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MTH 11203 Algebra

MTH 11203 Algebra. Subtraction of Real Numbers CHAPTER 1 Section 7. 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 )

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MTH 11203 Algebra

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  1. MTH 11203Algebra Subtraction of Real Numbers CHAPTER 1 Section 7

  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 thena – 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 = 4 12 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 = -22 24 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 ba + (-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 - 5 same 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

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