chapter 2 introduction to integers and algebraic expressions slide 1copyright 2012, 2008, 2004, 2000...
TRANSCRIPT
CHAPTER
2Introduction to Integers and Algebraic Expressions
Slide 1Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.1 Integers and the Number Line2.2 Addition of Integers2.3 Subtraction of Integers2.4 Multiplication of Integers2.5 Division of Integers and Order of Operations2.6 Introduction to Algebra and Expressions2.7 Like Terms and Perimeter2.8 Solving Equations
OBJECTIVES
2.1 Integers and the Number Line
aSolve applied problems
involving addition, subtraction, multiplication, or division of whole numbers.
Slide 2Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
a State the integer that corresponds to a real-worldsituation.
b Form a true sentence using < or >.c Find the absolute value of any integer.d Find the opposite of any integer.
2.1 Integers and the Number Line
a State the integer that corresponds to a real-worldsituation.
Slide 3Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
The integers to the left of zero on the number line are called negative integers and those to the right of zero are called positive integers. Zero is neither positive nor negative. We call –1 and 1 opposites of each other.
2.1 Integers and the Number Line
aState the integer that corresponds to a real-world
situation.
INTEGERS
Slide 4Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
EXAMPLE
2.1 Integers and the Number Line
a State the integer that corresponds to a real-worldsituation.
2 Stock Price Change.
Slide 5Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Tell which integers correspond to this situation: Hal owns a stock whose price decreased from $27 per share to $11 per share over a recent time period. He owns another stock whose price increased from $20 per share to $22 per share over the same time period.
The integer –16 corresponds to the decrease in the value of the first stock. The integer 2 represents the increase in the value of the second stock.
2.1 Integers and the Number Line
b Form a true sentence using < or >.
Slide 6Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Numbers are written in order on the number line, increasing as we move to the right. For any two numbers on the line, the one to the left is less than the one to the right. The symbol < means “is less than.” The symbol > means “is greater than.”
EXAMPLE
2.1 Integers and the Number Line
b Form a true sentence using < or >.
Slide 7Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.1 Integers and the Number Line
c Find the absolute value of any integer.
Slide 8Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
The absolute value of a number is its distance from zero on the number line. We use the symbol to represent the absolute value of a number x.
2.1 Integers and the Number Line
cFind the absolute value
of any integer.
ABSOLUTE VALUE
Slide 9Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Title 2.1Integers and the Number Line
c
2.1 Integers and the Number Line
aState the integer that corresponds to a real-world
situation.
Slide 10Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
To find the absolute value of a number:a) If a number is negative, its absolute value is its opposite.b) If a number is positive or zero, its absolute value is the same as the number.
EXAMPLE
2.1 Integers and the Number Line
c Find the absolute value of any integer.
Slide 11Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Find the absolute value of each number.
2.1 Integers and the Number Line
d Find the opposite of any integer.
Slide 12Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Given a number on one side of 0 on the number line, we can get a number on the other side by reflecting the number across zero.
2.1 Integers and the Number Line
dFind the opposite of any
integer.
NOTATION FOR OPPOSITES
Slide 13Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
The opposite of a number x is written –x (read “the opposite of x”).
EXAMPLE
2.1 Integers and the Number Line
d Find the opposite of any integer.
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Slide 14Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.1 Integers and the Number Line
d Find the opposite of any integer.
Slide 15Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
When the variable is replaced with a number, we say that we are evaluating the expression.
EXAMPLE
2.1 Integers and the Number Line
d Find the opposite of any integer.
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Slide 16Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.1 Integers and the Number Line
d Find the opposite of any integer.
Slide 17Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Replacing a number with its opposite, or additive inverse, is sometimes called changing the sign.
EXAMPLE
2.1 Integers and the Number Line
d Find the opposite of any integer.
Slide 18Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
Change the sign (find the opposite, or additive inverse) of each number.
EXAMPLE
2.1 Integers and the Number Line
d Find the opposite of any integer.
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Slide 19Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
2.1 Integers and the Number Line
d Find the opposite of any integer.
Slide 20Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.
When we change a number’s sign twice, we return to the original number.
EXAMPLE
2.1 Integers and the Number Line
d Find the opposite of any integer.
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Slide 21Copyright 2012, 2008, 2004, 2000 Pearson Education, Inc.