If n is a natural number / Agar n natural son bo'lsa:
xn - yn = (x - y)(xn-1 + xn-2y +...+ yn-2x + yn-1)
If n is even (n = 2k) / Agar n juft son bo'lsa (n= 2k) :
xn + yn = (x + y)(xn-1 - xn-2y +...+ yn-2x - yn-1)
If n is odd (n = 2k + 1) / Agar n toq son bo'lsa (n=2k+1) :
xn + yn = (x + y)(xn-1 - xn-2y +...- yn-2x + yn-1)
@Math_Emperor
xn - yn = (x - y)(xn-1 + xn-2y +...+ yn-2x + yn-1)
If n is even (n = 2k) / Agar n juft son bo'lsa (n= 2k) :
xn + yn = (x + y)(xn-1 - xn-2y +...+ yn-2x - yn-1)
If n is odd (n = 2k + 1) / Agar n toq son bo'lsa (n=2k+1) :
xn + yn = (x + y)(xn-1 - xn-2y +...- yn-2x + yn-1)
@Math_Emperor
Hello everyone. What's up? I have a great news for you. From today i am going to share useful materials and vocabulary for international universities in Tashkent! / Hammaga salom. Yaxshimisizlar? Siz uchun ajoyib yangilik bor. Bugundan boshlab men Toshkentdagi xalqaro universitetlarning matematika fanidan bo'lib o;tadigan imtihon uchun foydali materiallar va so'z boyliklari bilan ulashmoqchiman!
@Math_Emperor
@Math_Emperor
Theme : Basic operations with numbers, HCD and LCM
Terms
To add - qo'shmoq,
To subtract - ayirmoq,
To multiply - ko'paytirmoq,
To divide - bo'lmoq,
To compute = to calculate = to work out - hisoblamoq
A natural number - natural son,
Whole number - nomanfiy butun son,
Integer number - butun son,
Rational number - ratsional son,
Irrational number - irratsional son,
Mixed number - aralash sonlar, Negative number - manfiy son, Positive number - musbat son,
Prime number - tub son,
Composite number- murakkab son
@Math_Emperor
Terms
To add - qo'shmoq,
To subtract - ayirmoq,
To multiply - ko'paytirmoq,
To divide - bo'lmoq,
To compute = to calculate = to work out - hisoblamoq
A natural number - natural son,
Whole number - nomanfiy butun son,
Integer number - butun son,
Rational number - ratsional son,
Irrational number - irratsional son,
Mixed number - aralash sonlar, Negative number - manfiy son, Positive number - musbat son,
Prime number - tub son,
Composite number- murakkab son
@Math_Emperor
Continue of terms / terminlarni davomi
An ordinary fraction - oddiy kasr,
Proper fraction - to'g'ri kasr,
Improper fraction - noto'g'ri kasr, Decimal fraction - o'nli kasr,
Factor-ko'paytuvchi,
Prime factorization - tub koʻpaytuvchilarga ajratmoq
The highest (greatest) common divisor (HCD) - katta eng umumiy bo'luvchi (EKUB)
The lowest (least) common multiply (LCM) - eng kichik umumiy karrali (EKUK)
@Math_Emperor
An ordinary fraction - oddiy kasr,
Proper fraction - to'g'ri kasr,
Improper fraction - noto'g'ri kasr, Decimal fraction - o'nli kasr,
Factor-ko'paytuvchi,
Prime factorization - tub koʻpaytuvchilarga ajratmoq
The highest (greatest) common divisor (HCD) - katta eng umumiy bo'luvchi (EKUB)
The lowest (least) common multiply (LCM) - eng kichik umumiy karrali (EKUK)
@Math_Emperor
Learning terms / terminlarni yodlash
Natural numbers
1, 2, 3, 4, 5, 6, 7, ... ( used for counting / sanash uchun ishlatiladigan)
Whole numbers
0, 1, 2, 3, 4, 5, 6, 7, ...
Integers numbers
-3, -2, -1, 0, 1, 2, 3
Rational numbers
m/n (m = integers, n= natural) such as 7/11, 1/2, -4/5
Irrational numbers
√m such as √2, √5, √24,
Negative numbers
-1 -2 -3 ... -n (n= natural numbers)
Positive numbers
1 2 3 4 ... n (n= natural numbers)
Prime numbers
2 3 5 7 11
@Math_Emperor
Natural numbers
1, 2, 3, 4, 5, 6, 7, ... ( used for counting / sanash uchun ishlatiladigan)
Whole numbers
0, 1, 2, 3, 4, 5, 6, 7, ...
Integers numbers
-3, -2, -1, 0, 1, 2, 3
Rational numbers
m/n (m = integers, n= natural) such as 7/11, 1/2, -4/5
Irrational numbers
√m such as √2, √5, √24,
Negative numbers
-1 -2 -3 ... -n (n= natural numbers)
Positive numbers
1 2 3 4 ... n (n= natural numbers)
Prime numbers
2 3 5 7 11
@Math_Emperor
Number Divisibility / Sonlarning bo'linishi
For a number to be divisible by
2: the number must end with / raqamlarning oxiri 2 bilan tugashi kerak 0, 2, 4, 6, 8,
3: the sum of digits of the mumber must be divisible by 3 / raqamlar yig'indisi 3 ga bo'linishi kerak
4: the last twro digits must be divisibie by 4 or must end 00/ raqamning eng oxirgi ikkita raqami 4 ga bo'linishi kerak yoki 00 bilan tugashi kerak.
5. the number must end with O or 5 / raqamning eng oxiri 0 yoki 5 bilan tugashi kerak
6: the number must be divisible by both 2 and 3 / raqam bir vaqtni ozida 2 va 3 ga bo'linishi kerak.
8: the last three digits must be divisibie by 8 / sonning eng oxirgi uchta raqami 8 ga bo'linishi kerak.
9: the sum of digits must be divisible by 9 / sonning raqamlar yig'indisi 9ga bo'linishi kerak.
10: the number must end with O / son 0 raqami bilan tugashi kerak.
11: the difference between the sums of the digits at odd and even places of the number is divisibie by 11 / raqamning toq va juft joylaridagi yig'indilar orasidagi farq 11 ga karrali bo'linadi
12: the number must be divisible by both 3 and 4 / raqam bir vaqtni ozida 3 va 4 ga bo'linishi kerak.
@Math_Emperor
For a number to be divisible by
2: the number must end with / raqamlarning oxiri 2 bilan tugashi kerak 0, 2, 4, 6, 8,
3: the sum of digits of the mumber must be divisible by 3 / raqamlar yig'indisi 3 ga bo'linishi kerak
4: the last twro digits must be divisibie by 4 or must end 00/ raqamning eng oxirgi ikkita raqami 4 ga bo'linishi kerak yoki 00 bilan tugashi kerak.
5. the number must end with O or 5 / raqamning eng oxiri 0 yoki 5 bilan tugashi kerak
6: the number must be divisible by both 2 and 3 / raqam bir vaqtni ozida 2 va 3 ga bo'linishi kerak.
8: the last three digits must be divisibie by 8 / sonning eng oxirgi uchta raqami 8 ga bo'linishi kerak.
9: the sum of digits must be divisible by 9 / sonning raqamlar yig'indisi 9ga bo'linishi kerak.
10: the number must end with O / son 0 raqami bilan tugashi kerak.
11: the difference between the sums of the digits at odd and even places of the number is divisibie by 11 / raqamning toq va juft joylaridagi yig'indilar orasidagi farq 11 ga karrali bo'linadi
12: the number must be divisible by both 3 and 4 / raqam bir vaqtni ozida 3 va 4 ga bo'linishi kerak.
@Math_Emperor
Prime and compaostte number:
2, 3, 5, 7, 11, 18, 17, 19, 23, ... are prime (divisible by 1 and Itself / oziga va 1 ga bo'linadigan sonlar).
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, ... are composite (divisible by a number other than 1 and itself / ozidan va 1 dan boshqa sonlarga bolinadigan son).
@Math_Emperor
2, 3, 5, 7, 11, 18, 17, 19, 23, ... are prime (divisible by 1 and Itself / oziga va 1 ga bo'linadigan sonlar).
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, ... are composite (divisible by a number other than 1 and itself / ozidan va 1 dan boshqa sonlarga bolinadigan son).
@Math_Emperor
Forwarded from Math academy official posts
Do prime facorization of the number 462000
Anonymous Quiz
46%
2×2×2×2×3×5×5×5×7×11
35%
2×2×2×2×2×3×3×5×5×11
19%
2×2×2×3×3×3×5×13
@Math_Emperor congratulates all teachers of the world
No matter how old we grow, the lessons taught by our teachers can never be forgotten. They build the foundation for our moral values and nurture children with their love and care. This Teachers day, tell your lovable teachers how much you adore them. Feel proud and honoured to celebrate Teacher’s day.
Happy Teachers Day!!!
No matter how old we grow, the lessons taught by our teachers can never be forgotten. They build the foundation for our moral values and nurture children with their love and care. This Teachers day, tell your lovable teachers how much you adore them. Feel proud and honoured to celebrate Teacher’s day.
Happy Teachers Day!!!
💐💐💐💐💐💐💐💐💐💐
Sizgadir yurakda asragan so'zim,
Тo mangu ta'zimda turaman o'zim.
Dilimning tubida yangragan sozim —
Ezgulik yo'lida tolmang, Ustozim!
G'am ko'rmay bu dunyo turguncha turing,
Ming yillik mehnatlar huzurin ko'ring,
Shogirdlar baxtidan shod, masrur yuring,
Ezgulik yo'lida tolmang, Ustozim!
Hayot yo'llarimda dildosh, deb bildim,
Yo'limni yoritgan quyosh, deb bildim,
Тole yo'llarida yo'ldosh, deb bildim,
Ezgulik yo'lida tolmang, Ustozim!
@Math_emperor
Sizgadir yurakda asragan so'zim,
Тo mangu ta'zimda turaman o'zim.
Dilimning tubida yangragan sozim —
Ezgulik yo'lida tolmang, Ustozim!
G'am ko'rmay bu dunyo turguncha turing,
Ming yillik mehnatlar huzurin ko'ring,
Shogirdlar baxtidan shod, masrur yuring,
Ezgulik yo'lida tolmang, Ustozim!
Hayot yo'llarimda dildosh, deb bildim,
Yo'limni yoritgan quyosh, deb bildim,
Тole yo'llarida yo'ldosh, deb bildim,
Ezgulik yo'lida tolmang, Ustozim!
@Math_emperor
Math academy || Official pinned «@Math_Emperor congratulates all teachers of the world No matter how old we grow, the lessons taught by our teachers can never be forgotten. They build the foundation for our moral values and nurture children with their love and care. This Teachers day, tell…»
Find the L.C.M. of the following by listing their multiples.
(i) 5, 10, 15
(ii) 4, 10, 12
(iii) 3, 9, 12
(iv) 2, 8, 10
(v) 7, 14, 21
(vi) 10, 20, 25
Then send your answers @MathEmperor_bot
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(i) 5, 10, 15
(ii) 4, 10, 12
(iii) 3, 9, 12
(iv) 2, 8, 10
(v) 7, 14, 21
(vi) 10, 20, 25
Then send your answers @MathEmperor_bot
Checking servise is free. Don't shy feel free and just send
@Math_emperor