1 / 22

MTH 11203 Algebra

MTH 11203 Algebra. Addition of Real Numbers CHAPTER 1 Section 6. Addition of Real Numbers. The four basic operations of arithmetic are: Addition Subtraction Multiplication Division

fay-hart
Download Presentation

MTH 11203 Algebra

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. MTH 11203Algebra Addition of Real Numbers CHAPTER 1 Section 6

  2. Addition of Real Numbers • The four basic operations of arithmetic are: • Addition • Subtraction • Multiplication • 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 • Find a common denominator • Add the numerators • 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 + 9 8 + 4 16 12 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 19 15 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 = 3 13 – 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 = 8 21 – 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

More Related