Title: REAL RATIONAL NUMBERS
1REAL RATIONAL NUMBERS
- (as opposed to fake numbers?)
and Properties Part 1 (introduction)
2STANDARD AF 1.3 Apply algebraic order of
operations and the commutative, associative, and
distributive properties to evaluate expressions
and justify each step in the process.
- Student Objective
- Students will apply order of operations to solve
problems with rational numbers and apply their
properties, by performing the correct operations,
using math facts skills, writing reflective
summaries, and scoring 80 proficiency
3A collection of objects.
Set
Set Notation
Natural numbers
Counting numbers 1,2,3,
Whole Numbers
Natural numbers and 0. 0,1,2,3,
Positive and negative natural numbers and zero
-2, -1, 0, 1, 2, 3,
Integers
Vocabulary
Rational Number
A real number that can be expressed as a ratio of
integers (fraction)
Any real number that is not rational.
Irrational Number
Real Numbers
All numbers associated with the number line.
4Essential Questions
- How do you know if a number is a rational number?
- What are the properties used to evaluate rational
numbers?
5Two Kinds of Real Numbers
- Rational Numbers
- Irrational Numbers
6Rational Numbers
- A rational number is a real number that can be
written as a ratio of two integers. - A rational number written in decimal form is
terminating or repeating.
- EXAMPLES OF RATIONAL NUMBERS
- 16
- 1/2
- 3.56
- -8
- 1.3333
- -3/4
7Irrational Numbers
- An irrational number is a number that cannot be
written as a ratio of two integers. - Irrational numbers written as decimals are
non-terminating and non-repeating.
- Square roots of non-perfect squares
- Pi- ii
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9Rational Numbers
Natural Numbers -
Natural counting numbers.
1, 2, 3, 4
Whole Numbers -
Natural counting numbers and zero.
0, 1, 2, 3
Integers -
Whole numbers and their opposites.
-3, -2, -1, 0, 1, 2, 3
Rational Numbers -
Integers, fractions, and decimals.
-0.76, -6/13, 0.08, 2/3
Ex
10Making Connections
Biologists classify animals based on shared
characteristics. The horned lizard is an animal,
a reptile, a lizard, and a gecko. Rational
Numbers are classified this way as well!
Animal
Reptile
Lizard
Gecko
11Venn Diagram Naturals, Wholes, Integers,
Rationals
Real Numbers
Rationals
Integers
Wholes
Naturals
12Reminder
- Real numbers are all the positive, negative,
fraction, and decimal numbers you have heard of. - They are also called Rational Numbers.
- IRRATIONAL NUMBERS are usually decimals that do
not terminate or repeat. They go on forever. - Examples p
13Properties
A property is something that is true for all
situations.
14Four Properties
- Distributive
- Commutative
- Associative
- Identity properties of one and zero
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16Distributive Property
A(B C) AB BC
4(3 5) 4x3 4x5
17Commutative Propertyof addition and
multiplication
Order doesnt matter
A x B B x A A B B A
18Associative Property of multiplication and
Addition
Associative Property ? (a b) c a (b
c) Example (6 4) 3 6 (4 3)
Associative Property ? (a b) c a (b
c) Example (6 4) 3 6 (4 3)
19Identity Properties
If you add 0 to any number, the number stays the
same.
A 0 A or 5 0 5
If you multiply any number times 1, the number
stays the same.
A x 1 A or 5 x 1 5
20Example 1 Identifying Properties of Addition and
Multiplication Name the property that is
illustrated in each equation. A. (4) ? 9 9 ?
(4) B.
(4) ? 9 9 ? (4)
The order of the numbers changed.
Commutative Property of Multiplication
The factors are grouped differently.
Associative Property of Addition
21Example 2 Using the Commutative and Associate
Properties Simplify each expression. Justify each
step. 29 37 1
Commutative Property of Addition
29 37 1 29 1 37
Associative Property of Addition
(29 1) 37
30 37
Add.
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22Exit Slip!
Name the property that is illustrated in each
equation. 1. (3 1) 2 3 (1 2) 2. 6 ? y
? 7 6 ? 7 ? y Simplify the expression. Justify
each step. 3. Write each product using the
Distributive Property. Then simplify 4. 4(98) 5.
7(32)
Associative Property of Add.
Commutative Property of Multiplication
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