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1. 18 + (–25) =

–7

ANSWER

ANSWER

23º F

?

?

1

4

2.

–

–

=

2

3

2

3

Warm-Up #1

ANSWER

3.What is the difference between a daily low temperature of –5º F and a daily high temperature of 18º F ?

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

-5 -2 -1

Whole Numbers

0

Natural Numbers

1 2 3

5

Graph the real numbers – and 3 on a number line.

4

5

Note that –= –1.25. Use a calculator to approximate

3 to the nearest tenth:

4

3 1.7. (The symbol means is approximately equal to.)

5

So, graph – between –2 and –1, and graph 3 between

1 and 2, as shown on the number line below.

4

EXAMPLE 1

Graph real numbers on a number line

SOLUTION

1

7 + 4 = 4 + 7

13 = 1

13

EXAMPLE 3

Identify properties of real numbers

Identify the property that the statement illustrates.

SOLUTION

Commutative property of addition

SOLUTION

Inverse property of multiplication

(2 3) 9 = 2 (3 9)

15 + 0 = 15

for Examples 3 and 4

GUIDED PRACTICE

Identify the property that the statement illustrates.

SOLUTION

Associative property of multiplication.

SOLUTION

Identityproperty of addition.

4(5 + 25) = 4(5) + 4(25)

1 500 = 500

for Examples 3 and 4

GUIDED PRACTICE

Identify the property that the statement illustrates.

SOLUTION

Distributive property.

SOLUTION

Identityproperty of multiplication.

EXAMPLE 2

Evaluate an algebraic expression

Evaluate –4x2 – 6x + 11 when x = –3.

= –4(–3)2– 6(–3) + 11

–4x2 – 6x + 11

Substitute –3 for x.

= –4(9) – 6(–3) + 11

Evaluate power.

= –36 + 18 + 11

Multiply.

= –7

Add.

8x + 3x

5p2 + p – 2p2

3(y + 2) – 4(y – 7)

EXAMPLE 4

Simplify by combining like terms

= (8 + 3)x

Distributive property

= 11x

Add coefficients.

= (5p2– 2p2) + p

Group like terms.

= 3p2 + p

Combine like terms.

= 3y + 6 – 4y + 28

Distributive property

= (3y – 4y) + (6 + 28)

Group like terms.

= –y + 34

Combine like terms.

2x – 3y – 9x + y

EXAMPLE 4

Simplify by combining like terms

= (2x – 9x) + (– 3y + y)

Group like terms.

= –7x – 2y

Combine like terms.

for Example 5

GUIDED PRACTICE

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

5 from 5x, –6 from –6x2 , 7 from 7x

Coefficients:

Like terms:

5x and 7x, 2 and –3

Constants:

2 and –3

Simplify:

–6x2 +12x – 1

15m – 9m

2n – 1 + 6n + 5

for Example 5

GUIDED PRACTICE

Simplify the expression.

SOLUTION

6m

SOLUTION

8n + 4

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