Download presentation

Presentation is loading. Please wait.

1
**Describing Data with Sets of Numbers**

Section 1.1 Describing Data with Sets of Numbers

2
**Objectives Natural and Whole Numbers Integers and Rational Numbers**

Real Numbers Properties of Real Numbers

3
Types of Numbers Natural Numbers: The set of counting numbers. N = {1, 2, 3, 4, 5, 6, …} Set braces, { }, are used to enclose the elements of a set. Whole Numbers: W = {0, 1, 2, 3, 4, 5, …} Integers: I = {…, 3, 2, 1, 0, 1, 2, 3, …} Rational Number: any number that can be expressed as the ratio of two integers; p/q, where q is not equal to 0 because we cannot divide by 0.

4
Example Classify each number as one or more of the following: natural number, whole number, integer, or rational number. a. b. 8 c. 0 Solution a. natural number, whole number, integer, rational number b. integer, rational number c. whole number, integer, rational number

5
**Real Numbers: Can be represented by decimal numbers**

Real Numbers: Can be represented by decimal numbers. Every fraction has a decimal form, so real numbers include rational numbers. Irrational Numbers: A number that cannot be expressed by a fraction, or a decimal number that does not repeat or terminate. Examples:

6
Example Classify each real number as one or more of the following: a natural number, an integer, a rational number, or an irrational number. a. 8 b. 1.6 c. Solution a. natural number, integer, rational number b. rational number c. irrational number

7
Example A student obtains the following test scores: 91, 96, 89, and 84. a. Find the student’s average test score. b. Is this average a natural, rational, or a real number? Solution a. To find the average, we find the sum of the four test scores and divide by 4: b. rational and real numbers

8
**Properties of Real Numbers--Summary**

IDENTITY PROPERTIES For any real number a, a + 0 = 0 + a = a and a ·1 = 1 · a = a.

9
**For any real numbers a and b, a + b = b + a and a ·b = b · a.**

COMMUTATIVE PROPERTIES For any real numbers a and b, a + b = b + a and a ·b = b · a.

10
**For any real numbers a, b, and c, (a + b) + c = a + (b + c) and **

ASSOCIATIVE PROPERTIES For any real numbers a, b, and c, (a + b) + c = a + (b + c) and (a ·b) · c = a · (b · c).

11
Example State the property of real numbers that justifies each statement. a. 5 · (2x) = (5 · 2)x b. (1 · 3) · 6 = 3 · 6 c. 7 + xy = xy + 7 Associative property for multiplication Identity property of 1. Commutative property for addition

12
**For any real numbers a, b, and c, a(b + c) = ab + ac and **

DISTRIBUTIVE PROPERTIES For any real numbers a, b, and c, a(b + c) = ab + ac and a(b c) = ab ac.

13
Example Apply a distributive property to each expression. a. 5(2 + y) b. 8 – (2 + w) c. 5x – 2x d. 3y + 4y – y Solution a. b. c. d.

Similar presentations

OK

OTCQ 091509 Using [-11, 0) Write its associated: 1) inequality, or 2) set in braces, or 3) number line. (for integers only)

OTCQ 091509 Using [-11, 0) Write its associated: 1) inequality, or 2) set in braces, or 3) number line. (for integers only)

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on different types of houses for kids Ppt on instrument landing system ils Ppt on carburetor cleaner Ppt on mobile computing pdf Ppt on risk management in software project management Ppt on image compression using dct transform Differential display ppt online Maths ppt on surface area and volume class 9 Ppt on ideal gas law calculator Disaster management ppt on floods