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2.3: Division of Whole Numbers
https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/02%3A_Multiplication_and_Division_of_Whole_Numbers/2.03%3A_Division_of_Whole_Numbers
The educated guess can be made by determining how many times the divisor is contained in the dividend by using only one or two digits of the dividend. Use the first digit of the divisor and the first ...The educated guess can be made by determining how many times the divisor is contained in the dividend by using only one or two digits of the dividend. Use the first digit of the divisor and the first two digits of the dividend to make the educated guess. If, however, the division should result in a remainder, the calculator is unable to provide us with the particular value of the remainder.
1: Addition and Subtraction of Whole Numbers
https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/01%3A_Addition_and_Subtraction_of_Whole_Numbers
6.2: Converting a Decimal to a Fraction
https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/06%3A_Decimals/6.02%3A_Converting_a_Decimal_to_a_Fraction
be able to convert an ordinary decimal and a complex decimal to a fraction \(\begin{array} {rcl} {4 + .006 \dfrac{1}{4}} & = & {4 + \dfrac{6 \dfrac{1}{4}}{1000}} \\ {} & = & {4 + \dfrac{\dfrac{25}{4}}...be able to convert an ordinary decimal and a complex decimal to a fraction $\begin{array} {rcl} {4 + .006 \dfrac{1}{4}} & = & {4 + \dfrac{6 \dfrac{1}{4}}{1000}} \\ {} & = & {4 + \dfrac{\dfrac{25}{4}}{\dfrac{1000}{1}}} \\ {} & = & {4 + \dfrac{\begin{array} {c} {^1} \\ {\cancel{25}} \end{array}}{4} \cdot \dfrac{1}{\begin{array} {c} {\cancel{1000}} \\ {^{40}} \end{array}}} \\ {} & = & {4 + \dfrac{1 \cdot 1}{4 \cdot 40}} \\ {} & = & {4 + \dfrac{1}{160}} \\ {} & = & {4 \dfrac{1}{160}} \end{array}$
7.5: Fractions of One Percent
https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/07%3A_Ratios_and_Rates/7.05%3A_Fractions_of_One_Percent
\(\begin{array} {l} {\dfrac{1}{2} \% = \dfrac{1}{2} \text{ of } 1\% = \dfrac{1}{2} \cdot \dfrac{1}{100} = \dfrac{1}{200}} \\ {\dfrac{3}{5} \% = \dfrac{3}{5} \text{ of } 1\% = \dfrac{3}{5} \cdot \dfrac... $\begin{array} {l} {\dfrac{1}{2} \% = \dfrac{1}{2} \text{ of } 1\% = \dfrac{1}{2} \cdot \dfrac{1}{100} = \dfrac{1}{200}} \\ {\dfrac{3}{5} \% = \dfrac{3}{5} \text{ of } 1\% = \dfrac{3}{5} \cdot \dfrac{1}{100} = \dfrac{3}{500}} \\ {\dfrac{5}{8} \% = \dfrac{5}{8} \text{ of } 1\% = \dfrac{5}{8} \cdot \dfrac{1}{100} = \dfrac{5}{800}} \\ {\dfrac{7}{11} \% = \dfrac{7}{11} \text{ of } 1\% = \dfrac{7}{11} \cdot \dfrac{1}{100} = \dfrac{7}{1100}} \end{array}$
9: Measurement and Geometry
https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/09%3A_Measurement_and_Geometry
Thumbnail: A two-dimensional perspective projection of a sphere (CC BY-3.0; Geek3 via Wikipedia).
8.6: Exercise Supplement
https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/08%3A_Techniques_of_Estimation/8.06%3A_Exercise_Supplement
Exercise $\PageIndex{1}$ Exercise $\PageIndex{2}$ Exercise $\PageIndex{3}$ Exercise $\PageIndex{4}$ Exercise $\PageIndex{5}$ Exercise $\PageIndex{6}$ Exercise $\PageIndex{7}$ Exercise \(...Exercise $\PageIndex{1}$ Exercise $\PageIndex{2}$ Exercise $\PageIndex{3}$ Exercise $\PageIndex{4}$ Exercise $\PageIndex{5}$ Exercise $\PageIndex{6}$ Exercise $\PageIndex{7}$ Exercise $\PageIndex{8}$ Exercise $\PageIndex{9}$ Exercise $\PageIndex{10}$ Exercise $\PageIndex{11}$ Exercise $\PageIndex{12}$ Exercise $\PageIndex{13}$ Exercise $\PageIndex{14}$ Exercise $\PageIndex{15}$ Exercise $\PageIndex{16}$ Exercise $\PageIndex{17}$ Exercise $\PageIndex{18}$
3.4: The Greatest Common Factor
https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/03%3A_Exponents_Roots_and_Factorization_of_Whole_Numbers/3.04%3A_The_Greatest_Common_Factor
\(\begin{array} {rcl} {700 \ = \ 2 \cdot 350 \ = \ 2 \cdot 2 \cdot 175} & = & {2 \cdot 2 \cdot 5 \cdot 35} \\ {} & = & {2 \cdot 2 \cdot 5 \cdot 5 \cdot 7} \\ {} & = & {2^2 \cdot 5^2 \cdot 7} \\ {1,880...\(\begin{array} {rcl} {700 \ = \ 2 \cdot 350 \ = \ 2 \cdot 2 \cdot 175} & = & {2 \cdot 2 \cdot 5 \cdot 35} \\ {} & = & {2 \cdot 2 \cdot 5 \cdot 5 \cdot 7} \\ {} & = & {2^2 \cdot 5^2 \cdot 7} \\ {1,880 \ = \ 2 \cdot 940 \ = \ 2 \cdot 2 \cdot 470} & = & {2 \cdot 2 \cdot 2 \cdot 235} \\ {} & = & {2 \cdot 2 \cdot 2 \cdot 5 \cdot 47} \\ {} & = & {2^3 \cdot 5 \cdot 47} \\ {6,160 \ = \ 2 \cdot 3,080 \ = \ 2 \cdot 2 \cdot 1,540} & = & {2 \cdot 2 \cdot 2 \cdot 770} \\ {} & = & {2 \cdot 2 \cdot 2 \cdot 2…
4.6: Applications Involving Fractions
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{ $\begin{array} {c} {^3} \\ {\cancel{9}} \end{array}$ }{\begin{array} {c} {\cancel{4}} \\ {^1} \e... $\begin{array} {rcl} {M = \dfrac{9}{4} \div \dfrac{3}{8} = \dfrac{9}{4} \cdot \dfrac{8}{3}} & = & {\dfrac{\begin{array} {c} {^3} \\ {\cancel{9}} \end{array}}{\begin{array} {c} {\cancel{4}} \\ {^1} \end{array}} \cdot \dfrac{\begin{array} {c} {^2} \\ {\cancel{8}} \end{array}}{\begin{array} {c} {\cancel{3}} \\ {^1} \end{array}}} \\ {} & = & {\dfrac{3 \cdot 2}{1 \cdot 1}} \\ {} & = & {6} \end{array}$
4.4: Multiplication of Fractions
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{ $\begin{array} {c} {^3} \\ {\cancel{9}} \end{array}$ }{\begin{array} {c} {\cancel{2}} \\ ... $\begin{array} {rcl} {\dfrac{11}{8} \cdot 4 \dfrac{1}{2} \cdot 3 \dfrac{1}{8}} & = & {\dfrac{11}{8} \cdot \dfrac{\begin{array} {c} {^3} \\ {\cancel{9}} \end{array}}{\begin{array} {c} {\cancel{2}} \\ {^1} \end{array}} \cdot \dfrac{\begin{array} {c} {^5} \\ {\cancel{10}} \end{array}}{\begin{array} {c} {\cancel{3}} \\ {^1} \end{array}}} \\ {} & = & {\dfrac{11 \cdot 3 \cdot 5}{8 \cdot 1 \cdot 1} = \dfrac{165}{8} = 20 \dfrac{5}{8}} \end{array}$
2.8: Proficiency Exam
https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/02%3A_Multiplication_and_Division_of_Whole_Numbers/2.08%3A_Proficiency_Exam
In the multiplication of $8 \times 7 = 56$ , what are the names given to the 8 and 7 and the 56? 8 and 7 are factors; 56 is the product In the division $12 \div 3 = 4$ , what are the names given to ...In the multiplication of $8 \times 7 = 56$ , what are the names given to the 8 and 7 and the 56? 8 and 7 are factors; 56 is the product In the division $12 \div 3 = 4$ , what are the names given to the 3 and the 4? 3 is the divisor; 4 is the quotient Name the digits that a number must end in to be divisible by 2. Name the property of multiplication that states that the order of the factors in a multiplication can be changed without changing the product.
3.3: Prime Factorization of Natural Numbers
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_Numbers
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). 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.

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