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5.5: Perform Signed Number Arithmetic

https://math.libretexts.org/Courses/De_Anza_College/Pre-Statistics/5%3A_Operations_on_Numbers/5.5%3A_Perform_Signed_Number_Arithmetic

Even though negative numbers seem not that common in the real world, they do come up often when doing comparisons. For example, a common question is how much bigger is one number than another, which ...Even though negative numbers seem not that common in the real world, they do come up often when doing comparisons. For example, a common question is how much bigger is one number than another, which involves subtraction. In statistics we don't know the means until we collect the data and do the calculations. This often results in subtracting a larger number from a smaller number which yields a negative number. We need to be able to perform arithmetic on both positive and negative numbers.

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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8.7: Proficiency Exam

https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/08%3A_Techniques_of_Estimation/8.07%3A_Proficiency_Exam

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$\PageIndex{6}$ After you have made an estimate, find ...Exercise

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$\PageIndex{6}$ After you have made an estimate, find the exact value.

$1 + \dfrac{1}{2} = 1 \dfrac{1}{2}$ (

$1 \dfrac{9}{16}$ )

$0 + \dfrac{1}{2} + \dfrac{1}{2} = 1$ (

$1 \dfrac{47}{300}$ )

$8 \dfrac{1}{2} + 14 = 22 \dfrac{1}{2}$ (

$22 \dfrac{31}{48}$ )

$5 \dfrac{1}{2} + 1 \dfrac{1}{2} + 6 \dfrac{1}{2} = 13 \dfrac{1}{2}$ (

$13 \dfrac{1}{3}$ )

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}} \\ ...

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

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.

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…

5.8: Exercise Supplement

https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/05%3A_Addition_and_Subtraction_of_Fractions_Comparing_Fractions_and_Complex_Fractions/5.08%3A_Exercise_Supplement

$\dfrac{1}{4} + \dfrac{1}{8} + \dfrac{1}{4}$

$5 \dfrac{2}{3} + 8 \dfrac{1}{5} - 2 \dfrac{1}{4}$

$\dfrac{11}{12} + \dfrac{1}{9} - \dfrac{1}{16}$ \(8 \dfrac{3}{5} - 1 \dfrac{1}{14} \cdot \dfrac{3}...

$\dfrac{1}{4} + \dfrac{1}{8} + \dfrac{1}{4}$

$5 \dfrac{2}{3} + 8 \dfrac{1}{5} - 2 \dfrac{1}{4}$

$\dfrac{11}{12} + \dfrac{1}{9} - \dfrac{1}{16}$

$8 \dfrac{3}{5} - 1 \dfrac{1}{14} \cdot \dfrac{3}{7}$

$\dfrac{3 \dfrac{1}{4} + 2 \dfrac{1}{8}}{5 \dfrac{1}{6}}$

$\dfrac{3 + 2 \dfrac{1}{2}}{\dfrac{1}{4} + \dfrac{5}{6}}$

$\dfrac{1 \dfrac{2}{3} \cdot (\dfrac{1}{4} + \dfrac{1}{5})}{1 \dfrac{1}{2}}$

$\dfrac{2}{9}, \dfrac{1}{3}, \dfrac{1}{6}$

1.8: Exercise Supplement

https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/01%3A_Addition_and_Subtraction_of_Whole_Numbers/1.08%3A_Exercise_Supplement

$\begin{array} {r} {908} \\ {\underline{+\ \ 29}} \end{array}$

$\begin{array} {r} {529} \\ {\underline{+161}} \end{array}$

$\begin{array} {r} {549} \\ {\underline{+\ \ 16}} \end{array}$ \(\begin...

$\begin{array} {r} {908} \\ {\underline{+\ \ 29}} \end{array}$

$\begin{array} {r} {529} \\ {\underline{+161}} \end{array}$

$\begin{array} {r} {549} \\ {\underline{+\ \ 16}} \end{array}$

$\begin{array} {r} {726} \\ {\underline{+892}} \end{array}$

$\begin{array} {r} {390} \\ {\underline{+169}} \end{array}$

$\begin{array} {r} {166} \\ {\underline{+660}} \end{array}$ Add the sum of 19,161, 201, 166,127, and 44 to the difference of the sums of 161, 2,455, and 85, and 21, 26, 48, and 187.

5.5: Perform Signed Number Arithmetic

https://math.libretexts.org/Workbench/Math_C096%3A_Support_for_Statistics_Corequisite%3A_MATH_C160_(Tran)/05%3A_Operations_on_Numbers/5.05%3A_Perform_Signed_Number_Arithmetic

Even though negative numbers seem not that common in the real world, they do come up often when doing comparisons. For example, a common question is how much bigger is one number than another, which ...Even though negative numbers seem not that common in the real world, they do come up often when doing comparisons. For example, a common question is how much bigger is one number than another, which involves subtraction. In statistics we don't know the means until we collect the data and do the calculations. This often results in subtracting a larger number from a smaller number which yields a negative number. We need to be able to perform arithmetic on both positive and negative numbers.

2.5: Properties of Multiplication

https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/02%3A_Multiplication_and_Division_of_Whole_Numbers/2.05%3A_Properties_of_Multiplication

The product of two whole numbers is the same regardless of the order of the factors. If three whole numbers are multiplied, the product will be the same if the first two are multiplied first and then ...The product of two whole numbers is the same regardless of the order of the factors. If three whole numbers are multiplied, the product will be the same if the first two are multiplied first and then that product is multiplied by the third, or if the second two are multiplied first and that product is multiplied by the first.

$(\text{a first number } \cdot \text{ a second number}) \cdot \text{a third number} = \text{a first number} \cdot (\text{a second number } \cdot \text{ a third number})$

2.7: Exercise Supplement

https://math.libretexts.org/Bookshelves/PreAlgebra/Fundamentals_of_Mathematics_(Burzynski_and_Ellis)/02%3A_Multiplication_and_Division_of_Whole_Numbers/2.07%3A_Exercise_Supplement

In the multiplication

$5 \times 9 = 45$ , 5 and 9 are called and 45 is called the . In the multiplication

$4 \times 8 = 32$ , 4 and 8 are called and 32 is called the . In the division \(24 \div 6 = ...In the multiplication

$5 \times 9 = 45$ , 5 and 9 are called and 45 is called the . In the multiplication

$4 \times 8 = 32$ , 4 and 8 are called and 32 is called the . In the division

$24 \div 6 = 4$ , 6 is called the , and 4 is called the . In the division

$36 \div 2 = 18$ , 2 is called the , and 18 is called the . A number is divisible by 4 only if the rightmost two digits form a number that is . If the bookstore sells $1089 worth of books, what is the price of each book?

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