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Numbers Presentation

Transcript: PROPERTIES OF NUMBER SYSTEMS MELIS EROL ECE TETIK MEHMET EMIR KACAN In mathematics, numbers are divided into groups. These sets are described with special names and symbols. SETS OF NUMBERS 1 Explanation: Whole numbers and counting numbers make up natural numbers. Natural numbers start with zero and contains no fractions or negative numbers. Note: Whole Numbers: (0,1,2,3...) Counting Numbers: (1,2,3,4...) So natural numbers start with zero and contains no fractions. Symbol: N Natural Numbers (N) N Explanation: Natural numbers, their negatives and zero make up integers. (...-3,-2,-1,0,1,2,3...) Symbol: Z INTEGERS (Z) Z RATIONAL NUMBERS (Q) Q Symbol: Q Explanation: Rational numbers are numbers that can be written as c/d where c and d are integers and d is not equal to zero. Symbol: R Explanation: Real numbers are made up of N, Z and Q. REAL NUMBERS (R) R Explanation: A Complex Number is a number that is a combination of Real and Imaginary Numbers Symbol: C COMPLEX NUMBERS (C) C Sets of Numbers Picture Structure With Examples Deeper Information Structure 2 There are four basic properties of numbers: commutative, associative, distributive, and identity. There are other properties as well. For instance: closure property, zero product... PROPERTIES 2 Closure example a+b is real 4 + 5 = 9 is real a×b is real 7 × 2 = 14 is real Closure Property CLOSURE Commutative example a + b = b + a 4 + 6 = 6 + 4 ab = ba 4 × 2 = 2 × 4 COMMUTATIVE COMMUTATIVE Associative example (a + b) + c = a + ( b + c ) (1 + 6) + 3 = 1 + (6 + 3) (ab)c = a(bc) (4 × 2) × 5 = 4 × (2 × 5) ASSOCIATIVE ASSOCIATIVE Distributive example a × (b + c) = ab + ac 3 × (6+2) = 3 × 6 + 3 × 2 (b+c) × a = ba + ca (6+2) × 3 = 6 × 3 + 2 × 3 DISTRIBUTIVE DISTRIBUTIVE Identity example a + 0 = a 6 + 0 = 6 a × 1 = a 6 × 1 = 6 IDENTITY IDENTITY Zero Product If ab = 0 then a=0 or b=0, or both example a × 0 = 0 × a = 0 5 × 0 = 0 × 5 = 0 ZERO PRODUCT ZERO PRODUCT 3+4 = 7 4+3 = 7 2x6 = 12 6x2 = 12 2+(4+3) = 4+(3+2) = 2 (3+1) =2x3+2x1 6.1 =6 999.1 =999 4 + 0 = 4 5.0 = 0 987.0 = 0 EXERCISES 3 Commutative P. of Addition Commutative P. of Multiplication Associative Property Distributive property Multiplicative Identity Additive Identity Zero product P. VIDEO VIDEO https://www.mathsisfun.com/whole-numbers.html http://thinkzone.wlonk.com/Numbers/NumberSets.htm https://whatis.techtarget.com/definition/natural-number Google Images Math is Fun (Images) https://www.mathsisfun.com/sets/real-number-properties.html https://www.mathsisfun.com/sets/number-types.html UAA Course Materials REFERENCES 4 THANK YOU FOR LISTENING! THE END

Numbers Presentation

Transcript: Separation The Return Phase III Road of Trials Supernatural Aid Guide/Mentor Spider and Jem are close friends since they have had to deal with their troubles together. Their friendship formed in a very short amount of time. Spider was with Jem through many hardships and helped her after they ran away together. Spider thought about Jem also, and not just himself. Jem makes friends along the way of the journey. Even though she doesn't know these people, they help her by letting her stay in their home or place of work, and by giving her food. These few people helped Jem after Spider had been taken away. Amy Klezek Journey Map Numbers By: Rachel Ward Belly of the Whale Initiation Jem's threshold is getting along without Spider. Jem has been on her own for her whole life, being a foster child and never having many friends or father figures to look up to. Without Spider though, she doesn't know how to get through these new circumstances alone. Without Spider, Jem has trouble with knowing what to do. This is where her new companions come in play to help her. The police were constantly trying to take Jem and Spider into custody since they had run away from their homes. They succeeded in taking Spider, but Jem figured her way out of it with the aid of companions and by being smart with her actions. Jem never really had a place to call home because she has been in foster care almost her entire life. The only motherly figure that she has is her foster mom, Karen. After Spider's death, Jem and Karen live at home in London with Jem's son, Adam. Jem had to become Karen's mother figure about five years later when Karen has multiple strokes. After Karen dies, Jem settles with Adam in Weston, where Spider had always wanted to be. Call to Adventure Crossing the Return Threshold Phase I Jem goes through many tough events in her journey. There are many challenges she faces in a very short amount of time. Some of these challenges effect her ability to continue on to her destination of Weston. Some of these challenges included Jem tripping onto barbed wire, twisting her ankle, and running out of food very quickly. There were also even worse challenges, such as figuring out where they could sleep, trying not to be recognizable to the police, Jem saving Spider from drowning, running from the police, and when Spider was eventually taken into custody by the police. These were all challenges that Jem faced with Spider, and sometimes without him. Battle Jem faces an internal conflict when it gets later and later in the day of Spider's death. She thinks a lot about what everyone is asking her, telling her, and saying about her. She comes to the conclusion that if no one can see the numbers, they might as well not exist. She thinks the only way to get rid of the numbers is to kill herself, since she is the only one who sees them. It makes sense to her that if she kills herself, she could save Spider and all the other people that she has met or is close to. Threshold Guardians Crossing the Threshold Phase II Jem has always seen numbers when she made eye contact with people. She didn't know what they were until the day her mother died, they were death dates. Jem thought that she could possibly help people by knowing the date they would die, and keep them out of harms way. She thought that the system of fate and dying could be cheated by making yourself or someone else die sooner. Jem had kept her secret of being able to see a person's death date for 15 years. She was always scared to tell someone, but when she finally does, it comes more naturally to tell more people. Once she had told just a select few, she still didn't feel completely comfortable with the entire world knowing her story. There is no guide or mentor to help Jem along the way of her journey, with and without Spider. The only person that knows how Jem really feels and can relate to her is Val, Spider's grandmother. Val is not present during her journey, so she doesn't guide her along the way. Companions

Concrete Numbers (Free Template)

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