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10.4: Addition of Signed Numbers

https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/10%3A_Signed_Numbers/10.04%3A_Addition_of_Signed_Numbers

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 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.

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

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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).

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...

$\begin{array} {l} {\dfrac{1}{2} \% = \dfrac{1}{2} \text{ of } 1\% = \dfrac{1}{2} \cdot \dfrac{1}{100} = \dfrac{1}{200}} \\ {\dfrac{3}{5} \% = \dfrac{3}{5} \text{ of } 1\% = \dfrac{3}{5} \cdot \dfrac{1}{100} = \dfrac{3}{500}} \\ {\dfrac{5}{8} \% = \dfrac{5}{8} \text{ of } 1\% = \dfrac{5}{8} \cdot \dfrac{1}{100} = \dfrac{5}{800}} \\ {\dfrac{7}{11} \% = \dfrac{7}{11} \text{ of } 1\% = \dfrac{7}{11} \cdot \dfrac{1}{100} = \dfrac{7}{1100}} \end{array}$

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

$\begin{array} {rcl} {4 + .006 \dfrac{1}{4}} & = & {4 + \dfrac{6 \dfrac{1}{4}}{1000}} \\ {} & = & {4 + \dfrac{\dfrac{25}{4}}{\dfrac{1000}{1}}} \\ {} & = & {4 + \dfrac{\begin{array} {c} {^1} \\ {\cancel{25}} \end{array}}{4} \cdot \dfrac{1}{\begin{array} {c} {\cancel{1000}} \\ {^{40}} \end{array}}} \\ {} & = & {4 + \dfrac{1 \cdot 1}{4 \cdot 40}} \\ {} & = & {4 + \dfrac{1}{160}} \\ {} & = & {4 \dfrac{1}{160}} \end{array}$

9.6: Summary of Key Concepts

https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/09%3A_Measurement_and_Geometry/9.06%3A_Summary_of_Key_Concepts

Move the decimal point of the original number in the same direction and the same number of places as is necessary to move to the metric unit you wish to convert to. To multiply a denominate number by ...Move the decimal point of the original number in the same direction and the same number of places as is necessary to move to the metric unit you wish to convert to. To multiply a denominate number by a whole number, multiply the number part of each unit by the whole number and affix the unit to the product. To divide a denominate number by a whole number, divide the number part of each unit by the whole number beginning with the largest unit.

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}} \\ ...

$\begin{array} {rcl} {\dfrac{11}{8} \cdot 4 \dfrac{1}{2} \cdot 3 \dfrac{1}{8}} & = & {\dfrac{11}{8} \cdot \dfrac{\begin{array} {c} {^3} \\ {\cancel{9}} \end{array}}{\begin{array} {c} {\cancel{2}} \\ {^1} \end{array}} \cdot \dfrac{\begin{array} {c} {^5} \\ {\cancel{10}} \end{array}}{\begin{array} {c} {\cancel{3}} \\ {^1} \end{array}}} \\ {} & = & {\dfrac{11 \cdot 3 \cdot 5}{8 \cdot 1 \cdot 1} = \dfrac{165}{8} = 20 \dfrac{5}{8}} \end{array}$

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...

$\begin{array} {rcl} {M = \dfrac{9}{4} \div \dfrac{3}{8} = \dfrac{9}{4} \cdot \dfrac{8}{3}} & = & {\dfrac{\begin{array} {c} {^3} \\ {\cancel{9}} \end{array}}{\begin{array} {c} {\cancel{4}} \\ {^1} \end{array}} \cdot \dfrac{\begin{array} {c} {^2} \\ {\cancel{8}} \end{array}}{\begin{array} {c} {\cancel{3}} \\ {^1} \end{array}}} \\ {} & = & {\dfrac{3 \cdot 2}{1 \cdot 1}} \\ {} & = & {6} \end{array}$

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.

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.

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.

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