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- https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/05%3A_Addition_and_Subtraction_of_Fractions_Comparing_Fractions_and_Complex_Fractions/5.09%3A_Proficiency_ExamExercise \PageIndex1 715⋅2021+59 311+511 18+34178 \(4 \dfrac{5}{16} + 1 \dfrac{...Exercise \PageIndex1 715⋅2021+59 311+511 18+34178 4516+113−2524 518⋅(1516−38) 58,79 Exercise \PageIndex17 11516,11512 1932,916,58 916,1932,58
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Combinatorics_Through_Guided_Discovery_(Bogart)/06%3A_Groups_Acting_on_Sets/6.01%3A_Permutation_GroupsUntil now we have thought of permutations mostly as ways of listing the elements of a set. In this chapter we will find it very useful to think of permutations as functions. This will help us in using...Until now we have thought of permutations mostly as ways of listing the elements of a set. In this chapter we will find it very useful to think of permutations as functions. This will help us in using permutations to solve enumeration problems that cannot be solved by the quotient principle because they involve counting the blocks of a partition in which the blocks don’t have the same size.
- https://math.libretexts.org/Bookshelves/Mathematical_Logic_and_Proof/Gentle_Introduction_to_the_Art_of_Mathematics_(Fields)/08%3A_Cardinality/8.01%3A_Equivalent_SetsWe have seen several interesting examples of equivalence relations already, and in this section we will explore one more: we’ll say two sets are equivalent if they have the same number of elements. Us...We have seen several interesting examples of equivalence relations already, and in this section we will explore one more: we’ll say two sets are equivalent if they have the same number of elements. Usually, an equivalence relation has the effect that it highlights one characteristic of the objects being studied, while ignoring all the others. Equivalence of sets brings the issue of size (a.k.a. cardinality) into sharp focus while forgetting all about the many other features of sets.
- 4.3: Equivalent Fractions, Reducing Fractions to Lowest Terms, and Raising Fractions to Higher Termshttps://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/04%3A_Introduction_to_Fractions_and_Multiplication_and_Division_of_Fractions/4.03%3A_Equivalent_Fractions_Reducing_Fractions_to_Lowest_Terms_and_Raising_Fractions_to_Higher_TermsThe product of the remaining factors in the numerator and the product of remaining factors of the denominator are relatively prime, and this fraction is reduced to lowest terms.