Warm-Up from 1.1

Find the algebraic expression to represent the pattern given:

1. 5, 9, 13, 17, ….

2. 2, -3, -8, -13, …

3. -3, 0, 5, 12, 21, …

4. 5, 14, 29, 50, 77, …

5. 3, 10, 29, 68, …

1.2 – Properties of Real Numbers

Students will be able to:

•Graph and order real numbers

•Identify properties of real numbers

Lesson Vocabulary

•Opposite

•Additive inverse

•Reciprocal

•Multiplicative Inverse

1.2 – Properties of Real Numbers

1.2 – Properties of Real Numbers

The set of real numbers has several subsets related in particular ways.

Algebra involves operations on and relations among numbers, including real numbers and

imaginary numbers.

Rational numbers and irrational numbers form the set of real numbers.

1.2 – Properties of Real Numbers

You can graph every real number as a point on the number line.

1.2 – Properties of Real NumbersREAL NUMBERS

IRRATIONALRATIONAL

INTEGERS

WHOLE

NATURAL

•Have decimal representations that neither terminate nor repeat.

•Cannot be written as quotients of integers

• Are all numbers you can write as a quotient of integers

•Include terminating decimals

•Include repeating decimals

1.2 – Properties of Real Numbers

Problem 1:

Multiple Choice: Your school is sponsoring a charity race. Which set of numbers does not

contain the number of people p who participate in the race?

a. Natural numbers b. Integers

c. Rational numbers d. Irrational numbersThe number of people is a

natural number, which means it is also an integer and

rational number.

1.2 – Properties of Real Numbers

Problem 1b:

Multiple Choice: In the previous problem, if each participant made a donation d of

$15.50 to a local charity, which subset of real numbers best describes the amount of

money raised.

a. Natural numbers b. Integers

c. Rational numbers d. Irrational numberscorrect

1.2 – Properties of Real Numbers

Problem 2:

What is the graph of the numbers:

and ?5, 2,2

2.6

1.2 – Properties of Real Numbers

Problem 2b:

What is the graph of the numbers:

and ?3, 1.4,1

3

1.2 – Properties of Real Numbers

Problem 3:

How do and 3.8 compare? Use > or <. 17

1.2 – Properties of Real Numbers

Problem 3b:

How do and 6.25 compare? Use > or <. 26

1.2 – Properties of Real Numbers

Problem 3c:

Let a, b, and c be real numbers such that

a < b and b < c. How do a and c compare? Explain!!

1.2 – Properties of Real NumbersThe properties of real numbers are relationships

that are true for all real numbers (except, in one case, zero).

The opposite or additive inverse of any number a is –a. The sum of a number and

its opposite is 0, the additive identity.

Examples: 12 + (-12) = 0

-7 + 7 = 0

1.2 – Properties of Real Numbers

The reciprocal or multiplicative inverse of an nonzero number a is 1/a. The product of a

number and its reciprocal is 1, the multiplicative identity.

Examples:

8(1/8) = 1

-5(-1/5) = 1

1.2 – Properties of Real Numbers

1.2 – Properties of Real Numbers

Problem 4:

Which property does the equation illustrate?

a. (-2/3)(-3/2) = 1

b. (3 x 4)x 5 = (4 x 3)x 5

c. 3(g + h) + 2g = (3g + 3h) + 2g

d. - 5 + 0 = -5

1.2 – Properties of Real Numbers

Lesson Check

1.2 – Properties of Real Numbers

Lesson Check