100 Chapter 2 Integers and Algebraic Expressions Section 2.3 Subtraction of Integers 1. Subtraction of Integers In Section 2.2, we learned the rules for adding integers. Subtraction of integers is defined in terms of the addition process. For example, consider the following subtraction problem. The corresponding addition problem produces the same result. 6 4 2 3 6 142 2 In each case, we start at 6 on the number line and move to the left 4 units. Adding the opposite of 4 produces the same result as subtracting 4. This is true in general. To subtract two integers, add the opposite of the second number to the first number. Subtracting Signed Numbers For two numbers a and b, a b a 1b2. Therefore, to perform subtraction, follow these steps: Step 1 Leave the first number (the minuend) unchanged. Step 2 Change the subtraction sign to an addition sign. Step 3 Add the opposite of the second number (the subtrahend). For example: Subtracting 4 is the same as adding . Subtracting is the same as adding 4. Subtracting Integers Example 1 Subtract. a. 15 20 b. 7 12 c. 40 182 Solution: Add the opposite of 20. a. 15 20 15 1202 5 Change subtraction to addition. b. 7 12 7 1122 19 c. 40 182 40 182 48 4 10 142 10 142 14 10 142 10 142 6 f 4 10 4 10 142 6 10 4 10 142 14 f 5 Start 6 5 4 3 2 1 0 1 2 3 4 6 Rewrite the subtraction in terms of addition. Subtracting 20 is the same as adding 20. Rewrite the subtraction in terms of addition. Subtracting 12 is the same as adding 12. Rewrite the subtraction in terms of addition. Subtracting 8 is the same as adding 8. Concepts 1. Subtraction of Integers 2. Translations and Applications of Subtraction Concept Connections Fill in the blank to change subtraction to addition of the opposite. 1. 9 3 9 2. 9 3 9 3. 9 (3) 9 4. 9 (3) 9 Skill Practice Subtract. 5. 12 19 6. 8 14 7. 30 (3) Answers 1. 3 2. 3 3. 3 4. 3 5. 7 6. 22 7. 33
miller_prealgebra_2e_ch1_3
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