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- https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/04%3A_Introduction_to_Fractions_and_Multiplication_and_Division_of_Fractions/4.04%3A_Multiplication_of_Fractions\(\begin{array} {rcl} {\dfrac{11}{8} \cdot 4 \dfrac{1}{2} \cdot 3 \dfrac{1}{8}} & = & {\dfrac{11}{8} \cdot \dfrac{39}{\begin{array} {c} {\cancel{2}} \\ ...118⋅412⋅318=118⋅3921⋅51031=11⋅3⋅58⋅1⋅1=1658=2058
- https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/03%3A_Exponents_Roots_and_Factorization_of_Whole_Numbers/3.03%3A_Prime_Factorization_of_Natural_NumbersNow, using our knowledge of division, we can see that a first number is a factor of a second number if the first number divides into the second number a whole number of times (without a remainder). No...Now, using our knowledge of division, we can see that a first number is a factor of a second number if the first number divides into the second number a whole number of times (without a remainder). Notice that the whole number 1 is not considered to be a prime number, and the whole number 2 is the first prime and the only even prime number.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/An_Introduction_to_Number_Theory_(Veerman)These notes are intended for a graduate course in Number Theory. No prior familiarity with number theory is assumed. Chapters 1-6 represent approximately 1 trimester of the course. Eventually we inten...These notes are intended for a graduate course in Number Theory. No prior familiarity with number theory is assumed. Chapters 1-6 represent approximately 1 trimester of the course. Eventually we intend to publish a full year (3 trimesters) course on number theory.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Elementary_Number_Theory_(Raji)The notes contain a useful introduction to important topics that need to be addressed in a course in number theory. Proofs of basic theorems are presented in an interesting and comprehensive way that ...The notes contain a useful introduction to important topics that need to be addressed in a course in number theory. Proofs of basic theorems are presented in an interesting and comprehensive way that can be read and understood even by non-majors with the exception in the last three chapters where a background in analysis, measure theory and abstract algebra is required. The exercises are carefully chosen to broaden the understanding of the concepts.
- https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/08%3A_Techniques_of_Estimation/8.05%3A_Summary_of_Key_ConceptsEstimation is the process of determining an expected value of a computation. The rounding technique estimates the result of a computation by rounding the numbers involved in the computation to one or ...Estimation is the process of determining an expected value of a computation. The rounding technique estimates the result of a computation by rounding the numbers involved in the computation to one or two nonzero digits. The clustering technique of estimation can be used when The distributive property is a characteristic of numbers that involves both addition and multiplication. The distributive property can be used to obtain exact results for a multiplication.
- https://math.libretexts.org/Courses/SUNY_Schenectady_County_Community_College/Discrete_Structures/08%3A_Topics_in_Number_TheoryThumbnail: Golden spiral. Assuming a square has the side length of 1, the next smaller square is 1/φ wide. Then a width of 1/φ², 1/φ³ and so on. (Public Domain; Jahobr).
- https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/04%3A_Introduction_to_Fractions_and_Multiplication_and_Division_of_Fractions/4.05%3A_Division_of_Fractions\(\dfrac{17}{82} \cdot \dfrac{1520}...1782⋅1520213113357=1⋅1⋅12⋅1⋅7=114
- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Book%3A_Mathematical_Reasoning__Writing_and_Proof_(Sundstrom)/08%3A_Topics_in_Number_TheoryThumbnail: Golden spiral. Assuming a square has the side length of 1, the next smaller square is 1/φ wide. Then a width of 1/φ², 1/φ³ and so on. (Public Domain; Jahobr).
