Warm-Up from 1.1 Find the algebraic expression to represent the pattern given: 1.5, 9, 13, 17, …. 2.2, -3, -8, -13, … 3.-3, 0, 5, 12, 21, … 4.5, 14, 29,

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Presentation transcript:

Warm-Up from 1.1 Find the algebraic expression to represent the pattern given: 1.5, 9, 13, 17, …. 2.2, -3, -8, -13, … 3.-3, 0, 5, 12, 21, … 4.5, 14, 29, 50, 77, … 5.3, 10, 29, 68, …

1.2 – Properties of Real Numbers Students will be able to: Graph and order real numbers Identify properties of real numbers Lesson Vocabulary Opposite Additive inverse Reciprocal Multiplicative Inverse

1.2 – Properties of Real Numbers

The set of real numbers has several subsets related in particular ways. Algebra involves operations on and relations among numbers, including real numbers and imaginary numbers. Rational numbers and irrational numbers form the set of real numbers.

1.2 – Properties of Real Numbers You can graph every real number as a point on the number line.

1.2 – Properties of Real Numbers REAL NUMBERS IRRATIONAL RATIONAL INTEGERS WHOLE NATURAL Have decimal representations that neither terminate nor repeat. Cannot be written as quotients of integers Are all numbers you can write as a quotient of integers Include terminating decimals Include repeating decimals

1.2 – Properties of Real Numbers Problem 1: Multiple Choice: Your school is sponsoring a charity race. Which set of numbers does not contain the number of people p who participate in the race? a.Natural numbersb. Integers c. Rational numbersd. Irrational numbers The number of people is a natural number, which means it is also an integer and rational number.

1.2 – Properties of Real Numbers Problem 1b: Multiple Choice: In the previous problem, if each participant made a donation d of $15.50 to a local charity, which subset of real numbers best describes the amount of money raised. a.Natural numbersb. Integers c. Rational numbersd. Irrational numbers correct

1.2 – Properties of Real Numbers Problem 2: What is the graph of the numbers: and ?

1.2 – Properties of Real Numbers Problem 2b: What is the graph of the numbers: and ?

1.2 – Properties of Real Numbers Problem 3: How do and 3.8 compare? Use > or <.

1.2 – Properties of Real Numbers Problem 3b: How do and 6.25 compare? Use > or <.

1.2 – Properties of Real Numbers Problem 3c: Let a, b, and c be real numbers such that a < b and b < c. How do a and c compare? Explain!!

1.2 – Properties of Real Numbers The properties of real numbers are relationships that are true for all real numbers (except, in one case, zero). The opposite or additive inverse of any number a is –a. The sum of a number and its opposite is 0, the additive identity. Examples: 12 + (-12) = = 0

1.2 – Properties of Real Numbers The reciprocal or multiplicative inverse of an nonzero number a is 1/a. The product of a number and its reciprocal is 1, the multiplicative identity. Examples: 8(1/8) = 1 -5(-1/5) = 1

1.2 – Properties of Real Numbers

Problem 4: Which property does the equation illustrate? a. (-2/3)(-3/2) = 1 b.(3 x 4)x 5 = (4 x 3)x 5 c.3(g + h) + 2g = (3g + 3h) + 2g d = -5

1.2 – Properties of Real Numbers Lesson Check

1.2 – Properties of Real Numbers Lesson Check