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NS1.2 Add, subtract , multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers. NS2.5 Understand the meaning of the absolute value of a number; interpret the absolute value as the distance of the number from zero on a number line; and determine the absolute value of real numbers. California Standards
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When you subtract a positive integer, the difference is less than the original number. Therefore, you move to the left on the number line. To subtract a negative integer, you move to the right . You can also subtract an integer by adding its opposite. You can then use the rules for addition of integers.
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Additional Example 1: Subtracting Integers A. –7 – 4 – 7 – 4 = –7 + (–4) B. 8 – (–5) 8 – (–5) = 8 + 5 C. –6 – (–3) – 6 – (–3) = –6 + 3 = –11 = 13 = –3 Add the opposite of 4. Add the opposite of –5. Add the opposite of –3. Same sign; use the sign of the integers. Same sign; use the sign of the integers. 6 > 3; use the sign of 6. Subtract.
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Check It Out! Example 1 A. 3 – (–6) 3 – (–6) = 3 + 6 B. –4 – 1 – 4 – 1 = –4 + (–1) C. –7 – (–8) – 7 – (–8) = –7 + 8 = 9 = –5 = 1 Add the opposite of –6. Add the opposite of 1. Add the opposite of –8. Same signs; use the sign of the integers. Same sign; use the sign of the integers. 8 > 7; use the sign of 8. Subtract.
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– 9 – y for y = –4 – 9 + 4 – 5 Evaluate the expression for the given value of the variable. – 9 – y – 9 – (–4) Substitute –4 for y. Add the opposite of –4. 9 > 4; use the sign of 9. Additional Example 2A: Evaluating Expressions with Integers
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n – 6 for n = –2 n – 6 – 2 – 6 Substitute –2 for n. Evaluate the expression for the given value of the variable. – 2 + (–6) – 8 Add the opposite of 6. Same sign; use the sign of the integers. Additional Example 2B: Evaluating Expressions with Integers
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|8 – j | + |–2| for j = –6 |8 – j| + |–2 | |8 – (–6) | + |–2| Substitute –6 for j. Evaluate the expression for the given value of the variable. |14| + |–2| 14 + 2 Add the opposite of –6. 8 + 6 = 14. Additional Example 2C: Evaluating Expressions with Integers |8 + 6| + |–2| The absolute value of 14 is 14, and the absolute value of –2 is 2. Add. 16
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– 5 – r for r = –2 – 5 + 2 – 3 Evaluate the expression for the given value of the variable. – 5 – r – 5 – (–2) Substitute –2 for r. Add the opposite of –2. 5 > 2; use the sign of 5. Check It Out! Example 2A
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a – 7 for a = –9 a – 7 – 9 – 7 Substitute –9 for a. Evaluate the expression for the given value of the variable. – 9 + (–7) – 16 Add the opposite of 7. Same sign; use the sign of the integers. Check It Out! Example 2B
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|11 – m | + 7 for m = –3 |11 – m| + 7 |11 – (–3) | + 7 Substitute –3 for m. Evaluate the expression for the given value of the variable. |14| + 7 14 + 7 Add the opposite of –3. 11 + 3 = 14. Check It Out! Example 2C |11 + 3| + 7 The absolute value of 14 is 14. Add. 21
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The top of the Sears Tower, in Chicago, is 1454 feet above street level, while the lowest level is 43 feet below street level. How far is it from the lowest level to the top? Additional Example 3: Architecture Application 1454 – (–43) Subtract the lowest level from the top. 1454 + 43 Add the opposite of –43. 1497 Same sign; use the sign of the integers. It is 1497 feet from the lowest level to the top.
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The distance from the high dive to the swimming pool is 10 feet. The pool is 12 feet deep. What is the total distance from the high dive to the bottom of the pool? Check It Out! Example 3 10 – (–12) Subtract the depth of the pool from the height of the high dive. 10 + 12 Add the opposite of –12. 22 Same sign; use the sign of the integers. It is 22 feet from the diving board to the bottom of the pool.
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Lesson Quiz Subtract. 1. –6 – (–4) – 2 – 6 9 2. –3 – 3 3. 4 – (–5) Evaluate each expression for the given value of the variable. 4. 9 – s for s = –5 14 5. –4 – w + 5 for w = 21 – 20 6. Suretta is flying in an airplane and rises an additional 20 feet. Then she descends 190 feet toward the ground. How far below her original height did Suretta go? 170 feet
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