Chapter Two Integers ASSIGNMENT EXERCISES. +1 H 4. + I 6. + J 8. 4 K 10. 5 C 1. 6 B 14. 5, 0, 8, etc. 16. 0 18. For any integer, there is always at least one smaller 0. 0 >. 5 < 8 4. 1 < 8 6. 8 8 8. 0 0 0. +8 8. 5 5 4. The opposite of 8 is 8. 6. Zero has no opposite. 8. The opposite of 1 is +1. 40. The opposite of 156 is 156. 4. The opposite of 19 is +19. 44.-48. 50. III 5. + ( 8) 11 Like signs, add, use common sign. 54. 7 + 1 5 Unlike signs, subtract, use sign of larger absolute value. 56. 7 + ( 11) 4 Unlike signs, subtract, use sign of larger absolute value. 58. 6 + 6 0 These are opposites, so subtract absolute values. Zero has no sign. 60. 7 + 0 7 Zero added to a number does not change that number. 6. ( 7) + 7 0 Different signs, subtract. Zero has no sign. 64. +$56,87 + ( $8,956) $17,916 66. +5,000 8,000 7,000 Feet 68. $18 $4 $60 18
184 CHAPTER : INTEGERS 70. 8 5 8 + ( 5) 7. 7 ( ) 7 + (+) 5 Change subtraction sign to addition.change sign of subtrahend.add. Change subtraction sign to addition. Change sign of subtrahend. Add numbers with unlike signs. 74. 1 + + ( 8) 5 15 + ( 8) 5 7 5 76. 8 0 8 Subtracting zero from an integer results in the same number with the same sign. 78. 0 Subtracting an integer from zero results in the opposite of the number. 0 + ( ) 80. 5 5 10 8. +7 ( 8 ) 65 Same sign, add, use common sign 84. 47 ( 8 ) 19 86. 10 7 ft 88. 7 1 90. ( )(+) 6 Like signs give positive product. Unlike signs give negative product. 9. 7() 1 94. 0(5) 0 Unlike signs give negative product. Multiplying by zero results in zero. 96. 5( )( 1)( ) 0 Since the number of negative factors is odd, the product is negative. 98. ( ) ( )( ) +9 A negative number raised to an even-numbered power is positive. 100. ( 4) ( 4)( 4)( 4) 64 A negative number raised to an odd-numbered power is negative. 10. ( ) 8 104. 7( $.00) $14.00 $14.00 Change in price over 7 weeks. 106. 8 (5) 8 10 108. 8 ( 4) + Multiply, add, different signs negative. Like signs give positive quotient. 110. 18 9 Like signs give positive quotient. 11. 14 7 Different signs give negative quotient. 114. 16 4 4 116. 118. 0 0 8 10. 84 +4 Like signs give positive quotients. 51 17
COLLEGE MATHEMATICS FOR TECHNOLOGY 185 Zero divided by any non zero number is zero. 51 10. 17 1. 8 19 14. +,97 1,57,791 +,87 + 18,90 +,09 61,70 16. ( 1) Perform operations in parentheses. ( ) Multiply. 4 + ( 1 ) ( ) ( 1 ) 18. 0 4 ( ) Multiply and Divide. 5+ 6 Add. 1 0 + 4 + ( ) 0 4 ( ( ) ) 10. 7+ ( 4 6) Perform operations in parentheses. 7+ ( ) 7+ 6 Multiply. Add. 1 7 + ( 4 6 ) 7 + ( 4 6 ) 1. ( ) +1 8 7 + 1 8 6 8 6 + ( 8) 4 Exponentiation. Addition.
186 CHAPTER : INTEGERS + x y + 1 8 ( ( ) ) ^ + 1 8 14. 8 4( 6 ) + 7 5 8 4( 6+ ) + 7 5 10 4( 8) 5 Grouping. Multiplication and division. Subtraction. + ( 5) 7 4 ( 6 + ) ( 8 + ) ( 7 5 ) calculator steps (optiopn ): 4 ( ( ) 6 ) ( 8 + ) ( 7 5 ) 16. 71+ ( 19) 71 57 71+ ( 57) Multiply. 18 71 + + 19 + ( ) 71 + ( ( ) 19 ) 18. (a) 10 6 17,576,000 (b) 6 6 08,915,776 Chapter Concepts Analysis 1. Multiplication and division use the same rules for handling the signs: like signs give positive product or quotient, different signs give negative product or quotient.
COLLEGE MATHEMATICS FOR TECHNOLOGY 187. Absolute value is the distance a number is from zero without regard to direction. 5 5 0 0. Division by zero is not defined. 4. To add integers having unlike (different) signs: (1) Subtract the smaller absolute value from the larger absolute value. () Give the sum the sign of the number with the larger absolute value. 5. The symbol used for "is greater than" is ">": 5> 6> 7 1> 6. The order of operations with integers is: (1) Parentheses used as groupings and other grouping symbols. () Exponents (powers and roots). () Multiplications and divisions in order of occurrence from left to right. (4) Additions and subtractions in order of occurance from left to right. 7. A negative number raised to an even-numbered power is positive. A negative number raised to an odd-numbered power is negative. ( 5) +5 ( 4) 64 8. To multiply two integers having like signs: (1) Multiply their absolute values. () Make the sign of the product positive. ( )( 4) +1 or 1 9. -- 0 5 8 10. ( 8) () 16 () 1 () 6 correction: ( 8) +64 since ( 8) ( 8) +64 Multiplication before subtraction. ( 8) () 64 () 64 6 58 Chapter Trial Test. < 4. 1 1 6. 8 8+ ( ) 10 Change sign of subtrahend. Adding numbers with like signs: add, keep common sign. 8. 8 4 Dividing integers with unlike signs: divide absolute values, negative quotient.
188 CHAPTER : INTEGERS 10. 6 Dividing integers with like signs: positive. 1. 7 ( ) 7 + 10 Change sign of subtrahend. Add. 14. 7 + ( ) 10 Adding integers with like signs; add, sum has a common sign. 16. 0 0 Division of zero by a non zero integer results in zero. 18. + 5+ 0+ + ( 5) + 0+ + ( 5) + + ( 5) 4+ ( 5) 1 0. 4( 1) 5 Multiplying integers with unlike signs gives negative product.. 6 6 Dividing integers with unlike signs gives negative quotient. 1 4. + 10() + 6(7) + 0 + 4 + 4 64 8. 5( ) + 16 4 5( + ( )) + 16 4 5( 1) + 16 4 5 + 4 1 6. 10 4 6 + ( ) 1 5 ( ) + 16 4 5 ( ) + 16 4
COLLEGE MATHEMATICS FOR TECHNOLOGY 189 0. 18 6 calculator options: 18 + or 18 + a b c display 18 then 6. or ( ) 18 ENTER. 5; 5 Their absolute values are the same. Answers will vary. 4. 1 + 9, answers will vary. 6. 14 4 56