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1. Adding and Subtracting Real Numbers 1-2 Holt Algebra 1 Warm Up Lesson Presentation Lesson Quiz

2. 2 2 2 2 3 5 Warm Up Simplify. 1. –4 –|4| 2. |–3| 3 Write an improper fraction to represent each mixed number. 6 2 14 55 3. 4 4. 7 3 7 3 7 Write a mixed number to represent each improper fraction. 12 24 5. 6. 5 9

3. Objectives Add real numbers. Subtract real numbers.

4. 11 10 7 6 5 4 3 2 1 9 8 0 Example 1A: Adding and Subtracting Numberson a Number line Add or subtract using a number line. –4 + (–7) Start at 0. Move left to –4. To add –7, move left 7 units. + (–7) –4 –4+ (–7) = –11

5. -3 -2 -1 0 1 2 3 4 5 6 8 9 7 Example 1B: Adding and Subtracting Numbers on a Number line Add or subtract using a number line. 3 – (–6) Start at 0. Move right to 3. To subtract –6, move right6units. –6 + 3 3 – (–6) = 9

6. -3 -1 0 1 2 3 4 6 8 9 -2 7 5 Check It Out! Example 1a Add or subtract using a number line. –3 + 7 Start at 0. Move left to –3. To add 7, move right 7 units. +7 –3 –3 + 7 = 4

7. Check It Out! Example 1b Add or subtract using a number line. –3 – 7 Start at 0. Move left to –3. To subtract 7 move left 7 units. –3 –7 11 10 6 9 8 7 5 4 3 2 1 0 –3 – 7 = –10

8. Check It Out! Example 1c Add or subtract using a number line. –5 – (–6.5) Start at 0. Move left to –5. To subtract negative 6.5 move right 6.5 units. –5 – (–6.5) 8 7 6 5 2 1 0 1 2 4 3 –5 – (–6.5) = 1.5

9. The absolute value of a number is the distance from zero on a number line. The absolute value of 5 is written as |5|. 5 units 5units - - - - - 6 5 - 1 0 1 2 3 4 5 6 4 3 2 |–5| = 5 |5| = 5

11. When the signs of numbers are different, find the difference of the absolute values: Example 2A: Adding Real Numbers Add. Use the sign of the number with the greater absolute value. The sum is negative.

12. Example 2B:Adding Real Numbers Add. y + (–2) for y = –6 y + (–2) = (–6) + (–2) First substitute –6 for y. When the signs are the same, find the sum of the absolute values: 6 + 2 = 8. (–6) + (–2) –8 Both numbers are negative, so the sum is negative.

13. Check It Out! Example 2a Add. –5 + (–7) –5 + (–7) = 5 + 7 When the signs are the same, find the sum of the absolute values. 5 + 7 = 12 Both numbers are negative, so the sum is negative. –12

14. Check It Out! Example 2b Add. –13.5 + (–22.3) –13.5 + (–22.3) When the signs are the same, find the sum of the absolute values. 13.5 + 22.3 –35.8 Both numbers are negative so, the sum is negative.

15. Check It Out! Example 2c Add. x + (–68) for x = 52 First substitute 52 for x. x + (–68)= 52 + (–68) When the signs of the numbers are different, find the difference of the absolute values. 68 – 52 Use the sign of the number with the greater absolute value. –16 The sum is negative.

16. Two numbers are opposites if their sum is 0. A number and its opposite are on opposite sides of zero on a number line, but are the same distance from zero. They have the same absolute value.

18. Example 3A:Subtracting Real Numbers Subtract. –6.7 – 4.1 –6.7 – 4.1 = –6.7 + (–4.1) To subtract 4.1, add –4.1. When the signs of the numbers are the same, find the sum of the absolute values: 6.7 + 4.1 = 10.8. = –10.8 Both numbers are negative, so the sum is negative.

19. Example 3B:Subtracting Real Numbers Subtract. 5 – (–4) 5 − (–4) = 5 + 4 To subtract –4 add 4. Find the sum of the absolute values. 9

20. First substitute for z. , add . To subtract Rewrite with a denominator of 10. Example 3C:Subtracting Real Numbers Subtract.

21. When the signs of the numbers are the same, find the sum of the absolute values: . Example 3C Continued Write the answer in the simplest form. Both numbers are negative, so the sum is negative.

22. Check It Out! Example 3a Subtract. 13 – 21 13 – 21 To subtract 21 add –21. = 13 + (–21) When the signs of the numbers are different, find the difference of the absolute values: 21 – 13 = 8. Use the sign of the number with the greater absolute value. –8

23. 1 2 –3 To subtract add . When the signs of the numbers are the same, find the sum of the absolute values: = 4. 1 2 3 1 2 1 2 3 + Check It Out! Example 3b Subtract. 4 Both numbers are positive so, the sum is positive.

24. Check It Out! Example 3c Subtract. x – (–12) for x = –14 First substitute –14 for x. x– (–12) = –14 – (–12) –14 + (12) To subtract –12, add 12. When the signs of the numbers are different, find the difference of the absolute values: 14 – 12 = 2. Use the sign of the number with the greater absolute value. –2

25. Example 4: Oceanography Application An iceberg extends 75 feet above the sea. The bottom of the iceberg is at an elevation of –247 feet. What is the height of the iceberg? Find the difference in the elevations of the top of the iceberg and the bottom of the iceberg. elevationat bottom of iceberg –247 elevation at top of iceberg 75 Minus – 75 – (–247) 75 – (–247) = 75 + 247 To subtract –247, add 247. Find the sum of the absolute values. = 322 The height of the iceberg is 322 feet.

26. Check It Out! Example 4 What if…?The tallest known iceberg in the North Atlantic rose 550 feet above the oceans surface. How many feet would it be from the top of the tallest iceberg to the wreckage of the Titanic, which is at an elevation of –12,468 feet? Minus elevationof the Titanic –12,468 elevation at top of iceberg 550 – 550 – (–12,468) To subtract –12,468, add 12,468. 550 – (–12,468) = 550 + 12,468 Find the sum of the absolute values. = 13,018 Distance from the iceberg to the Titanic is 13,018 feet.

27. Lesson Quiz Add or subtract using a number line. –2 2. –5 – (–3) 1. –2 + 9 7 Add or subtract. 3. –23 + 42 19 4. 4.5 – (–3.7) 8.2 5. 6. The temperature at 6:00 A.M. was –23°F. At 3:00 P.M. it was 18°F. Find the difference in the temperatures. 41°F