CHAPTER 3 ADDING AND SUBTRACTING FRACTIONS

3.1 Adding and Subtracting Like Fractions 83 CHAPTER 3 ADDING AND SUBTRACTING FRACTIONS 3.1 Adding and Subtracting Like Fractions 3.1 Margin Exercises 1. (a && The denominators are the same, so & and & are like fractions. (b The denominators are different, so and are unlike fractions. (c ( ( The denominators are the same, so and are like fractions. (d 2. (a ' The denominators are different, so and ' are unlike fractions. (b ƒ ƒ * & * Lowest terms (b '! (! ' ( *!! & & & &! (c & (d ' & ' * 3.1 Section Exercises 1. 3. 5. 7. 9. & & ' ' ' ' ƒ ƒ *!! Lowest terms * * ƒ '!!!!! ƒ & & * Add (c (d 3. (a numerators. The denominator stays the same. & ( * * ' ' ' ' ƒ ' ƒ!!!! ƒ!! ƒ & Lowest terms Lowest terms & & ƒ ' ' ' ' 'ƒ 11. 13. 15. 17. * ƒ * * * * *ƒ ' '!!!!! & & & & & & & ( ( ƒ ƒ & & & & & ƒ & ƒ (

84 Chapter 3 Adding and Subtracting Fractions 19. 21. 23. 25. 27. 29. 31. ( (!! ' * * ' 'ƒ!!!!! ƒ & ( ( ( ƒ ƒ ( ( (! *! ( * ( * ƒ!!!!! ƒ & ( & ( & ƒ' ( ' ' ' ' ' ƒ ' ' ' ( ( ( ( '' ''ƒ' '! '! '! '! '! ƒ '!! 33. Three steps to add like fractions are: 1. Add the numerators of the fractions to find the numerator of the sum (the answer. 2. Use the denominator of the fractions as the denominator of the sum. 3. Write the answer in lowest terms. 35. Add the two amounts to find the total fraction raised. & & ( * * * * They raised ( * of their target goal. 37. Add the two amounts to find the total fraction saved. & ( ( ( ( He saved & ( of the amount needed. 39. First, add the two fractions of land that were purchased. * *!!!! Next, subtract the fraction of land that was planted in carrots. ( ( &!!!! acre is planted in squash. 3.2 Least Common Multiples 3.2 Margin Exercises 1. (a The multiples of & are &ß!ß &ß!ß &ß!ß &ß!ß á. (b The multiples of are ß 'ß ß ß!ß ß &'ß á. (c Look at the answers for (a and (b.! is the only number found in both lists, so it is the least common multiple. 2. (a and & The multiples of & are &ß!ß &ß!ß á. The first multiple of & that is divisible by is!, so the least common multiple of the numbers and & is!. (b and * The multiples of * are *ß ß (ß 'ß &ß á. The first multiple of * that is divisible by is *, so the least common multiple of the numbers and * is *. (c ' and The multiples of are ß 'ß ß ß!ß ß á. The first multiple of that is divisible by ' is, so the least common multiple of the numbers ' and is. (d and ( The multiples of ( are (ß ß ß ß &ß ß á. The first multiple of ( that is divisible by is, so the least common multiple of the numbers and ( is. 3. (a & and & & To find the LCM of & and, we'll start with the factors of,. Now & only has and & as factors and we already have a in the LCM, so we just need to include a &. LCM & *! The least common multiple of & and is *!.

3.2 Least Common Multiples 85 (b and!! & LCM & '! The least common multiple of and! is '!. 4. (a ' and & & & LCM &! The least common multiple of and & is!. & (b and ' ' ( LCM ( The least common multiple of ' and is. & ( (c ß ßand * * LCM ( The least common multiple of *,, and is (. 5. (a ß ß * * LCM ( The least common multiple of,, and * is (. (b ß 'ß ' LCM The least common multiple of, ', and is. (c *ß 'ß * ' LCM The least common multiple of *, ', and is. (d &ß!ß!ß! & &! &! &! & LCM &! The least common multiple of &,!,!, and! is!. 6. (a The least common multiple of ' and & is the product of the numbers on the left side. LCM &! (b The least common multiple of! and ' is the product of the numbers on the left side. LCM &! 7. (a ß 'ß and! y '! &y & y y & The LCM of, ', and! is &!. (b & and! & y! & y! & y! & &y & & & The LCM of & and! is &!. (c * and * y * y * y ' * y The LCM of * and is (.

86 Chapter 3 Adding and Subtracting Fractions (d ß ß and y y y ' y ( y ( y The LCM of,, and is ( '.? 8. (a ' Divide ' by, getting. Now multiply both the numerator and the denominator by of by. '? (b & Divide & by, getting &. Now multiply both the numerator and the denominator by of by &. &! & & (? (c ' Divide by ', getting. Now multiply both the ( numerator and the denominator by of ' by. ( ( ' ' '? (d Divide by, getting. Now multiply both the ' numerator and the denominator by of by. ' ' 3.2 Section Exercises 1. and ' Multiples of ': 'ß ß ß ß!ß á ' is the first number divisible by. Ð'ƒ Ñ The least common multiple of and ' is '. 3. and & Multiples of &: &ß!ß &ß!ß &ß á & is the first number divisible by. Ð& ƒ &Ñ The least common multiple of and & is &. 5. and * Multiples of *: *ß ß (ß 'ß &ß á ' is the first number divisible by. Ð' ƒ *Ñ The least common multiple of and * is '. 7. and ( Multiples of (: (ß ß ß ß &ß á is the first number divisible by. Ð ƒ (Ñ The least common multiple of and ( is. 9. ' and! Multiples of!:!ß!ß!ß!ß &!ß á! is the first number divisible by '. Ð! ƒ ' &Ñ The least common multiple of ' and! is!. 11.! and &! Multiples of &!: &!ß!!ß &!ß!!ß &!ß á!! is the first number divisible by!. Ð!! ƒ! &Ñ The least common multiple of! and &! is!!. 13. ß!! &y & y & The LCM of and! is &!. 15. ß!! '! &y & y & The LCM of and! is & '!.

3.2 Least Common Multiples 87 17. 'ß *ß ' * y y y* ' * y y The LCM of ', *, and is '. 19. ß 'ß ß! '! & LCM &! The LCM of, ',, and! is!. 21. ß &ß ß! & &! & LCM &! The LCM of, &,, and! is!. 23. ß!ß ß 'ß ' 25. 27. 29. 31.! & ' ' LCM & (! The LCM of,!,, ', and ' is (!.? ƒ '? ƒ ' ' ' &? ƒ' '! ' '? 'ƒ ' '? 33. 'ƒ ' ' (? 35. ƒ ( (? 37. 'ƒ' ' ' ' ' '? 39.!ƒ& &!! *? 41. &'ƒ( ( &' * * ( ( ( &' (? 43. ƒ ( (? 45. ƒ *'? 47. ƒ ' * ' * ( ' ' * 49. Answers will vary. A sample answer follows: It probably depends on how large the numbers are. If the numbers are small, the method using multiples of the largest number seems best. If the numbers are larger, or if there are more than two numbers, then the factorization method will be better. 51. & ß!!!! Multiples of!!:!!ß '!!ß &!!ß á '!! is the first number divisible by!!. Ð'!! ƒ!! *Ñ The LCM of the denominators is '!!.

88 Chapter 3 Adding and Subtracting Fractions 53.!* ß & * & * (&' *' ( * * * y ' * y * y ( ( * ( y ( The LCM of the denominators is ( (!,&Þ 55. Fractions with the same denominators are like fractions and fractions with different denominators are unlike fractions. 56. To subtract like fractions, first subtract the numerators to find the numerator of the difference. Write the denominator of the like fractions as the denominator of the difference. Finally, write in lowest terms. 57. The least common multiple (LCM of two numbers is the smallest whole number divisible by both of those numbers. 58. The smallest number in both lists is!, so! is the least common multiple of and!. 59. &ß (ß ß! & & ( ( (! & LCM & ( (! The LCM of &, (,, and! is (!. 60. &ß ß!ß & & & &! & & & LCM & & &! The LCM of &,,!, and & is &!. 61. & &! & LCM &! The LCM of,, &,, and! is!.! is a common multiple, but it is not the least common multiple. 62. The least common multiple can be no smaller than the largest number in a group and the number ('! is a multiple of && Ð('! ƒ && ÑÞ 3.3 Adding and Subtracting Unlike Fractions 3.3 Margin Exercises 1. (a Step 1 ÐLCD Ñ ( Step 2 (b Step 1 ÐLCD Ñ ' ' ' ( Step 2 (c Step 1 ÐLCD!Ñ &! '! ' ' * Step 2 &!!!!! & (d Step 1 ÐLCD Ñ '! ' ' &!! Step 2 ' 2. (a Step 1! &!! & Step 2!!!! & Step 3! & & (b Step 1 & & Step 2! & (c Step 1! '!!!! &! & Step 2!!!!! Step 3! &

3.3 Adding and Subtracting Unlike Fractions 89 & 3. (a ( ( ( (b ' ' ' ' & & 4. (a Step 1 & & Step 2 ' & (b Step 1 &!! ' & ' & Step 2!!!! ( ( 5. (a ' &! (b ' ' * 3.3 Section Exercises 1. 3. 5. ' LCD is 8 ' ( ' LCD is 9 * * * ' * * * * ' LCD is 20!!!! * '! & In lowest terms! 7. 9. 11. 13. 15. 17. 19. 21. 23. & LCD is 40 &!! &! *! & & LCD is 36 * ' ' & ' ' & * LCD is 15 & & & & * & & * LCD is 36 * ' ' ' * ' * ' ' LCD is 20! &!!!! '! (! &! LCD is 30 & '!!! &!!! LCD is 8! LCD is 48 ' ' & & LCD is 6 ' ' ' & ' In lowest terms '

90 Chapter 3 Adding and Subtracting Fractions 25. 27. 29. 31. 33. 35. LCD is 6 ' ' ' ' In lowest terms '! LCD is 15 & & &! & ( & & & LCD is 12 & In lowest terms ' (! LCD is 45 * & & &! & * & ( ( & & LCD is 40 &!!!! LCD is 48 ' ' ( 37. The widest blades have widths and. The difference is inch. 39. Subtract the area used for general admission from the total area. LCD is 40! & & &! (! The fraction of the total area used for reserved ( seating is.! 41. Add the fractions to find the total length. &! ' &!!! &! '!! The total length of the screw is! LCD is 40 inch. 43. First add to find the amount used. * * ( Then subtract to find the amount remaining. ( ( ( The fraction of the tank of fuel that remains is. 45. Answers will vary. A sample answer follows: You cannot add or subtract until all the fractional pieces are the same size. For example, halves are larger than fourths, so you cannot add until you rewrite as. 47. Add the time spent in class and study. ( ( ' of the student's day was spent in class and study. 49. One way to compare fractions accurately is to rewrite each fraction with a common denominator. ( ß ß ß ß ' The fraction with the largest numerator is the largest fraction. This is or, which is Work and Travel. To find the number of hours, multiply. y y hours were spent on work and travel. Note that this is just the numerator in the equivalent fraction. Now add the fractions for Work and Travel and Class. ' ' ' ' ' The fraction of the day spent on these activities is Þ

3.4 Adding and Subtracting Mixed Numbers 91 51. First add the lengths on either side of the hole. ' Then subtract this length from the total length. & & & ' ' ' ' ' The diameter is ' inch. 3.4 Adding and Subtracting Mixed Numbers 3.4 Margin Exercises 1. (a * Ã Whole number part * Ã Remainder (b (c * Ã ' Ã 4 Whole number part Remainder ' ' * 4 * (d ( ( ( 2. (a Estimate: Exact: ( ( ( ' ' * * * * (b & &! Estimate: ' Exact: ' * & & ( &!!!! (c Estimate: Exact: ( ( & * * ' * * 3. (a Estimate: Exact:! * * ( ( ' & & & ' ' ' ( (b Estimate: Exact: ' & & & &! * & ( & ( ( ( ( ( & & & & 4. (a Estimate: Exact: ( ( ( ' & & & ' ' Regroup: ' ( ( ' ' ' ' ' ' ' ' ' ' ' & ' ' (b Estimate: Exact: &! & ' & & ' ' Regroup:!!! '! ' ' ' ' ' ' ' continued

92 Chapter 3 Adding and Subtracting Fractions ' ' & ' ' (c Estimate: & ' * Regroup: Exact: & ' * * * & * * * * ' * & * ( ( 5. (a &! ( ( & ( (b ' &' & 3.4 Section Exercises 1. Estimate: Exact: ' & & ' * ' & ' 3. Estimate: Exact: ( ( ( ' ' ' ' 5. Estimate: Exact: & & ( & * * * & & 7. Estimate: Exact: & & ' * & '! '! ' ' 9. Estimate: Exact: ' &! * & &! &! & & &!!! 11. Estimate: Exact: & & & ( ( & & ( ( 13. Estimate: Exact: ' &! * & &! ( (!! &&! && & & &!! '

3.4 Adding and Subtracting Mixed Numbers 93 15. Estimate: Exact: ( ( & & 17. Estimate: Exact:! & & & ( & 19. Estimate: Exact: *!! ' ' ' &! (! 21. Estimate: Exact: ( ( (! ' & Regroup: ( ' ' ' ' &! 23. Estimate: Exact: & *! ' ' & & &! Regroup: & &! & & ( ( (!!!!! ( &! & '! *! 25. Estimate: Exact:! * * * Regroup:! *! * ( & ' ' 27. ( ( * 29. ' & ' ' ' ' '* ' ' ' 31. ' ( ( ' ' ' & ' ' * 33. ' 35. ( & ' '& ( 37. ' ' ' & '

94 Chapter 3 Adding and Subtracting Fractions & (! 39. ( ( ( & ( * ( 41. ( &' ( ' 43. * & &! & (&!!* * &!! & & 45. ' ( ( &' (* ' 47. Find the least common denominator. Change the fraction parts so that they have the same denominator. Add the fraction parts. Add the whole number parts. Write the answer as a mixed number. 49. Subtract from & to determine the difference. Estimate: ' & feet!! Exact: & * & The current world record is first world record. & & feet taller than the 51. The longest wrench is and the second to shortest wrench is. Subtract to find the difference. Estimate: * inches ' Exact: & & The longest wrench is inches longer than the second to shortest wrench. 53. The three longest wrenches measure,, and. Add to find the total length. Estimate: '' inches Exact: '& '& '' The total length of the three longest wrenches is '' inches. 55. The largest hose clamp is and the smallest hose clamp is * '. Subtract to find the difference. Estimate: inches Exact: ' * * ' ' ' The largest hose clamp is ' inches larger than the smallest hose clamp. 57. Add the four measurements. Estimate: ' * *! ft Exact: & &!! ( ( * Andre needs * feet of fencing to go around the garden.

3.4 Adding and Subtracting Mixed Numbers 95 59. Add the lengths of the four sides. Estimate: & & in. Exact:! ' The craftsperson needs ' inches of lead stripping. 61. Subtract the amounts used from the total amount. Estimate:!!! * *! gallons Exact: Add up the amounts used.!! ( ( ' * * ( ( Now subtract from 100. There are &!! ** ( ( & gallons of water remaining. 63. Subtract the known lengths from the total length. Estimate: &(! & * * ft Exact: Add up the lengths of the known sides. '!(!( &! &! & & * *& *& *( Now subtract from &(. &( *(! The length of the fourth side is! feet. 65. Add the weights. Estimate: &* ( * & ( tons Exact: & & & & &! ' ' ' ' * * & & ' ' The total weight is tons. ' 67. First add the two given portions of the line. ' Then subtract to find the unknown length. ( ( * * ' ' ' ' ' ' ' The unknown length is inches. '

96 Chapter 3 Adding and Subtracting Fractions 69. Add the length of the sections at each end. ' ' ( ( * ( ( Then subtract this total from the total length of the arrow. * * The unknown length is inches. &? 71. (a &ƒ* ' * & '! * * ' & (? (b ƒ ( ( &? (c!ƒ &! & & &!? (d! ƒ & &! ' & &! 72. When rewriting unlike fractions as like fractions with the least common multiple as a denominator, the new denominator is called the least common denominator, or LCD. 73. (a (b (c & & & * & &( & &( &! '! '! '! '! & ( * ' ' ' (d ( 74. A common method for adding or subtracting mixed numbers is to add or subtract the fraction parts and then add or subtract the whole number parts. 75. Another method for adding or subtracting mixed numbers is to first change the mixed numbers to improper fractions. After adding or subtracting, write the answer as a mixed number in lowest terms. This method is difficult to use if the mixed numbers are large. 76. (a First Method: & & ' ( ( & ( ( Second Method: &! '( ' &' (b First Method: &!! ( & &!!! ' *' Second Method: & &! ( ( &&!!! Both methods give the same answer. Preferences will vary. A sample answer follows: When a problem requires regrouping, it is easier to change all the numbers to improper fractions. Otherwise, adding the whole numbers and then adding the fractions seems easier.

3.5 Order Relations and the Order of Operations 97 3.5 Order Relations and the Order of Operations 3.5 Margin Exercises 1. (a (c & 2. (a is to the left of on the number line, & so is less than. 3. & (b is to the right of on the number line, so is greater than. (c! is to the left of on the number line, so! is less than.! ( (d is to the right of on the ( number line, so is greater than. (a (b (c (d ( (** LCD is 8 ** ' ( ' ( ** & LCD is 72 ** * ( &! and ( * ( (! & ( ( * *** ( LCD is 12 ** * ( ( and ( * ( * ** LCD is 30! ** & * ( and!! &! ( *!!! & 4. (a Π' (b Π* ' (c ΠΠΠΠy y y y (d ΠΠ& ΠΠ& & & & & y y & & &y y& * & & 5. (a y y ΠΠ* * y y & LCD is 18 *! * y (b ΠΠy & & y y &! ( ( y (c ΠΠy Π( LCD is 12 (

98 Chapter 3 Adding and Subtracting Fractions (d ˆ & ' 3.5 Section Exercises 1. 12. 13. 15. 17. 19. 21. 23. Œ & & ƒ ' ' & & ' ' & y & ' ' y & ** LCD is 8 ** &** LCD is 12 '** &! '! & ' & ** LCD is 24 ** &! * and! * & ( ** LCD is 36 ** ( and ' ' ( ' ' ** & LCD is 18 ** * &! *! & * ( ** LCD is 100 &! **! ( ( '& and &!!!!!! ( '& (!!!! &!! 25. Œ * 27. Œ & & & & ' 29. Œ * ' 31. Œ ' & & & & & 33. Œ & ' ' 35. Œ &' 37. Answers will vary. A sample answer follows: A number line is a horizontal line with a range of numbers placed on it. The lowest number is on the left and the greatest number is on the right. It can be used to compare the size or value of numbers. 39. ÐÑ ' ÐÑ ' ' ' 41. '! 43. Œ 45. Œ Œ Œ y y '

3.5 Order Relations and the Order of Operations 99 47. Œ Œ & Œ Œ & & & ' & & ' ' y y y y & & &y y& y' y' * 49. ' Œ Œ ' Œ Œ y 'y y y y y y y 51. & & y & y y Œ Œ Œ Œ & y LCD is 10 &!!! &! 53. Œ ' 55. Œ Œ ' ' ' ' y 'y LCD is 8 59. Œ ( ƒ Œ ( ' ƒ ƒ y y 61. Œ y y y y y y Œ 63. Œ Œ ƒ Œ Œ ƒ ' ' ' Œ ' * y y ' y' y * LCD is 16 ' * ' ' & ' 65. Œ ( Œ Œ ( Œ & y * y y y' & 57. * * * * ƒœ ƒœ ƒ *y y y y*

100 Chapter 3 Adding and Subtracting Fractions & 67. Œ Œ Œ * ' & Œ Œ Œ * * Œ * y y * y y ' ** & 69. LCD is 150 & **! & & and & &!! &! & & &! &! &! &! in Atlanta is greater. 71. When comparing the size of two numbers, the symbol means is less than and the symbol means is greater than. 72. (a To identify the greater of two or more fractions, we must first write the fractions as like fractions and then compare the numerators. The fraction with the greater numerator is the greater fraction. (b Answers will vary. A sample answer follows: ß ß ß & &! ' ' ( 73. 1. Do all operations inside parentheses or other grouping symbols. 2. Simplify any expressions with exponents and find any square roots. 3. Multiply or divide proceeding from left to right. 4. Add or subtract proceeding from left to right. & 74. Œ Œ ƒ &! & Œ Œ ƒ!! & & Œ ƒ! & *! & & y y * y! & y & LCD is 45 * &! & & & For Exercises 75 80, see the number line following Exercise 80. 75. Œ 76. Œ 77. Œ & & & * * ( & & & Use & & to help place the answer on the number line. 78. Œ & & ' Use number line. & & * ' ' 79. ' to help place the answer on the

Summary Exercises on Fractions 101 & ( & ( 80. Œ Œ ƒ Œ Œ ƒ & & Œ ƒ & & ' & & y ' y & & ' & ' & ' ' &( ' &' ( Use ' to help place the answer on the number line. Summary Exercises on Fractions 1. is a proper fraction since the numerator is less than the denominator.! 3.! is an improper fraction since the numerator is greater than or equal to the denominator. 5. 7. 9.!! ƒ ' & ' ' ƒ ' ' & & ƒ & & & ƒ & ( y y y y & y &' ( & ( & & 11. &' & y &! & & 13. ƒ & & &! ( yy & & y& y! ( ( ' ' ( ( ' 15. ' ( 17. 19. ( & (! (! ' & ( &!! 21. Estimate: Exact: ( * ' ( ( 23. & Estimate: ' *' y ( * Exact: & =!( y ( 25. ' ƒ Estimate: (ƒ ( && Exact: ' ƒ ƒ && && ( ' ' 27. Estimate: Exact: ' & &! * 29. Estimate: Exact: * & & &! '!! & * & & & & 31. Estimate: Exact: ( ( ( ( ' &

102 Chapter 3 Adding and Subtracting Fractions 33. 35. Œ Œ & & & & y & & y & & Œ ' * ' &! & & 37. *ß ß 39. 41. 43. * LCM ( The LCM of *,, and is (. &? ƒ' ( ' ( & ' ' (? '!ƒ & '! & && & '! ' ** LCD is 60! **! ' ' and! '!! '! ' ' '! '!!! Chapter 3 Review Exercises 1. 2. 3. 4. 5. 6. & & ' ( ( ( ( ( * * * * ' & & ' ' ' ' & &!!!! & & & ' '! '! ' 7. ' ' ' ' ' ' & 8. (& (& (& (& 9. Add to find what fraction of his total income comes from the two activities. ( ( of his total income comes from the two activities. 10. Subtract to find the answer. They completed 11. &ß Multiples of &: & & Web page less in the afternoon. &ß!ß &ß!ß &ß!ß á! is the first number divisible by. (! ƒ & The least common multiple of & and is!. 12. ß Multiples of : ß ß ß 'ß!ß ß á is the first number divisible by. ( ƒ The least common multiple of and is. 13.!! & y '! & y y& & & y & LCM & '! 14. y y y y y y LCM 15. 'ß ß &ß & ' & & & & LCM &! The LCM of ',, &, and & is!.

Chapter 3 Review Exercises 103 16. & y * y! & y * y! & * &y & y y& & & y & LCM &! 17. 18. 19. 20. 21. 22. 23. 24. 25. 26.? ƒ? &'ƒ ( &' ( ( &'? &ƒ& & & & &! & & &? ƒ* * * * & * * *?!ƒ& &!! &? 'ƒ' ' '! ' ' ' ' ' ' & ' & &!!!! &! & (! &! & & & & & ( 27. 28. ' ' * ' ( ' 29. Add the fractions. *! &! & '!!! ( *!! of the total students participated in these activities. 30. Add the fractions. * ' of her business comes from these three categories. 31. Estimate: Exact: & & * ' 32. Estimate: Exact: ' * & & & * *! ( ( * * *

104 Chapter 3 Adding and Subtracting Fractions 33. Estimate: Exact: *! &! & &!! & &!! '!!!!!! 34. Estimate: Exact: * & ( ( 35. Estimate: Exact: ' & & 36. Estimate: Exact: & ' (* ( & ' ' (* ( ' ( & 37. & & &! ( ( (!!! * *!! * &( 38. ( ' & & &! &! 39. & ( ( * 40. ' ' & * * ' ' '! ' ' & &! 41. ' & ( ( ' ' ' & & ' ' & '&! 42. & & ' '( * 43. Subtract the uphill and downhill distances from the total distance. Estimate: * ' (' miles Exact: Add the uphill and downhill distances. & & & & ( ( Now subtract from. ( & * The level portion of the course was 44. Add to find the total weight. Estimate: * & & tons & * miles. Exact: * ( & & & & & The total weight of the newspapers was tons. & &

Chapter 3 Review Exercises 105 45. Add to find the total weight. Estimate: *! (' pounds ( Exact: * * ' ' & & The total weight of the three largemouth bass was & pounds. 46. Subtract the two parcels from the total amount she needs. Estimate: * acres 47. 50. 51. 52. Exact: Add the two parcels. ' ' ' ( ( ' ' ' Now subtract from 1 2. ' ( ( ' ' ' She needs to buy an additional acres. ** LCD is 12 ** * and * ** ( LCD is 8 ** ' ' ( ( ' 53. 54. 55. 56. 57. 58. ** ( LCD is 30 ** & & ( and! &! & (!! & ( ** LCD is 30! ** & ( ' and!! &! ' (!!! & * ** & LCD is 16 ' ** &! ' *! * & ' ' ' ( ** LCD is 100! ** & ( & and!!! &!! & (!!!!! & * ** * LCD is 108 ' ** & * &( * & and '! &! &( & * *!! ' & * ** ( LCD is 660 ** && * *& ( and ''! && ''! *& * ( ''! ''! && 59. Œ 60. Œ * 61. Œ (!!!!!!! 62. Œ!*'

106 Chapter 3 Adding and Subtracting Fractions 63. Œ y y y y 64. Œ y y ( ' 65. Œ Œ y y y y y y y y ' 66. 67. Œ ( ( ' ƒœ ƒœ ( ( ƒ (y y y ( y Œ Œ ' 68. Œ Œ & ' Œ LCD is 64 ' ' ' * & ' ' 69. [3.1] ( ( ' 70. [3.1] ( (!!!! & 71. [3.3] * & *! *! * ' 72. [3.3] & & & ' ' ' ' ' ' 73. [3.4] ' ' ' ' ' 74. [3.4] * * ' ' & & & ' 75. [3.4] ( ' & & & 76. [3.4] &! & &!! & & '!!!!!! 77. [3.4] & ( & & ( ( ' 78. [3.3] ( ' ' 79. [3.5] Œ y y y Œ & y y & & & y &!

Chapter 3 Review Exercises 107 80. [3.5] ƒœ ƒœ ƒ y y y y 81. [3.5] Œ Œ Œ Œ ' ' ' y 3 1 y 6 2 * 82. [3.5] Œ Œ & Œ Œ ' & * * * * ( * ( ( ( ** ( 83. [3.5] LCD is 12 ** ( ( ** & 84. [3.5] LCD is 72 *** ' & & and * ( ( ' & & ( ( * ( ** ' 85. [3.5] LCD is 60! ** '! (! '! ' ( ' '! '!! '! &** ( 86. [3.5] LCD is 120 **! & (& ( ' and!!! (& ' & (!!! 87. [3.2] ß ' *y * y LCM ' 88. [3.2] ',,!, '! & LCM &! 89. [3.2] *,, * y y * ( y ( y ( y ( y ( ( LCM ( '? 90. [3.2] (ƒ * ( * * ( *? 91. [3.2] ƒ * *!? 92. [3.2] (&ƒ& & & (& & '! & (& 93. [3.4] Subtract the amounts of wire mesh from the total length of the roll. Estimate: * &( feet Exact: Add the amounts of wire mesh. & ( Now subtract from *. continued

108 Chapter 3 Adding and Subtracting Fractions ' * * * ( ( ( & & & &' ( After completing the two jobs, &' ( feet of wire mesh remain. 94. [3.4] Multiply to determine the total amount of sugar available. Then subtract the amounts of sugar used. Estimate: &!!! pounds of sugar!! '* (( pounds of sugar Exact: Add the amounts of sugar used. ' ' & & (' (' (( (( ( Now subtract from!!. & Chapter 3 Test!! ** ( ( & pounds of sugar remain. 1. & & ' 2. ( ( ' ' ' ' 3. ( (!!!! & 4. ( & ( & ' 5. ß ß y y y y y LCM The LCM of,, and is. 6. 'ß ß &ß & ' & & & & LCM &! The LCM of ',, &, and & is!. 7. 'ß *ß (ß ' ' * ( ' LCM! The LCM of ', *, (, and ' is!. 8. LCD is 8 & & & 9. LCD is 36 * ' ' & ' ' ( ' 10. LCD is 24 ' & ' & 11. LCD is 40 &!! ' &!! & 12. ( ' Estimate: & & & Exact: ( ( ' ' ' * ' ' 13. ' & Estimate: ' ' Exact: ' ' & & & &!! & & &

Chapter 3 Test 109 14. * & Estimate: * *! & Exact: '! * * & '!! '! * * * * *! '! '! '! 15. Estimate: ' Exact: & & 16. Probably addition and subtraction of fractions is more difficult because you have to find the least common denominator and then change the fractions to the same denominator. 17. Round mixed numbers to the nearest whole number. Then add or subtract to estimate the answer. The estimate may vary from the exact answer but it lets you know if your answer is reasonable. 18. Add the number of pounds. Estimate:! & (! pounds Exact: *!! &! ' ' ' *! The total number of pounds used was!. 19. Subtract the number of gallons that were used from the amount the contractor had when he arrived to find the number of gallons remaining. Estimate: '* ( ' ' gallons Exact: Add the number of gallons that were used. ' ' ( ( ' & & & &!! Now subtract from (. ( ( ' & & & & ( The number of gallons remaining is & (. ** ( 20. LCD is 24 ** ( ( * ** ( 21. LCD is 72 ** ' * &( ( and ( ' ( &( * ( ( ( ' 22. Π& Π& & y ( y 23. ΠΠ( ( * ( LCD is 48 ' ( ( ( ( 24. ΠΠ' ' ' ( ' y ( ' y (

110 Chapter 3 Adding and Subtracting Fractions 25. & & y y Œ ' ' y Œ y & ' & ' ' & ' ' ' Cumulative Review Exercises (Chapters 1 3 1. &', *, & is in the millions place. is in the ten-thousands place. * is in the thousands place. is in the hundreds place. LCD is 6 2. To the nearest ten: &*,! Next digit is or less. Tens place does not change. All digits to the right of the underlined place are changed to zero. &*,!! To the nearest hundred: &*,! Next digit is or less. Hundreds place does not change. All digits to the right of the underlined place are changed to zero. &*,!! To the nearest thousand: &*,! Next digit is & or more. All digits to the right of the underlined place are changed to zero. Add *. Write! and carry. '!,!!! 3. Estimate: Exact:!,!!!!,!!!!,!!! ' / / '/ ' / /,/ (/ '/ * (, * 4. Estimate: Exact: &!!!!!,!!! &, &!& ( (! & & &! to 5. * (&,** &,( &(*', &&'!*,, & / * 6.,*'/, &/!/ /,!*,! (,!,' * & 7. &ÐÑÐÑ!ÐÑ '! 8. *' (' * ' ' '*,! 9. &!!!!! 10.,'( ƒ & &, ' ( à *' à *' à *' ' * R 11. To find the perimeter, add the six measurements of the four sides. Estimate:! * &! * &' ft Exact: * & * &'ft The perimeter of this parking space is ' feet. 12. To find the area of the parking space, multiply the length ( and the width (. Estimate:!!!! ft Exact: ( & The area of the parking space is & ft.

Cumulative Review Exercises (Chapters 1 3 111 13. Multiply the length and the width to find the area. Estimate: ' yd Exact: ( y y The area of the pool table is yd. 14. Multiply the height of the person by!. Estimate: (!! *!! in. Exact: (!!! ', &! * A human could jump * inches high. 15. ' * 16. & ÐÑ & ÐÑ & ' * 17. È & & * '& & * ' & & ' &! ' 18. 19. 20.! Œ Œ & & & & & ƒœ ƒœ ' ' & ƒ ' ' y * y &! ( ( Œ Œ ( * ' * ' ' ' ' * ' ' ' ' ' ' ' ' ( ' ' 21. y y y y 22. ( y ( ( ( ' y 23. y& &! y& ƒ &! & y! y! ' ' 24. * *ƒ ( 25. Estimate: Exact: & ( ( 26. Estimate: Exact: ' 27. Estimate: Exact: 28 31. 32. 33. ( &! ( ( & & ' & & & ** & LCD is 40 &** & & and &!! & &!! & ( ** LCD is 20! ** &! ( & (!!!

112 Chapter 3 Adding and Subtracting Fractions 34. ( ** LCD is 36 ** ( and ' ' ( ' '