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- https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/10%3A_Signed_Numbers/10.04%3A_Addition_of_Signed_NumbersAlso, notice that the sign of the number with the larger absolute value is negative and that the sign of the resulting sum is negative. Addition of numbers with unlike signs: To add two real numbers t...Also, notice that the sign of the number with the larger absolute value is negative and that the sign of the resulting sum is negative. Addition of numbers with unlike signs: To add two real numbers that have unlike signs, subtract the smaller absolute value from the larger absolute value and associate with this difference the sign of the number with the larger absolute value.
- 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)/04%3A_Introduction_to_Fractions_and_Multiplication_and_Division_of_Fractions/4.06%3A_Applications_Involving_Fractions\(\begin{array} {rcl} {M = \dfrac{9}{4} \div \dfrac{3}{8} = \dfrac{9}{4} \cdot \dfrac{8}{3}} & = & {\dfrac{39}{\begin{array} {c} {\cancel{4}} \\ {^1} \e...M=94÷38=94⋅83=3941⋅2831=3⋅21⋅1=6
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/02%3A_Logic/2.01%3A_Formal_LogicThis page defines statements and distinguishes them from non-statements, introduces logic operations and truth tables for combining statements, and explains equivalence of statements using DeMorgan's ...This page defines statements and distinguishes them from non-statements, introduces logic operations and truth tables for combining statements, and explains equivalence of statements using DeMorgan's Laws. It highlights conditions for compound statements to be false and includes practice checklists for truth tables and equivalence inquiries from previous exercises.
- https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/05%3A_Addition_and_Subtraction_of_Fractions_Comparing_Fractions_and_Complex_Fractions/5.03%3A_Addition_and_Subtraction_of_Mixed_NumbersA particular diet program claims that 4316 pounds can be lost the first month, 314 pounds can be lost the second month, and 112 pounds can be lost the thir...A particular diet program claims that 4316 pounds can be lost the first month, 314 pounds can be lost the second month, and 112 pounds can be lost the third month. If the diet program described in the problem above makes the additional claim that from the fourth month on, a person will lose 118 pounds a month, how much will a person who begins the program weighing 20834 pounds weight after 8 months?
- https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/11%3A_Algebraic_Expressions_and_Equations/11.04%3A_Solving_Equations_of_the_Form_ax__b_and_x_a__bRecall that the equal sign of an equation indicates that the number represented by the expression on the left side is the same as the number represented by the expression on the right side. We can obt...Recall that the equal sign of an equation indicates that the number represented by the expression on the left side is the same as the number represented by the expression on the right side. We can obtain an equivalent equation by multiplying both sides of the equation by the same nonzero number, that is, if c≠0. We can obtain an equivalent equation by dividing both sides of the equation by the same nonzero number, that is, if c≠0, then a=b is equivalent to
- https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/01%3A_Addition_and_Subtraction_of_Whole_Numbers/1.04%3A_Addition_of_Whole_NumbersStart at the right (in the ones position) and move to the left, placing the sum at the bottom. \(\begin{array} {lcl} {6 + 5 + 1 + 7 = 19} & \ \ & {\text{Write 9, carry the 1.}} \\ {1 + 1 + 0 + 5 + 1 =...Start at the right (in the ones position) and move to the left, placing the sum at the bottom. 6+5+1+7=19 Write 9, carry the 1.1+1+0+5+1=8 Write 8.0+9+9+8=26 Write 6, carry the 2.2+8+9+8+6=33 Write 3, carry the 3.3+7+3+5=18 Write 8, carry the 1.1+8=9 Write 9.
- https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/03%3A_Exponents_Roots_and_Factorization_of_Whole_Numbers/3.01%3A_Exponents_and_Roots62⋅62⋅62⋅62⋅62⋅62⋅62⋅62⋅62. 9⋅9⋅9⋅9⋅9⋅9⋅9⋅9⋅9⋅9 \(4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot ...62⋅62⋅62⋅62⋅62⋅62⋅62⋅62⋅62. 9⋅9⋅9⋅9⋅9⋅9⋅9⋅9⋅9⋅9 4⋅4⋅4⋅4⋅4⋅4⋅4 5 is called the exponent, or power. 85 is read as "eight to the fifth power," or more simply as "eight to the fifth," or "the fifth power of eight." 6⋅6⋅6⋅6⋅6⋅6⋅6⋅6⋅6=10,077,696
- https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/08%3A_Techniques_of_Estimation/8.02%3A_Estimation_by_Clusteringbe able to estimate the result of adding more than two numbers when clustering occurs using the clustering technique When more than two numbers are to be added, the sum may be estimated using the clus...be able to estimate the result of adding more than two numbers when clustering occurs using the clustering technique When more than two numbers are to be added, the sum may be estimated using the clustering technique. The rounding technique could also be used, but if several of the numbers are seen to cluster (are seen to be close to) one particular number, the clustering technique provides a quicker estimate.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/01%3A_Basics/1.02%3A_SetsThis page offers an overview of sets as key mathematical data structures, detailing their definitions, characteristics, and notations. It emphasizes well-defined sets, membership, and element order ab...This page offers an overview of sets as key mathematical data structures, detailing their definitions, characteristics, and notations. It emphasizes well-defined sets, membership, and element order absence. Through checkpoints, it encourages analysis of set membership and subsets and introduces the empty set concept. Activities are included to explore subset relationships and object membership within sets.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/01%3A_Basics/1.05%3A_Combinatorics-_First_CountsThis page introduces combinatorics, focusing on counting and key terms like "alphabet," "string," and "permutation." It defines "string" as an ordered set of characters and explains "permutation" as a...This page introduces combinatorics, focusing on counting and key terms like "alphabet," "string," and "permutation." It defines "string" as an ordered set of characters and explains "permutation" as any arrangement of those characters. The text provides examples and includes practice checkpoints for generating strings and permutations of varying lengths and characters.
