Download - Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers
![Page 1: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/1.jpg)
Ch 1.1 Warm Up Problems
Objectives:
- understand/use properties & classifications of real numbers
163
1x 3154 x
))((4 xx 84 x 416 x
![Page 2: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/2.jpg)
Properties of Real Numbers
The properties of real numbers
allow us to manipulate expressions
and equations and find the values
of a variable.
![Page 3: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/3.jpg)
Number Classification
• Natural numbers are the counting numbers. • Whole numbers are natural numbers and zero. • Integers are whole numbers and their opposites.• Rational numbers can be written as a fraction.• Irrational numbers cannot be written as a
fraction.• All of these numbers are real numbers.
![Page 4: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/4.jpg)
Number Classifications
Subsets of the Real Numbers
I - IrrationalZ - Integers
W - Whole
N - Natural
Q - Rational
![Page 5: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/5.jpg)
Classify each number -1 real, rational, integer
real, rational, integer, whole, natural
real, irrational
real, rational
real, rational, integer, whole
real, rational
6
1
2
-2.2220
![Page 6: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/6.jpg)
Properties of Real Numbers
Commutative Property• Think… commuting to work.• Deals with ORDER. It doesn’t matter
what order you ADD or MULTIPLY.
• a+b = b+a• 4 • 6 = 6 • 4
![Page 7: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/7.jpg)
Properties of Real Numbers
Associative Property• Think…the people you associate
with, your group.• Deals with grouping when you
Add or Multiply.• Order does not change.
![Page 8: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/8.jpg)
Properties of Real Numbers
Associative Property
• (a + b) + c = a + ( b + c)
• (nm)p = n(mp)
![Page 9: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/9.jpg)
Properties of Real Numbers
Additive Identity Property• s + 0 = s
Multiplicative Identity Property • 1(b) = b
![Page 10: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/10.jpg)
Properties of Real Numbers
Additive Inverse Property• a + (-a) = 0
Multiplicative Inverse Property
• a∙( ) = 1, a 0a
1
![Page 11: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/11.jpg)
Distributive Property
• a(b + c) = ab + ac
• (r + s)9 = 9r + 9s
Properties of Real Numbers
![Page 12: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/12.jpg)
• 5 = 5 + 0• 5(2x + 7) =
10x + 35• 8 • 7 = 7 • 8• 24(2) = 2(24)• (7 + 8) + 2 = 2 +
(7 + 8)
Additive Identity
Distributive
Commutative
Commutative
Commutative
Name the Property
![Page 13: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/13.jpg)
Name the Property
• 7 + (8 + 2) = (7 + 8) + 2• 1 • v + -4 = v + -4
• (6 - 3a)b = 6b - 3ab• 4(a + b) = 4a + 4b
• Associative• Multiplicative
Identity• Distributive • Distributive
![Page 14: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/14.jpg)
![Page 15: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/15.jpg)
Homework #1
P. 975: 1-10P. 6: 1-5, 9-13, 17-37 odd, 39-44, 57-60, 66, 69, 72, 75, 78
![Page 16: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/16.jpg)
Properties of Real Numbers
Reflexive Property
• a + b = a + b
The same expression is written on both sides of the equal sign.
![Page 17: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/17.jpg)
Properties of Real Numbers
• If a = b then b = a
• If 4 + 5 = 9 then 9 = 4 + 5
Symmetric Property
![Page 18: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/18.jpg)
Properties of Real NumbersTransitive Property
• If a = b and b = c then a = c
• If 3(3) = 9 and 9 = 4 +5, then 3(3) = 4 + 5
![Page 19: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/19.jpg)
Properties of Real Numbers
Substitution Property
• If a = b, then a can be replaced by b.
• a(3 + 2) = a(5)
![Page 20: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/20.jpg)
Name the property• 5(4 + 6) = 20 + 30• 5(4 + 6) = 5(10)• 5(4 + 6) = 5(4 + 6)• If 5(4 + 6) = 5(10) then
5(10) = 5(4 + 6)• 5(4 + 6) = 5(6 + 4)• If 5(10) = 5(4 + 6) and
5(4 + 6) = 20 + 30 then 5(10) = 20 + 30
• Distributive• Substitution• Reflexive• Symmetric
• Commutative• Transitive
![Page 21: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/21.jpg)
Solving Equations
• To solve an equation, find replacements for the variables to make the equation true.
• Each of these replacements is called a solution of the equation.
• Equations may have {0, 1, 2 … solutions.
}
}
![Page 22: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/22.jpg)
Solving Equations
• 3(2a + 25) - 2(a - 1) = 78
• 4(x - 7) = 2x + 12 + 2x
1 3 5 1 3772 4 6 4 6
x x x
![Page 23: Ch 1.1 Warm Up Problems Objectives: - understand/use properties & classifications of real numbers](https://reader036.vdocuments.us/reader036/viewer/2022062805/5697bfcf1a28abf838ca9de1/html5/thumbnails/23.jpg)
Solving Equations
• Solve: V = πr2h, for h
• Solve: de - 4f = 5g, for e