1. ADDITION OF REAL NUMBERS CHAPTER 1 SECTION 6 MTH 11203 Algebra

2. Addition of Real Numbers The four basic operations of arithmetic are: 1. Addition 2. Subtraction 3. Multiplication 4. Division Negative numbers: overdrawn bank account, temperatures below zero, coal miner under ground, football lost yards in a play, profit/loss, surplus/deficit.

3. Adding Real Numbers Using a Number Line Using Number line to add numbers.  Represent the first number to be added by an arrow starting at 0  Move the arrow left for a negative number and to the right for a positive number. Any number without a sign in front of it is positive.  The second number is counted from the tip of the first number.  The sum is found at the tip of the second arrow. Example #26 pg 48: -8 + 2 = -6

4. Adding Real Numbers Using a Number Line Example #30 pg 48: -3 + (-5) = -8 Example #36 pg 48: 6 + (-5) = 1

5. Adding Real Numbers Using a Number Line Example #31 pg 48: 6 + (-6) = 0 Example: 6 + (-2) = 4

6. Adding Real Numbers Using a Number Line Example: -7 + (3) = -4 Example: -2 + (-5) = -7

7. Adding Real Numbers Using a Number Line Example: 10 + (-10) = 0 Example: A miner descends 120 feet into a mine shaft. Later, he descends another 145 feet. Find the depth of the miner -120 + (-145) = -265 ft

8. Adding Fractions Adding fraction, where one or more or the fractions are negative 1. Find a common denominator 2. Add the numerators 3. Keep the common denominator Example # 78 pg 48: Use the sign of the larger number

9. Adding Fractions Example: Use the sign of the larger number.

10. Adding Fractions Example # 89 pg 48: When adding two negatives we get a negative answer

11. Adding Fractions Example # 89 pg 48: When adding two negatives we get a negative answer

12. Identify Opposites Opposites or Additive Inverses are any two numbers whose sum is zero. If a is any real number then –a is its opposite, because a + (-a) = 0 Negative signs are thought of as “opposites of” -(-3) = 3 Example #13 pg 48: Write the opposite of 9 The opposite of 9 is -9 because 9 + (-9) = 0

13. Identify Opposites Example #14 pg 48: Write the opposite of -7 The opposite of -7 is 7 because (-7) + 7 = 0 Example #20 pg 48: Write the opposite of -¼ The opposite of -¼ is ¼ because (- ¼ ) + ¼ = 0

14. Identify Opposites Example: Write the opposite of 6 The opposite of 6 is -6 because 6 + (-6) = 0 Example: Write the opposite of -3/5 The opposite of -3/5 is 3/5 because (- 3/5 ) + 3/5 = 0

15. Add Using Absolute Value Rule # 1: Adding Real Numbers with the same sign To add real numbers with the same sign, both positive or both negative, add their absolute values. The sum has the same sign as the numbers being added Example # 49 pg 48:Example # 51 pg 48: 7 + 9 = 16-8 + (-4) = -12 |7| + |9| |-8| + |-4| 7 + 98 + 4 1612 Use the sign of the numbers being added The sum of two positives will always be positive The sum of two negatives will always be negative

16. Add Using Absolute Value Example:Example # 51 pg 48: 12 + 7 = 19 -5 + (-10) = -15 |12| + |7| = 19 |-5| + |-10| 12 + 7 5 + 10 1915 Use the sign of the numbers being added The sum of two positives will always be positive The sum of two negatives will always be negative

17. Add Using Absolute Value Rule # 2: Adding Real Numbers with different sign, one positive and one negative. Subtract the smaller absolute value from the larger absolute value. The sum has the sign of the larger absolute value. Example # 28 pg 48:Example # 44 pg 48: 9 + (-12) = -3 -9 + 13 = 4 |-12| - |9| |13| - |-9| 12 – 9 = 313 – 9 = 4 |-12| is larger, therefore -3|13| is larger, therefore 4 Use the sign of larger absolute value

18. Add Using Absolute Value Example:Example: 13 + (-5) = -8 14 + (-21) = -7 |13| - |5| |21| - |14| 13 – 5 = 821 – 14 = 7 |13| is larger, therefore 8|21| is larger, therefore -7 Use the sign of larger absolute value

19. Add Using Absolute Value Example:Example: -16 + (9) = -7 |16| - |9| 16 – 9 = 7 |16| is larger, therefore -7 Use the sign of larger absolute value

20. Add Using Absolute Value Example: -17.56 + (-19.23) = -36.79 |17.56| + |19.23| 17.56 + 19.23 36.79 |19.23| is larger, therefore -36.79 Use the sign of larger absolute value Appendix A may help with operation with decimals.

21. Add Using Absolute Value Example: The Taggerty Bakery has a profit of $450,567 for the first five months of the year, and a loss of $52,987 for the reminder of the year. Find the net profit or loss for the year. 450,567 + (-52,987) = 397,580 profit |450,567| - |52,987| 450,567 – 52,987 397,580 |450,567| is larger, therefore 397,580 Use the sign of larger absolute value

22. HOMEWORK 1.6 Page 48 - 49 15, 17, 23, 25, 29, 33, 53, 93, 107, 109