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2-1 Integers and Absolute Value
How are integers used to model real-world situations?
Rainfall• The summer of 1999 was unusually dry in parts of the United States. In the
graph below, a value of -8 represents 8 inches below the normal rainfall.
• What does a value of -7 represent?7 in. below normal rainfall
• Which city was farthest from its normal rainfall?Jackson, MS
• How could you represent 5 inches above normal rainfall?+5
Vocabulary
• negative number – a number less than zero• integers – negative numbers, positive
numbers, and zero• coordinate – a number that corresponds to a
point• inequality – a mathematical sentence
comparing numbers or quantities• absolute value – distance from zero
Compare and Order Integers
The set of integers can be written {…-3,-2,-1,0,1,2,3…}
where … means continues indefinitely.
In other words, the negative numbers keep getting smaller and the positive numbers keep getting larger.
Write Integers for Real-World Situations
Here are a few examples:• 500 feet below sea level
The integer is -500.• A temperature increase of 12
The integer is +12.• A loss of $240
The integer is -240
Graphing on a Number Line
• To graph integers, locate the point named on the number line.
• The number that corresponds to that point is called the coordinate of that point.
• Notice that the numbers on a number line increase as you move from left to right. This fact can help you determine which of two numbers is greater.
• Words: -4 is less than 2• Symbols: -4 < 2
• Words: 2 is greater than -4• Symbols: 2 > -4
• There are two ways to remember> means “greater than” and< means “less than”
• First, note that the symbol will always point to the lesser number and open to the greater number.
II
• Second, I like to think the < makes the “L” in the words “less than”
• And the > helps make the “R” in the words “greater than”
ess than
g eater than
Compare Two Integers• Use the integers graphed on the number line
below.
• Write two inequalities involving -3 and 4.Since -3 is to the left of 4, write -3 < 4Since 4 is to the right of -3, write 4 > -3
• Replace the with < or > in -5 -1 to make a true sentence.-5 < -1
Woman in Golf
• Karrie Webb finished the 2000 World Championship at under 2 par.
• In 2000, she was LPGA’s leading money winner at around $1.8 million.
Order Integers• The final round scores of the top ten finishers in the 2000
Word Championship LPGA tournament were -4, -14, -1, +1, +2, +5, 0, +3, -10, and -2. Order the scores from least to greatest.
• First, graph each number on a number line.
• Now, order the scores from least to greatest.• -14, -10, -4, -2, -1, 0, 1, 2, 3, 5
Absolute Value
• On the number line, notice that 5 and -5 are on opposite sides of zero, and they are the same distance from zero.
• In mathematics, we say they have the same absolute value, 5.
5 units5 units
• The symbol for absolute value is two vertical lines on either side of the number.
The absolute value of 5 is five.
The absolute value of -5 is 5.
55
55
• The absolute value of a number is the distance the number is from zero on the number line. The absolute value of a number is always greater than or equal to zero.
• WARNING!!!!!!!– It is not always true that the absolute value of a
number is the opposite of that number. – Remember that the absolute value is always
positive or zero.
Expressions with Absolute Value
8 8
79 79 16
34 34 1
Algebraic Expressions with Absolute Value
• Evaluate if 3x 5x
35
35
2
Once you finish this slide, you have one more slide before continuing on to textbook work.
Plug your value for x in for x.
Simplify absolute values.
Simplify the expression.
• Please visit our textbook’s website to take a self-check quiz.
• Please send the results to [email protected]
• If you do not want to use your e-mail, when it asks you for it, you may use mine, [email protected]
