54 Chapter 1 The Set of Real Numbers Section 1.5 Subtraction of Real Numbers Concepts 1. Subtraction of Real Numbers 2. Translations 3. Applications Involving Subtraction 4. Applying the Order of Operations 1. Subtraction of Real Numbers In Section 1.4, we learned the rules for adding real numbers. Subtraction of real numbers is defined in terms of the addition process. For example, consider the following subtraction problem and the corresponding addition problem: 6 5 4 3 2 1 0 1 2 3 4 5 6 In each case, we start at 6 on the number line and move to the left 4 units. That is, adding the opposite of 4 produces the same result as subtracting 4. This is true in general.To subtract two real numbers, add the opposite of the second number to the first number. Subtracting Real Numbers If a and b are real numbers, then . Subtracting 4 is the same as adding Subtracting is the same as adding 4. 10 4 10 142 14 10 142 10 142 14 10 142 10 142 6 Subtracting Integers Example 1 4 Subtract the numbers. a. b. c. d. Solution: a. b. 4 192 6 9 11 152 7 10 4 192 6 9 4 192 13 6 192 15 Take the opposite of 9. Take the opposite of 9. Change subtraction to addition. Change subtraction to addition. 11 152 7 10 c. d. 11 152 6 7 1102 3 Take the opposite of 5. Take the opposite of 10. Change subtraction to addition. Change subtraction to addition. Skill Practice Subtract. 1. 1 132 2. 2 2 3. 6 1112 4. 8 15 4. 10 4 10 142 6 a b a 1b2 Start 6 4 2 3 6 142 2 f f Answers 1. 4 2. 4 3. 5 4. 7
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