2-1 Integers and Absolute Value

1. 2-1 Integers and Absolute Value How are integers used to model real-world situations?

2. 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

3. 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

4. Compare and Order Integers

5. 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.

6. 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

7. 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.

8. 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

9. 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.

10. 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 I g eater than I

11. 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 < 4 Since 4 is to the right of -3, write 4 > -3 • Replace the  with < or > in -5  -1 to make a true sentence. -5 < -1

12. 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.

13. 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

14. 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 units 5 units

15. 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.

16. 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.

17. Expressions with Absolute Value

18. Algebraic Expressions with Absolute Value • Evaluate if Plug your value for x in for x. Simplify absolute values. Simplify the expression. Once you finish this slide, you have one more slide before continuing on to textbook work.

19. Please visit our textbook’s website to take a self-check quiz. • Please send the results to kmclead@upperdarbysd.org • If you do not want to use your e-mail, when it asks you for it, you may use mine, kmclead@upperdarbysd.org