EVEREST EDUCATION MATHEMATICS - CHAPTER I.NUMBERS - I.1.Basic operations with numbers.HCD and LCM

Aug 25, 2026

Course guide focuses on preparing for international universities (WIUT, INHA, TTPU, YEOJU) through topic-based learning. The provided section covers arithmetic operations on numbers, including addition, subtraction, multiplication and division, and the computation of expressions using HCD (highest common divisor) and LCM (lowest common multiple). It explains key terms such as fractions, factors, primes, composites, divisibility rules, order of operations, and includes structured exercises with numeric evaluation and problem solving.

LanguageEnglish

CategoryExam

FormatPDF

Pages164

Reading Time6 h 53 min

AccessFree to download

CHAPTER I. NUMBERS

I.1. Basic operations with numbers.HCD and LCM

Terms

Learning Objectives

Natural numbers

Whole numbers

Integers

Order of operations

Number notation

Number Divisibility

Prime and composite numbers

Expressions involving fractions

Exercises

| EVEREST
EDUCATION
MATHEMATICS | | --- | Bu o`quv qo`llanma xalqaro mualliflar guruhi tomonidan yaratilgan.Hammamavzular oxirgi yillardagi imtihon savollariga ko`ra tuzilgan.Ushbu qo`llanmayordamida siz xalqaro universitetlarga(WIUT,INHA,TTPU,YEOJU)tayyorgarlik ko`rishingiz mumkin. -/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-1-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/ 3To yue6Hoe πocoome 6bIJIO CO3IaHo rpynoǔMexKTIyHapoIHbIX aBTopoB.BKa>KπOň Teme coπepxkMTCs psI BOIIpoCOB,KOTOpble 6bIJI B 9K3ameHax πOCJIeIHMX JeT.C πOMOIbIO 3Toro yueOHoro πocooM9 BbI MOkeTe roTOBITbCS K9K3ameHaM MeKIyHapoHbIX BY30B(WIUT,INHA,TTPU,YEOJU). -/-/-/-/-/-/-/-/-/-/-1-/-/-/-/-/-/-1-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-1-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/-/ This course guide was written by an international group of authors.All questionsare topic based.By learning it you can prepare and apply for internationaluniversities(WIUT,INHA,TTPU,YEOJU). Tashkent 2019 Like the crest of a peacock,so is mathematicsat the head of all knowledge.Indian Proverb # CHAPTER I.NUMBERS ## I.1.Basic operations with numbers.HCD and LCM # Terms 1.to add(subtract,multiply,divide)-qo'shmoq(ayirmoq,ko'paytirmoq,bo'lmoq)|cKnaAbIBaTb(Bbl4MTaTb,YMHOaTb,nenMTb); 2.to compute,to calculate,to work out-hisoblamoq|Bbl4NCnaTb; 3.a natural(whole,integer,rational,irrational,mixed,negative,positive,prime,composite)number-natural(nomanfiy butun,butun,ratsional,irratsional,aralash,manfiy,musbat,tub,murakkab)son |HaTypanbHoe(HeoTpuuatenbHoe uenoe,uenoe,pauMOHanbHoe,wppauMOHanbHoe,cMewaHHOe,OTpuuaTenbHoe,nonOKMTenbHoe,npocToe,cOCTaBHoe)qMcn0; 4.an ordinary(proper,improper,decimal)fraction-oddiy (to’g'ri,noto'g'ri,o'nli)kasr|o6blKHOBeHHag(npaBMnbHaa,HenpaBMnbHaa,necATMYHaa)Apo6b; 5.factor-ko'paytuvchi|MHOKMTenb; 6.prime factorizationtub ko'paytuvchilargaajratmoqlpa3n0KeHue Ha npOCTble MHOMTenn; 7.the highest(greatest)common divisor(HCD)-eng kattaumumiy bo'luvchi(EKUB)|Han6onbunǔo6unǔnennTenb(HOA); 8.the lowest(least)common multiple(LCM)-eng kichik umumiyko'paytuvchi(EKUK)|HanMeHbwee o6uee kpaTHoe(HOK); 9.numerator (denominator)-surat (mahraj)|4ncnMTenb(3HaMeHaTenb); 10.numerical expression-sonli ifoda|uucnoBoe BblpaxkeHne; 11.remainder-qoldiq|ocTaTOK; 12.to simplify-soddalashtirmoqlynpouaTb; 13.product-ko'paytma|npon3BeneHne. # Learning Objectives: -to have an understanding of arithmetic operations on numberssuch as addition,subtraction,multiplication and division; -to know how to compute expressions using the concepts of HCDand LCM. Natural numbers 1,2,3,4,5,...(Used for counting) # Whole numbers 0,1,2,3,4,.. Integers …,-2,-1,0,1,2,…. # Order of operations BEDMAS-brackets,exponents,division,multiplication,addition,subtraction. HCD (25,35)=5(5 is the largest number that divides both numberswithout remainder). LCM (25,35)=175(175 is the smallest number that can be dividedby both numbers without remainder). # Number notation 1.4 and 1,023,145(in American and British system)are written as 1,4and 1.023.145(in Uzbek,German and Russian system). Also,1.4 is pronounced as "one point four". # Number Divisibility For a number to be divisible by 2: the number must end with 0,2,4,6 or 8. 3: the sum of digits of the number must be divisible by 3. 4: the last two digits must be divisible by 4. 5. the number must end with 0 or 5. 6: the number must be divisible by both 2 and 3. 8: the last three digits must be divisible by 8. 9: the sum of digits must be divisible by 9. 10:the number must end with 0. 11:the difference between the sums of the digits at odd and evenplaces of the number is divisible by 11. 12:the number must be divisible by both 3 and 4. # Prime and composite numbers 2,3,5,7,11,13,17,19,23,...are prime(divisible by 1 and itself). 4,6,8,9,10,12,14,15,16,18,20,21,22,...are composite(divisible by anumber other than 1 and itself). # Expressions involving fractions 1)To ad

FAQs

What topics are covered in the section about basic operations with numbers?

It explains addition, subtraction, multiplication and division, then shows how to compute expressions using HCD and LCM.

How do HCD and LCM relate to common prime factors?

HCD is found using common prime factors in the smallest powers, while LCM uses common prime factors in the largest powers.

What are the key divisibility rules mentioned in the guide?

Rules cover divisibility by 2, 3, 4, 5, 6, 8, 9, 10, and 11, based on digit patterns such as the ending digits and sums of digits.

Aug 25, 2026

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