Download 1.2 - Brookville Local Schools

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 Numbers
REAL NUMBERS
RATIONAL
INTEGERS
• Are all numbers you can write as a quotient
of integers
WHOLE
•Include terminating decimals
NATURAL
•Include repeating decimals
IRRATIONAL
•Have decimal
representations
that neither
terminate nor
repeat.
•Cannot be
written as
quotients of
integers
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
c. Rational numbers
b. Integers
d. Irrational numbers
The 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
c. Rational numbers
correct
b. Integers
d. Irrational numbers
1.2 – Properties of Real Numbers
Problem 2:
What is the graph of the numbers:
5
 , 2, and 2.6 ?
2
1.2 – Properties of Real Numbers
Problem 2b:
What is the graph of the numbers:
1
?
3, 1.4, and
3
1.2 – Properties of Real Numbers
How do
17
Problem 3:
and 3.8 compare? Use > or <.
1.2 – Properties of Real Numbers
How do
Problem 3b:
26 and 6.25 compare? Use > or <.
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 Numbers
The 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