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Mastering Subtraction of Real Numbers Using Additive Inverses

In this section, we explore the concept of subtraction of real numbers and how any subtraction problem can be transformed into an addition problem by using the additive inverse. Examples illustrate how to apply this principle, from simple numbers to more complex expressions involving negative numbers. We cover key strategies for evaluating expressions containing multiple operations while adhering to the Order of Operations. Practice problems are included to reinforce learning and ensure a solid understanding of subtracting real numbers.

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Mastering Subtraction of Real Numbers Using Additive Inverses

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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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