Absolute Value Notes
- 1. Integers, Absolute Value, and Opposites What do I need on my desk: Pencil Ticket in the Door Slip START WORKING ON YOUR TICKET IN THE DOOR! Upcoming Events: Family Connect Night – Tonight Absolute Value Quiz – Next Class Unit 1 Test – September 17 or 18 Fall Break – Starts September 19
- 2. Integers & Absolute Value What is absolute value? The distance of a number from zero on a number line.
- 3. Absolute Value Notation The notation we use to show absolute value is a pair of vertical bars like those seen below. | |
- 4. Absolute Value Because absolute value refers to distance on a number line, it is always a positive number. I'm positive! |-3| Are you sure?
- 5. What does absolute value look like? the absolute value of 7 | 7 | = 7 the absolute value of – 7 | – 7 | = 7 Integers & Absolute Value
- 6. What does absolute value look like? 7 units 7 units -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 Integers & Absolute Value
- 7. Reading an Absolute Value Expression To read the expression |-9| you would say, “the absolute value of negative nine.” How would you read |14| ? “the absolute value of fourteen” `
- 8. Recap: Absolute Value • The absolute value of a number is its distance from zero. • Distance is always positive!! • Absolute value is represented by 2 lines surrounding the number. 2=-2 2 = 2-2 and 2 are both a distance of 2 units from zero!
- 9. Evaluating Absolute Value Expressions When evaluating an expression that contains absolute value bars, simplify the values within the bars first. Example #1: |-12| + |-3| = 12 + 3 = 15 Example #2: |18| - |-5| = 18 – 5 = 13
- 10. Absolute Value Evaluate the expression. Example 1: | 3 | Example 2: | - 68 | Example 3: | 6 | + | - 9 | Example 4: | - 11 | - | - 8 | Integers & Absolute Value 3 68 6 + 9 = 15 11 – 8 = 3
- 11. Absolute Value Evaluate the expression. Practice 1: | 16 | Practice 2: | - 74 | Practice 3: | 12 | + | - 14 | Practice 4: | - 23 | - | - 18 | Practice 5: | - 19 | - | - 15 | Integers & Absolute Value
- 12. Absolute Value Evaluate the expression. Practice 1: | 16 | = 16 Practice 2: | - 74 | =74 Practice 3: | 12 | + | - 14 | = 12 + 14 = 26 Practice 4: | - 23 | - | - 18 | = 23 – 18 = 5 Practice 5: | - 19 | - | - 15 | = 19 – 15 = 4 Integers & Absolute Value
- 13. Absolute Value Video Integers & Absolute Value
- 14. How can we use absolute value in everyday life when talking about elevation, direction and distance?
- 15. When measuring the distance between two values, one lying above zero and one lying below zero, we simply take the absolute value of each and then add the values.
- 16. Measuring Distance Jamie walked 8 yards towards her locker, then realized she left her binder in class. She walked back to class to get it, and then she walked 12 yards to her locker. Write the answer using absolute value notation. │+8│+│-8│+│+12│ 8 + 8 + 12 She walked 28 yards.
- 17. Measuring Distance Amy dove in the pool 6 feet. Then she came up 4 feet before swimming back down 5 feet. She swam back up 7 feet. What is the total distance she swam? Write the answer using absolute value notation. │-6│+│+4│+│-5│+ │+7│ 6 + 4 + 5 + 7 She swam 22 feet.
- 18. The pilot ascended 3000 feet in the air. After ten minutes, he ascended 7000 more feet. He then descended 5000 feet in the air before ascending 6000 feet. What is the distance the pilot traveled in all? Write the answer using absolute value notation. │+3000│+│+7000│+│-5000│+│+6000│ 3000 + 7000 + 5000 + 6000 The place traveled 21,000 feet.
- 19. Jessica loves to ride her scooter through her neighborhood! On Saturday she rides 50 yards North to her aunt’s house, and then 30 yards South to her best friend’s house. She spends the night. On Sunday she rides 20 yards East to the store, and then 20 yards west back to her friend’s house. How many yards did Jessica ride her scooter in all this past weekend? │+50│+│-30│+│+20│+ │-20│ 50 + 30 + 20 + 20 Jessica rode 120 yards.
- 20. Woman 2005 2007 Change from 2005-2007 Kate 93 88 Maddie 77 74 Tess 100 100 Awbree 91 95 The following table shows the weight change from 2005 to 2007 for four different women. Which woman had the greatest change in weight from 2005 to 2007? - 5 -3 0 4 Kate
- 21. The OPPOSITE of Absolute Value
- 22. Absolute Value • The absolute value of a number is its distance from zero. • Distance is always positive!! • Absolute value is represented by 2 lines surrounding the number. 2=-2 2 = 2 -2 and 2 are both a distance of 2 units from zero!
- 23. 23 • numbers that are the same distance from zero • two exact numbers with different signs Opposite Numbers
- 24. The Opposite of… • If you see a number written like, -(-5) that means the opposite of -5 which would be 5. • The same is true with an absolute value sign. OPPOSITE • What does –(-56) equal? • What does -|5| equal? - -2 = -2 “the opposite of negative 56” 56 “the opposite of the absolute value of 5” -5
- 25. Evaluate the expression. Example 1: -| -3 | Example 2: (- 68) Example 3: -| - 9 | Example 4: -(-12) Example 5: -| 9 | Integers & Absolute Value
- 26. Absolute Value Evaluate the expression. Example 1: -| 3 | = -3 Example 2: (- 68) = -68 Example 3: -| - 9 | = -9 Example 4: -(-12) = 12 Example 5: - | 9 | = –9 Integers & Absolute Value
- 27. Use < , > , or = to compare the two expressions. Example 1: -| 3 | ___ -| 10 | Example 2: (- 68) ___ - 68 Example 3: | - 11 | ___ - (-9) Example 4: - | - 77 | ___ - ( -77) Comparing Absolute value
- 28. Use < , > , or = to compare the two expressions. Example 1: -| 3 | > -| 10 | Example 2: (- 68) = - 68 Example 3: | - 11 | > = - (-9) Example 4: - | - 77 | < - ( -77) Comparing Absolute value