UNIT 1 Chapter 1-1 Number Systems

Vocabulary A number line – is used to show a set of natural numbers, whole numbers, and integers Positive Numbers – to the right side of zero Negative Numbers – to the left side of zero -4 -3 -2 -1 1 2 3 4 Negative Numbers Positive Numbers

Vocabulary Real Numbers: Include Rational and Irrational Numbers Natural Numbers: 1, 2, 3… Whole Numbers: 0, 1, 2, 3, 4… Integers: -3, -2, -1, 0, 1, 2, 3… Rational Numbers: Any ordinary number in arithmetic. Any number that you can write as a quotient in 𝐴 𝐵 of two integers where, b ≠ 0. Examples: 1, -6, 5.8, .227, −3 4 Irrational Numbers: Numbers that cannot be expressed as terminating or repeating decimals, or in the form of 𝐴 𝐵 , where a and b are integers and b≠ 0

Real Numbers Rational Numbers Integers Irrational Numbers Whole Numbers Natural Numbers Irrational Numbers www.prealgebrateachers.com

Number Systems Real Numbers Rational Numbers Irrational Numbers Integers Whole Numbers Natural Numbers Irrational Numbers

From least to greatest = Examples 1) Write two lists of fractions equivalent to 𝟏 𝟐 List 1: Positive numerator and denominator 1 2 = 2 4 = 3 6 = … List 2: Negative numerator and denominator 1 2 = −2 −4 = −3 −6 =… 2) Put each rational number from least to greatest .25, 𝟑 𝟒 , -.2, 3 From least to greatest = -.2, .25, 3 4 , 3

Let’s Try Some Examples Name the set (s) of numbers to which each real number belongs 25 2) 6 11 3) √7 List three fractions equivalent to each fraction 4) 1 10 5) −5 6 List each rational number from least to greatest 5) 1 4 , 3, -2, -.2 6) 1, -4, −10 10

Let’s Check Our Answers Name the set (s) of numbers to which each real number belongs 25 2) 6 11 3) √7 Natural Number, Rational Irrational Whole Number, Integer, Rational Number List three fractions equivalent to each fraction 4) 1 10 5) −5 6 = 𝟐 𝟐𝟎 = 𝟑 𝟑𝟎 = 𝟒 𝟒𝟎 = −𝟏𝟎 𝟏𝟐 = −𝟏𝟓 𝟏𝟖 = −𝟐𝟓 𝟑𝟎 List each rational number from least to greatest 5) 1 4 , 3, -2, -.2 6) 1, -4, −10 10 = -.2, -2, 1 4 , 3 = -4, −10 10 , 1