Entry Task 10/03/2012 5.) 6.) 7.)
Algebra 1Section 2.1 Objective: Graph and compare real numbers using a number line.
Vocabulary • Real Number- all numbers except imaginary numbers • Real Number Line- a horizontal line used to picture real numbers • Origin- the point labeled zero on the number line • Integers- whole numbers plus the opposite of each whole number and zero • The opposite of a number is the number that is the same distance from zero on the other side of the number line. • Ex. The opposite of 2.5 is -2.5 • The absolute value of a number is the distance that number is from zero on the number line. Absolute value of x is notated • the absolute value of -2.3 is 2.3 and the absolute value of 4 is 4.
Graphing Real Numbers • Graph the numbers 2 and -4 on the number line
Opposite of a Number • The opposite of a number is the number that is the same distance from zero on the other side of the number line. • Ex. Find the opposite of 2.5 The opposite of 2.5 is -2.5
Absolute Value • The absolute value of a number is the distance that number is from zero on the number line. Absolute value of x is notated • Find the absolute value of -2.3 and 4. The absolute value of -2.3 is 2.3 and the absolute value of 4 is 4.
Entry Task 10/04/2011 • Get out your notebook. • You may use: • A calculator • Your notebook • Your knowledge folder • When you are done work on finishing 1.7 and 2.1
Entry Task 10/06/2011 • 1.) write the statement as an expression “3 more than the product of 4 and a number n.” • write the sentence as an equation or inequality 2.) “Fourteen plus the product of twelve and a number y is less than or equal to fifty.” 3.) A number x squared plus forty-four is equal to the number x to the fourth power times three. • Describe the domain and range of the function y=2x-4
Algebra 1Section 2.2 and 2.3 Objectives: Add real numbers and subtract real numbers.
Properties of Additionwrite these down and then come up with an example for each • Commutative Property- The order in which two numbers are added does not change the sum. i.e. a+b = b+a • Associative Property- The way you group addition does not change the sum. i.e. (a+b)+c = a+(b+c) • Identity Property- The sum of a number and 0 is the number. i.e. a+0 = a • Inverse Property- the sum of a number and the opposite of the number is 0. i.e. a+(-a) = 0
Subtraction Rule • To subtract b from a, add the opposite of b to a. i.e. a - b = a + (-b) • Example: 3 – 5 = 3 + (-5) = -2
Using a number line to add or subtract • To add a positive number move right on the number line • To add a negative number move left. • To subtract turn the expression into an addtion expression. • Find -2 + 5 using a number line -2 + 5 = 3
Another Example • find the difference: 4 - 3 First turn it into an addition problem: 4 + (-3) Then use the number line to do the addition
Home Fun • Worksheet 2.2 and worksheet 2.3
Quiz Retake Get out your math notebook Get out your knowledge folder Make sure there is at lease 1 foot between you and your neighbor. Make sure you have a pencil, calculator and eraser to take the quiz.
Home Fun • Worksheet 2.2 and worksheet 2.3 • If finished do real numbers worksheet
Section 2.5 Objective: Multiply real numbers
Multiplication Patterns • Negative times a Negative is positive • Positive times Positive is positive • Positive times Negative is negative • Negative times Positive is negative
Multiplication Properties • Multiplication is Associative and Commutative (see definitions in last section). • The Multiplicative Identity is 1, so anything times 1 is that number back • Property of Zero: the product of any number and zero is zero
Examples • (16)(-x) = -16x • (4)(v)(v)(v)(-v) = -4v4 • (-8)(n)4(-n)3 = 8n7
Homework • Worksheet 2.5
Chapter 1 test Get out your math notebook Get out your knowledge folder Make sure there is at lease 1 foot between you and your neighbor. Make sure you have a pencil, calculator and eraser to take the quiz.
Distributive Property • The distributive property is a way to multiply numbers even when there are parenthesis and we can’t do the stuff inside. It is as follows. a(c+b)= a(c)+a(b) Or a(c-b)= a(c)-a(b) For example: 2(4-x) = 2(4)-2(x)= 8-2x
Home Fun • 2.6 practice B
Vocabulary • Reciprocal- The product of a number and its reciprocal is 1 • Example: • so is the reciprocal of 3 • To divide a number a by a nonzero number b, multiply the reciprocal of b
Examples • 5.)
Entry Task 10/18/2011 If you are retaking the Chapter 1 test: • Get out your math notebook • Get out your knowledge folder • Make sure there is at lease 1 foot between you and your neighbor. • Make sure you have a pencil, calculator and eraser to take the quiz. If you received an A then you may do anything you want that is a quiet activity.