. GUIDED PRACTICE
for Examples 1, 2, and 3
3y2 – 4y when y = – 2
SOLUTION 20
(z + 3)3 when z = 1
SOLUTION 64

15. Simplify by combining like terms
EXAMPLE 4
Simplify by combining like terms
8x + 3x
= (8 + 3)x
Distributive property
= 11x
Add coefficients.
5p2 + p – 2p2
= (5p2 – 2p2) + p
Group like terms.
= 3p2 + p
Combine like terms.
3(y + 2) – 4(y – 7)
= 3y + 6 – 4y + 28
Distributive property
= (3y – 4y) + (6 + 28)
Group like terms.
= –y + 34
Combine like terms.

16. Simplify by combining like terms
EXAMPLE 4
Simplify by combining like terms
2x – 3y – 9x + y
= (2x – 9x) + (– 3y + y)
Group like terms.
= –7x – 2y
Combine like terms.

17. GUIDED PRACTICE
for Example 5
8. Identify the terms, coefficients, like terms, and constant terms in the expression 2 + 5x – 6x2 + 7x – 3. Then simplify the expression.
SOLUTION
Terms:
2, 5x, –6x2 , 7x, –3
Coefficients:
5 from 5x, –6 from –6x2 , 7 from 7x
Like terms:
5x and 7x, 2 and –3
Constants:
2 and –3
Simplify:
–6x2 +12x – 1

18. Simplify the expression.
GUIDED PRACTICE
for Example 5
Simplify the expression.
15m – 9m
SOLUTION 6m
2n – 1 + 6n + 5
SOLUTION
8n + 4

19. GUIDED PRACTICE
for Example 5
3p3 + 5p2 – p3
SOLUTION
2p3 + 5p2
2q2 + q – 7q – 5q2
SOLUTION
–3q2 – 6q

20. GUIDED PRACTICE
for Example 5
8(x – 3) – 2(x + 6)
SOLUTION
6x – 36
–4y – x + 10x + y
SOLUTION
9x –3y

21. Classwork 1.1/1.2
WS 1.1 (2-18 even)
WS 1.2 (2-26 even)

22. In the Practice Workbook:
Homework 1.1/1.2
In the Practice Workbook:
WS 1.1 (1-19 odd)
WS 1.2 (1-21 odd)