Aritmatika & Aljabar -...
Transcript of Aritmatika & Aljabar -...
![Page 1: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/1.jpg)
Matematika Industri I
Pengantar Aritmatika & Aljabar
Determinan
Matriks
Vektor
![Page 2: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/2.jpg)
![Page 3: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/3.jpg)
Numerals & places value
• 0,1,2,3,4,5,6,7,8,9
• 246 -> 2 hundreds 4 tens 6 units -> 200+40+6
Points on a line and order
First natural number
8>56<7
![Page 4: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/4.jpg)
-5 < 4
-2 > -4
-1 < 0
![Page 5: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/5.jpg)
Bracket
• Addition and subtraction
• What is the value of?
8 + (-3) = ….
9 - (-6) = ….
(-4) + (-8) = ….
(-14) - (-7) = ….
![Page 6: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/6.jpg)
Bracket
• Multiplication and division
12 x 2 = 24 & (-12) x (-2) = 24
12 : 2 = 6 & (-12) : (-2) = -2
What is the value of :
(-5) x 3 = ….
12 : (-6) = ….
(-2) x (-8) = ….
(-14) : (-7) = ….
![Page 7: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/7.jpg)
Bracket & Presedence Rule
![Page 8: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/8.jpg)
Bracket & Presedence Rule
![Page 9: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/9.jpg)
1. Commutativity
2. Associativity
![Page 10: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/10.jpg)
3. Distributivity
Distributed from the right but not from the left
![Page 11: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/11.jpg)
Factors Prime Factorization126 = ….?
![Page 12: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/12.jpg)
![Page 13: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/13.jpg)
Ex. 3
7
Proper
Ex. 12
7
Improper
Ex. 62
3
Mixed
![Page 14: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/14.jpg)
Multiplying Fraction
Equivalent Fraction
![Page 15: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/15.jpg)
Dividing Fractions
![Page 16: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/16.jpg)
Adding & Subtracting Fraction
![Page 17: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/17.jpg)
Powers
The Laws of Powers
![Page 18: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/18.jpg)
The Laws of Powers
![Page 19: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/19.jpg)
The Laws of Powers
![Page 20: Aritmatika & Aljabar - miftakhurrizal.lecture.ub.ac.idmiftakhurrizal.lecture.ub.ac.id/files/2017/09/Aritmatika-Aljabar.pdf · 3. Distributivity Distributed from the right but not](https://reader030.fdocuments.us/reader030/viewer/2022041123/5d20820f88c993ec448d3486/html5/thumbnails/20.jpg)
n x mnm
n
n
n
nn
n-m
n
m
nmnm
a a .5
b
a
b
a .4
a.b b . a .3
a a
a 2.
a a x a .1
n
n
1n
1 -
n-
n
nnn
n
m
n m
0
a
1 a .10
a a
1 .9
a.b b . a .8
a a 7.
1 a .6
The Laws of Powers