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Chapter 2: Integers and Introduction to Variables
3. The average of a list of numbers is sum of numbers . number of numbers
ISM: Basic College Mathematics with Early Integers
Exercise Set 2.6 2. −24 = −(2 ⋅ 2 ⋅ 2 ⋅ 2) = −16
4. To simplify 5[−9 + (−3)] ÷ 4, which operation should be performed first? addition
4. (−2)4 = (−2)(−2)(−2)(−2) = 16
5. To simplify −2 + 3(10 − 12) ⋅ (−8), which operation would be performed first? subtraction
6. 5 ⋅ 23 = 5 ⋅ 23 = 5 ⋅ 8 = 40
6. To evaluate x − 3y for x = −7 and y = −1, replace x with −7 and y with −1 and evaluate −7 − 3(−1). 7. In the expression −32 , the base is 3 and the exponent is 2. 8. In the expression (−3)2 , the base is −3 and the exponent is 2.
8. (−1)(−2) + 1 = 2 + 1 = 3 10. 10 − 23 − 12 = 10 + (−23) + (−12) = −13 + (−12) = −25 12. −8 + 4(3) = −8 + 12 = 4 14. 7(−6) + 3 = −42 + 3 = −39 16. (−12) + 6 ÷ 3 = (−12) + 2 = −10
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9. In the expression 4 ⋅ 2 , one base is 2 and its exponent is 3. The other base is 4 and its exponent is 1. 6
10. In the expression 9 ⋅ 5 , one base is 5 and its exponent is 6. The other base is 9 and its exponent is 1. 11. In the expression (−7)5 , the base is −7 and the exponent is 5. 12. In the expression −94 , the base is 9 and the exponent is 4. 13. In the expression 57 ⋅10, one base is 5 and its exponent is 7. The other base is 10 and its exponent is 1. 14. In the expression 28 ⋅11, one base is 2 and its exponent is 8. The other base is 11 and its exponent is 1. 15. A fraction bar means “divided by” and is a grouping symbol. 16. To make sure that the entire value of −2, including the sign, is squared. 17. Finding the average is a good application of both order of operations and adding and dividing integers.
68
18. 5 + 9 ⋅ 4 − 52 = 5 + 36 + (−52) = 41 + (−52) = −11 20.
20 − 15 5 = = −5 −1 −1
22.
88 88 = = −8 −8 − 3 −11
24. 7(−4) − (−6) = −28 − (−6) = −28 + 6 = −22 26. (−24) − 14(2) = −24 − 28 = −52 28. −12 + 33 = −12 + 27 = 15 30. [9 + (−2)]3 = [7]3 = 343 32. 7 ⋅ 6 − 6 ⋅ 5 + (−10) = 42 − 6 ⋅ 5 + (−10) = 42 − 30 + (−10) = 12 + (−10) =2 34. 20 − (−5)2 = 20 − 25 = 20 + (−25) = −5 36.
−3 + 7 ⋅ 7 2 = 4 ⋅ 72 = 4 ⋅ 7 2 = 4 ⋅ 49 = 196
38. 10 ⋅ 53 + 7 = 10 ⋅125 + 7 = 1250 + 7 = 1257 40. 82 − (5 − 2)4 = 64 − (3)4 = 64 − 81 = −17 42. |12 − 19| ÷ 7 = |−7| ÷ 7 = 7 ÷ 7 = 1
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