1. SUBTRACTION OF REAL NUMBERS CHAPTER 1 SECTION 7 MTH 11203 Algebra

2. Subtract Numbers Any subtraction problem can be rewritten as an addition problem using the additive inverse. If a and b represent any two real numbers then a – b = a + (-b) In other words to subtract b from a, add the opposite or additive inverse of b to a.

3. Subtract Numbers Example # 14 pg 58: 17 – (+8) = 17 + (-8) = 9 Example # 16 pg 58: 9 – 4 = 9 + (-4) = 5 Example # 18 pg 58: -6 - 3 = -6 + (-3) = -9 Example: 8 – (+3) = 8 + (-3) = 5

4. Subtract Numbers Example: 7 – 10 = 7 + (-10) = -3 Example # 16 pg 58: 6 – 2 = 6 + (-2) = 4 Example # 18 pg 58: -11 - 13 = -11 + (-13) = -24 Example: 27.54 – 29.86 = 27.54 + (-29.86) = -2.32

5. Subtract Numbers When we subtract a negative number, we can replace the two negative signs with a plus sign. Example # 24 pg 58: 9 – (-9) = 9 + 9 = 18 Example # 31 pg 58: 6 – (-3) = 6 + 3 = 9 Example # 41 pg 58:The difference in 12 and 8 is 4 -8 – (-12) = -8 + 12 = 412 is larger so positive answer

6. Subtract Numbers Example: 15 – (-19) = 15 + 19 = 34 Example: 6 – (-5) = 6 + 5 = 11 Example:The difference in 24 and 2 is 22 -24 – (-2) = -24 + 2 = -2224 is larger so negative answer

7. Subtract Numbers Example: Subtract 16 from 5 5 – 16 = 5 + (-16) = -11 Example: Subtract 33 from 33 33 – 33 = 33 + (-33) = 0 Example: Subtract -7.38 from 3.59 3.59 – (-7.38) = 3.59 + 7.38 = 10.97

8. Subtract Fractions Example # 70 pg 58: Example # 87 pg 58:

9. Subtract Fractions Example:

10. Subtract Fractions Example:

11. Evaluate Expression Containing More Than Two Numbers Work from left to right unless parentheses or other grouping symbols appear. Remember the Order of Operations. Parentheses, Exponents, Multiply or Divide, Add or Subtract. The expression “Please Excuse My Dear Aunt Sally” may help you remember In General, any real numbers a and b a + (-b) = a – b and a – (-b) = a + b

12. Evaluate Expression Containing More Than Two Numbers Example # 118 pg 58: -7 + 6 – 3 -1 – 3 same as -1 + (-3) -4 Example # 122 pg 58: -2 – 7 – 13 same as -2 + (-7) + (-13) -9 – 13 same as -9 + (-13) -22

13. Evaluate Expression Containing More Than Two Numbers Example: -6 - 13 - 5 same as -6 + (-13) -19 - 5same as -19 + (-5) -24 Example: -7 – (-3) + (-13) + (-2) same as -7 + 3 -4 + (-13) + (-2) same as -4 + (-13) -17 + (-2) -19

14. Evaluate Expression Containing More Than Two Numbers Example # 126 pg 58: -9 – 3 – (-4) + 5 -9 – 3 -12 – (-4) same as -12 + 4 -8 + 5 -3 Example # 127 pg 58: 17 + (-3) – 9 – (-7) same as 17 – 3 14 – 9 same as 14 + (-9) 5 – (-7) same as 5 + 7 12

15. Evaluate Expression Containing More Than Two Numbers You can also simplify first then evaluate Example # 129 pg 58: -9 + (-7) + (-5) – (-3) -9 – 7 – 5 + 3 -16 – 5 + 3 -21 + 3 -18

16. HOMEWORK 1.7 Page 58 - 59 13, 15, 21, 23, 38, 46, 57, 61, 65, 69, 107, 120, 131