2. Add real numbers. Subtract real numbers. Objectives

3. Vocabulary real numbers number line negative numbers absolute value

4.  All the numbers on a number line are called real numbers.  Number lines can be used to model addition and subtraction of real numbers.  A negative number is any real number whose value is less than zero. They are represented using a negative (-) symbol.

5.  Negative numbers are always represented by a minus (-), or negative sign.  Sometimes the negative sign will be inside or outside of a parenthesis. ◦ Ex: Negative Eight  -8  -(8)  (-8)  Positive numbers will either have a plus (+) sign or no sign. ◦ Ex: Positive Four 44  +(4)  +4

6.  Temperature ◦ -15℉  Money ◦ Debt: Owing money; Negative bank account balance ◦ - $20  Distance below sea level ◦ -67 ft

9.  Ex. 1: On one particularly cold winter day, your thermometer shows that it is 5℉ outside. According to the meteorologist, it will be 10 degrees colder tomorrow. What temperature will it be tomorrow?

10.  Ex. 2: Before going to the movies with a friend, you check your bank account and see that you have a balance of $10. At the movies you end up spending $25 in tickets and food. How much money do you have in your account?

11. Example 1A: Adding and Subtracting Numbers on a Number Line Add or subtract using a number line. Start at 0. Move left to –4. 1110 98 7 654321 0 + (–7) –4+ (–7) = –11 To add –7, move left 7 units. –4 –4 + (–7)

12. Example 1B: Adding and Subtracting Numbers on a Number Line Add or subtract using a number line. Start at 0. Move right to 3. To subtract –6, move right 6 units. -3-20123456 7 89 + 3 3 – (–6) = 9 3 – (–6) –6 –6

13. Add or subtract using a number line. –3 + 7 Check It Out! Example 1a Start at 0. Move left to –3. To add 7, move right 7 units. -3 -2 01234 5 6 7 89 –3 +7 –3 + 7 = 4

14. 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. –3–3 –7–7 11 10 987 6 54 3210 –3 – 7 = –10

16. 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 2101 234 56 6543 -- - -- - |5| = 5|–5| = 5 Absolute Value

17.  Find the absolute value of the following numbers: 1. 12 |12|=12 2. -6 |-6|=6 3. 42 |42|=42 4. -42 |-42|=42

18. Adding/Subtracting Real #’s

19.  Steps: 1. Simplify the signs 2. If the signs are the same, add their absolute values and keep the same sign. 3. If the signs are different, subtract their absolute values and keep the sign of the number with the greater absolute value.

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

21. Additional Example 2: Adding Real Numbers Add. B.–6 + (–2) (6 + 2 = 8) –8–8 Both numbers are negative, so the sum is negative. When the signs of numbers are the same, add the absolute values :

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

23. Check It Out! Example 2c c. 52 + (–68) (68 – 52 = 16) –16 Use the sign of the number with the greater absolute value. Different signs: subtract the absolute values. Add.

25.  Section 1.2 Practice Worksheet  Section 1.2 Questions: ◦ #3, 11, 15, 19-25 odd ◦ #29, 33-37 odd ◦ Use your answer key & selected answers in your student handbook (online) to check your answers! ◦ If you’re having trouble, watch the example lesson tutorial videos.