The naturall numbers

Stella Seremetaki

www.mathschool-online.comContentsGeneral Repetitive Themes.......................................................................... 1Key Stage 3,4 ................................................................................................ 2The natural numbers ................................................................................. 2Ι) Write the partition capacity multiplication in addition andsubtraction. ................................................................................................. 2ΙΙ) Make partitioning operations............................................................... 2Ι) Write the identity of the Euclidean division ........................................ 2II) When do we say that the Euclidean division is perfect? ................... 2I) What is the priority of the actions? ....................................................... 3II) Make things happen.............................................................................. 3I) What do we call minimum common multiple and what two-digitmax common divider? ............................................................................... 3II) To find the minimum common multiple and max common dividerof the numbers ............................................................................................. 3III) a) Number 5 is the first and why? ..................................................... 3b) The Max Common Divider (2,7) = 1.What are the numbers 2 and 7?...................................................................................................................... 4I) What are the criteria of divisibility? .................................................... 4II) Find the dividers of the numbers ........................................................ 4Answers ......................................................................................................... 4Distributive property ................................................................................... 4Ι) α.(β+γ)=α.β+α.γ .......................................................................................... 4D is called divisible, divisor, quotient, and remainder......................... 5II) The Euclidean division is perfect WHEN.............................................. 5υ=0................................................................................................................. 5so the Euclidean identity is written.......................................................... 5The priority of the actions is ...................................................................... 6Forces → Multiplications and divisions → Insertions and deductions. 6II) Τhe minimum common multiple......................................................... 7III) The maximum common divisor ......................................................... 7I) The criteria of divisibility: ..................................................................... 8 1

General Repetitive Themes Key Stage 3,4 The natural numbers Ι) Write the partitioncapacity multiplication in addition and subtraction. ΙΙ) Make partitioning operations a) 2.(a+b)= b) 4.(a+1)= c) 2.(a-b)= d) 2.(2+1)= Ι) Write the identity of the Euclidean division II) When do we say that the Euclidean division is perfect? www.mathschool-online.com 2

www.mathschool-online.com III) Which of the following equations express Euclidean division? α) 120=28.4+8, β) 1345=59.21+10 1. What is the priority of the actions? II) Make things happen α) 22-2.2+ (3+1)= β) (22-2.2).2+ 1=1. I) What do we call minimum common multiple and what two-digit max common divider? II) To find the minimum commonmultiple and max common divider of the numbers 2,6 III) a) Is number 5 a prime number and why ? www.mathschool-online.com 3

www.mathschool-online.com b) The Max Common Divider (2,7) =1.What are the max common divider of the numbers 2 and 7?I) What are the criteria of divisibility? II) Find the dividers of the numbers α) 222, β) 200, γ) 255, δ) 112 Answers Distributive propertyΙ) α.(β+γ)=α.β+α.γ , α.(β-γ)=α.β-α.γ α)2.(α+β)=2.α+2.β β)4.(α+1)=4.α+4.1=4.α+4 c) 2.(2-1)=2.2-2.1=4-2=2 d) 3.(3+2)=3.3+3.2=9+6=15 www.mathschool-online.com 4

www.mathschool-online.com D=δ.π+υ , 0≤υ≤δ D is called divisible, divisor, quotient, and remainder.II) The Euclidean division is perfect WHEN the rest of the division is zero υ=0 so the Euclidean identity is written D=δ.πΙΙΙ) α)120=28.4+8υ=8<28, the rest of the division and 28=δ is 28.That is, the balance u=28less than the divisor δ which isSo a) expresses the Euclidean division.www.mathschool-online.com 5

www.mathschool-online.com β) 1345=59.21+106, υ=106>59, υ=106 > 21That is, the balance u = 106 is greaterthan 59 and from 21Therefore, b) does not express theEuclidean divisionThe priority of the actions is Forces → Multiplications and divisions → Insertions and deductions II) α) 22-2.2+ (3+1)=4- 4+4=0+4=4 β) (22-2.2).2+ 1=(4-4).2+1= 0.2+1=0+1=1 www.mathschool-online.com 6

www.mathschool-online.com1. I) The smallest of the common multiple of two numbers is called minimum common multiple2. ΙΙ) The largest of the common divisors having two numbers is called MCD (maximum common divisor) II) Τhe minimum common multiple III) The maximum common divisor 2,6 MCM=6 MCD=2 ΙΙΙ) α) Number 5 is the first because it is divided by itself and the unit. www.mathschool-online.com 7

www.mathschool-online.com β) Ο ΜCD (2,7) = 1.Numbers 2 and 7 are called first amongthem I) The criteria of divisibility: A physical number is divided by 2 if it ends at 0,2,4,6,8 with 5 if it ends at 0, 5 with 3 or 9 if the sum of its digits is divided by 3 or 9 www.mathschool-online.com 8

www.mathschool-online.com eg, 36 is divided by 3 and 9,because 36: 3 + 6 = 9 which is divided by both 3 and 9 II) Find the dividers of the numbersa) 222, b) 200, c) 255, d) 112 we have got:22 2 3 220 10 2 5 0025 3 5 5112 2 4If you have any questions contact mathschool-online!www.mathschool-online.com 9