01-12-2012, 03:38 PM
Math Review
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Integers
The integers are the numbers 1, 2, 3, and so on, together with their negatives, and 0. Thus, the set of integers is 1,2,3,...,---{}...,3,2,1,0,1,2,3,..---
The positive integers are greater than 0, the negative integers are less than 0, and 0 is neither positive nor negative. When integers are added, subtracted, or multiplied, the result is always an integer; division of integers is addressed below. The many elementary number facts for these operations, such as 7815,+=78879,-=-()7182--= and () should be familiar to you; they are not reviewed here. Here are some general facts regarding multiplication of integers. ()7856,=
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The product of two positive integers is a positive integer.
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The product of two negative integers is a positive integer.
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The product of a positive integer and a negative integer is a negative integer.
When integers are multiplied, each of the multiplied integers is called a factor or divisor of the resulting product. For example, ()()()231060,= so 2, 3, and 10 are factors of 60. The integers 4, 15, 5, and 12 are also factors of 60, since ()()41560= and ()()51260.= The positive factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60. The negatives of these integers are also factors of 60, since, for example, ()()23060--= There are no other factors of 60. We say that 60 is a multiple of each of its factors and that 60 is divisible by each of its divisors. Here are some more examples of factors and multiples.
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The positive factors of 100 are 1, 2, 4, 5, 10, 20, 25, 50, and 100.
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25 is a multiple of only six integers: 1, 5, 25, and their negatives.
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The list of positive multiples of 25 has no end: 25, 50, 75, 100, 125, 150, etc.; likewise, every nonzero integer has infinitely many multiples.
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1 is a factor of every integer; 1 is not a multiple of any integer except 1 and 1.
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0 is a multiple of every integer; 0 is not a factor of any integer except 0.
Decimals
The decimal number system is based on representing numbers using powers of 10. The place value of each digit corresponds to a power of 10. For example, the digits of the number 7,532.418 have the following place values.
Real Numbers
The set of real numbers consists of all rational numbers and all irrational numbers. The real numbers include all integers, fractions, and decimals. The set of real numbers can be represented by a number line called the real number line.