number & algebra review (with your built-in calculator!) by mr. barnard
TRANSCRIPT
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NUMBER & ALGEBRA REVIEW
NUMBER & ALGEBRA REVIEW
(With your built-in calculator!)
By Mr. Barnard
![Page 3: NUMBER & ALGEBRA REVIEW (With your built-in calculator!) By Mr. Barnard](https://reader037.vdocuments.mx/reader037/viewer/2022110303/5517935455034645368b56e4/html5/thumbnails/3.jpg)
Number Types
Whole Numbers (0, 1, 2, 3,…)
Integers (…, -2, -1, 0, 1, 2, …)
Decimals (…,-1.9, 0.8, …) Rational (…,-1 4/7, 1/5, …)
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We will:
Simplify numerical operations
Correctly use order of operations
Simplifying algebraic expressions
(ALL WITHOUT A CALCULATOR)
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Expressions
Statements without an equals sign.
Simplifying an expression means to combine “like” terms.
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Answers to expressions include:
Addition Sum Subtraction Difference Multiplication Product Division Quotient
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Algebraic Expressions
4x - 9
Variable
ConstantCoefficient
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Whole Number Operations
30 + 80 = ?Think 3 +
8!110Think 12 -
4!80
120 - 40 = ?
65 + 97 = ?Think 60 + 90!162
142 – 57 = ?Think 13 - 5!
85Think 12 -
7!Think 5 + 7!
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More Whole Number Operations
82x3
246 324360
36x19
684
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Even More Whole Number Operations
142837 -14 0
-28 03
2 0 4 0
2 8
7
3
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Whole Number Practice
A.70 + 40
B. 180 – 130
C. 110 + 40
D.150 – 90
E. 84 + 97
F. 125 - 86
A.110
B. 50
C. 150
D.60
E. 181
F. 39
ANSWERS>>>
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Whole Number Practice
G.90 x 4
H.180 6
I. 36 x 9
J. 312 7
K.30 x 9
L. 413 4
ANSWERS>>>
7
4
G. 360H. 30
I. 324
J. 44
K. 270L. 103
4
1
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Integer Operations
-19 + 245
-11 - 18THINK -11 + -18
-29
90 x -7-630
-3500 -7050
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Integer Practice M.-18 + -39
N.-40 - -65
O.12 x - 6
P. -240 -60
M.-57
N.25
O.-72
P. 4
ANSWERS>>>
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Decimal Operations
3.8 + 11.29 = ?15.09
-0.7 - -2.39 = ?THINK -0.7 +
2.391.69
225250
-2.5x 0.19
-0.475
3.60.8 4.
-32 4
0
0
5
-40 0
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Decimal Practice Q.-2.91 + -
32.4
R.6.7 - 0.32
S. 4.4 x 0.3
T. -22.5 0.05
Q.-35.31
R.6.38
S. 1.32
T. -450
ANSWERS>>>
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Rational Operations
3
23
4
32
12
83
12
92
12
56
12
175
4
18
2
12
2
12
4
18 THINK
4
22
4
18
4
22
4
57
4
35
7+4
4
35
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More Rational Operations
3
13
8
3
8
3
2
14
3
10
8
3
3
10
8
3
1
14
5
4
11
4
5
3
8
2
9
3
1
4
1
=12
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Rational Practice
4
33
6
51
ANSWERS>>>
4
34
8
15
3
12
8
11
4
32
8
5
12
75
8
3
8
52
22
5
U.
V.
W.
X.
U.
V.
W.
X.
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Simplifying Expressions
7 + 3 8 ÷ 4 – 97 + 6 – 9
4
2 – 3(4 + 1)2 – 3 52 – 15-13
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More Simplifying Expressions
3x + 5x – 88x - 8
9x +10y - x8x + 10y
3 – 5(2x – 4)3 – 10x + 20
-10x + 23
(x – 3)(2x + 4)2x2 -6x + 4x - 122x2 -2x - 12
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Tools to Help You Simplify Algebraic Expressions!
What is the formula for the area of a rectangle? L
W
AREA = LW
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(x + 3)(x + 5) x +3
x x2 3x
+5 5x 15
Combine like terms!!!
x2 + 8x + 15
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Algebra Tiles
x
x x2 x
1
x
11 1
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(x + 3)(x + 2) x
x
11
1 1 1
?
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(x + 3)(x + 2) x
x
11
1 1 1
x2 x x x
x
x1 1 11 1 1
x2
5x
6
+
+
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Use tiles and/or area method!
(x + 4)(x + 1)
(2x + 1)(x + 2)
(x + 5)(x + 2)
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Use tiles to answer this question:
Is (x + 3)2 = x2 + 32 ?
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Simplifying Rational Expressions
10x + 86
5x + 43
5
3
4 15x2 + 7x
5x
2x2 + 6xx2 + 5x +
615x + 75
2x(x + 3)(x + 2)(x +
3)2xx + 2
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Simplifying Practice Y. -2 + 5 3 – 8 4
Z. 5x - 2(3x – 4)
AA.(3x – 1)(5x +
2)
AB. 6x2 – 14x
10x
Y. 11
Z. -x + 8
AA. 15x2 + x - 2
AB. 3x – 7
5 ANSWERS>>>
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It is expected that YOU can independently complete all of the previous numeric and algebraic examples without a calculator. If you are able
to, GREAT!, as you will be able to really focus on
Geometry this year!!! Seek immediate help if you are unable to perform these
necessary ideas!
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YOUR FIRST PRACTICE!
BE ABLE TO COMPLETE PROBLEMS WITHOUT A CALCULATOR
CHECK YOUR WORK WITH EACH OTHER, WITH A CALCULATOR, OR
WITH THE ONLINE TOOLS!
WE’LL DISCUSS THE PRACTICE AT THE END OF THIS LESSON…BE READY FOR
THE CONCEPT QUIZ!!!