Integers & Absolute Value

1. Integers & Absolute Value

2. Vocabulary • Integers • Positive Integers • Negative Integers • Coordinate • Graph • Inequality • Absolute Value

3. Integers

4. Writing Integers for Real World Situations • 500 feet below sea level • A temperature increase of 12 degrees • A loss of $240 • A football play with a loss of 20 yards • A bonus of $25 • A loss of 6 pounds

5. Graphing Integers To graph integers, locate the points named by the integers on the number line. The number that corresponds to a point is called the coordinate of that point.

6. Graph the following points on the same number line • -4 • 0 • 2 • -5 • 7

7. Comparing Two Integers Any mathematical sentence containing < or > is called an inequality. It compares numbers or quantities.

8. Replace the __ with < or >. • 6 __ -7 • 0 __ 6 • -3 __ 0 • -6 __ -9 • -7 __ -10 • 7 ___ 9

9. Order Integers Integers are used to compare numbers is many real-world situations

10. Compare and order these integers. • { 2, -7, 0, 1, -3} • { 123, -54, 27, -48, 115} • {28, -6, 0, 5, -52, 115} • {-34, 25, -40, 50, -125, 0}

11. Absolute Value • The distance that a number is from zero. • The absolute value of a number is always greater than or equal to zero. • Symbol is two vertical bars on either side of the number. Ex. lxl

12. Find l5l and l-5l…. The answer is 5 because 5 and -5 are both 5 units from zero.

13. Expressions with Absolute Value Remember AV is always positive or zero.

14. Evaluate each absolute value. • l4l • l-8l + l-1l • l6l - l-4l • l-9l • l67l • l-40l + l20l

15. Algebraic Expressions with Absolute Value Since variables represent numbers, you can use it with algebraic expressions.

16. Evaluate each expression if x=2. • lxl – 8 • l-xl + 2 • l4 + xl • lx – 6l

17. Use the graph to answer the questions • Graph the temperatures on a number line 2. Write the numbers in order from least to greatest. 3. Compare the lowest temperature in the U.S. and the lowest temperature east of the Mississippi using the < symbol. 4. Compare the lowest temperature in the U.S. and the lowest temperature west of the Mississippi using the < symbol.

18. Homework Write an integer for each situation, then graph it on a number line. • A bank withdrawal of $100 • A salary increase of $250 • 12 degrees above zero • A gain of 9 yards • 5 seconds before liftoff

19. Homework cont… Replace ___ with < or >. 6. -18 __ -8 7. 0 ___ -3 8. 9 __ -9 9. -6 __ -2

20. Homework cont… Evaluate each expression. 10. l-15l 11. l46l 12. l0+9l 13. l-5l + l4l 14. l0l + l-2l