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1 f7 on cross-multiplication Presentation Transcript

  • 1. Cross Multiplication Back to Algebra Pg
  • 2. Cross Multiplication In this section we look at the useful procedure of cross multiplcation.
  • 3. Cross Multiplication In this section we look at the useful procedure of cross multiplcation. Cross Multiplication
  • 4. Cross Multiplication In this section we look at the useful procedure of cross multiplcation. Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below.
  • 5. Cross Multiplication In this section we look at the useful procedure of cross multiplcation. Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below. a b c d
  • 6. Cross Multiplication In this section we look at the useful procedure of cross multiplcation. Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below. a b c d
  • 7. Cross Multiplication In this section we look at the useful procedure of cross multiplcation. Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below. a b c d ad bc
  • 8. Cross Multiplication In this section we look at the useful procedure of cross multiplcation. Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below. Take the denominators and multiply them diagonally across. a b c d ad bc
  • 9. Cross Multiplication In this section we look at the useful procedure of cross multiplcation. Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below. Take the denominators and multiply them diagonally across. What we get are two numbers. a b c d ad bc
  • 10. Cross Multiplication In this section we look at the useful procedure of cross multiplcation. Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below. Take the denominators and multiply them diagonally across. What we get are two numbers. a b c d ad bc Make sure that the denominators cross over and up so the numerators stay put.
  • 11. Cross Multiplication In this section we look at the useful procedure of cross multiplcation. Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below. Take the denominators and multiply them diagonally across. What we get are two numbers. a b c d ad bc Make sure that the denominators cross over and up so the numerators stay put. Do not cross downward as shown here. a b cd bc ad
  • 12. Cross Multiplication In this section we look at the useful procedure of cross multiplcation. Cross Multiplication Many procedures with two fractions utilize the operation of cross– multiplication as shown below. Take the denominators and multiply them diagonally across. What we get are two numbers. a b c d ad bc Make sure that the denominators cross over and up so the numerators stay put. Do not cross downward as shown here. a b cd bc ad
  • 13. Cross Multiplication Here are some operations where we may cross multiply.
  • 14. Cross Multiplication Here are some operations where we may cross multiply. Rephrasing Fractional Ratios
  • 15. Cross Multiplication Here are some operations where we may cross multiply. Rephrasing Fractional Ratios If a cookie recipe calls for 3 cups of sugar and 2 cups of flour, we say the ratio of sugar to flour is 3 to 2,
  • 16. Cross Multiplication Here are some operations where we may cross multiply. Rephrasing Fractional Ratios If a cookie recipe calls for 3 cups of sugar and 2 cups of flour, we say the ratio of sugar to flour is 3 to 2, and it’s written as 3 : 2 for sugar : flour.
  • 17. Cross Multiplication Here are some operations where we may cross multiply. Rephrasing Fractional Ratios If a cookie recipe calls for 3 cups of sugar and 2 cups of flour, we say the ratio of sugar to flour is 3 to 2, and it’s written as 3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is 2 : 3.
  • 18. Cross Multiplication Here are some operations where we may cross multiply. Rephrasing Fractional Ratios If a cookie recipe calls for 3 cups of sugar and 2 cups of flour, we say the ratio of sugar to flour is 3 to 2, and it’s written as 3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is 2 : 3. For most people a recipe that calls for the fractional ratio of 3/4 cup sugar to 2/3 cup of flour is confusing.
  • 19. Cross Multiplication Here are some operations where we may cross multiply. Rephrasing Fractional Ratios If a cookie recipe calls for 3 cups of sugar and 2 cups of flour, we say the ratio of sugar to flour is 3 to 2, and it’s written as 3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is 2 : 3. For most people a recipe that calls for the fractional ratio of 3/4 cup sugar to 2/3 cup of flour is confusing. It’s better to cross multiply to rewrite this ratio in whole numbers.
  • 20. Cross Multiplication Here are some operations where we may cross multiply. Rephrasing Fractional Ratios If a cookie recipe calls for 3 cups of sugar and 2 cups of flour, we say the ratio of sugar to flour is 3 to 2, and it’s written as 3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is 2 : 3. For most people a recipe that calls for the fractional ratio of 3/4 cup sugar to 2/3 cup of flour is confusing. It’s better to cross multiply to rewrite this ratio in whole numbers. Example A. rewrite a recipe that calls for the fractional ratio of 3/4 cup sugar to 2/3 cup of flour into ratio of whole numbers.
  • 21. Here are some operations where we may cross multiply. Rephrasing Fractional Ratios If a cookie recipe calls for 3 cups of sugar and 2 cups of flour, we say the ratio of sugar to flour is 3 to 2, and it’s written as 3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is 2 : 3. For most people a recipe that calls for the fractional ratio of 3/4 cup sugar to 2/3 cup of flour is confusing. It’s better to cross multiply to rewrite this ratio in whole numbers. Example A. rewrite a recipe that calls for the fractional ratio of 3/4 cup sugar to 2/3 cup of flour into ratio of whole numbers. Write 3/4 cup of sugar as and 2/3 cup of flour as 3 4 S 2 3 F. Cross Multiplication
  • 22. Cross Multiplication Here are some operations where we may cross multiply. Rephrasing Fractional Ratios If a cookie recipe calls for 3 cups of sugar and 2 cups of flour, we say the ratio of sugar to flour is 3 to 2, and it’s written as 3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is 2 : 3. For most people a recipe that calls for the fractional ratio of 3/4 cup sugar to 2/3 cup of flour is confusing. It’s better to cross multiply to rewrite this ratio in whole numbers. Example A. rewrite a recipe that calls for the fractional ratio of 3/4 cup sugar to 2/3 cup of flour into ratio of whole numbers. Write 3/4 cup of sugar as and 2/3 cup of flour as 3 4 S 2 3 F. We have the ratio 3 4 S : 2 3 F
  • 23. Cross Multiplication Here are some operations where we may cross multiply. Rephrasing Fractional Ratios If a cookie recipe calls for 3 cups of sugar and 2 cups of flour, we say the ratio of sugar to flour is 3 to 2, and it’s written as 3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is 2 : 3. For most people a recipe that calls for the fractional ratio of 3/4 cup sugar to 2/3 cup of flour is confusing. It’s better to cross multiply to rewrite this ratio in whole numbers. Example A. rewrite a recipe that calls for the fractional ratio of 3/4 cup sugar to 2/3 cup of flour into ratio of whole numbers. Write 3/4 cup of sugar as and 2/3 cup of flour as 3 4 S 2 3 F. We have the ratio 3 4 S : 2 3 F cross multiply we’ve 9S : 8F.
  • 24. Cross Multiplication Here are some operations where we may cross multiply. Rephrasing Fractional Ratios If a cookie recipe calls for 3 cups of sugar and 2 cups of flour, we say the ratio of sugar to flour is 3 to 2, and it’s written as 3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is 2 : 3. For most people a recipe that calls for the fractional ratio of 3/4 cup sugar to 2/3 cup of flour is confusing. It’s better to cross multiply to rewrite this ratio in whole numbers. Example A. rewrite a recipe that calls for the fractional ratio of 3/4 cup sugar to 2/3 cup of flour into ratio of whole numbers. Write 3/4 cup of sugar as and 2/3 cup of flour as 3 4 S 2 3 F. We have the ratio 3 4 S : 2 3 F cross multiply we’ve 9S : 8F. Hence in integers, the ratio is 9 : 8 for sugar : flour.
  • 25. Cross Multiplication Here are some operations where we may cross multiply. Rephrasing Fractional Ratios If a cookie recipe calls for 3 cups of sugar and 2 cups of flour, we say the ratio of sugar to flour is 3 to 2, and it’s written as 3 : 2 for sugar : flour. Or we said the ratio of flour : sugar is 2 : 3. For most people a recipe that calls for the fractional ratio of 3/4 cup sugar to 2/3 cup of flour is confusing. It’s better to cross multiply to rewrite this ratio in whole numbers. Example A. rewrite a recipe that calls for the fractional ratio of 3/4 cup sugar to 2/3 cup of flour into ratio of whole numbers. Write 3/4 cup of sugar as and 2/3 cup of flour as 3 4 S 2 3 F. We have the ratio 3 4 S : 2 3 F cross multiply we’ve 9S : 8F. Hence in integers, the ratio is 9 : 8 for sugar : flour. Remark: A ratio such as 8 : 4 should be simplified to 2 : 1.
  • 26. Cross Multiplication Cross–Multiplication Test for Comparing Two Fractions
  • 27. Cross Multiplication Cross–Multiplication Test for Comparing Two Fractions When comparing two fractions to see which is larger and which is smaller.
  • 28. Cross Multiplication Cross–Multiplication Test for Comparing Two Fractions When comparing two fractions to see which is larger and which is smaller. Cross–multiply them, the side with the larger product corresponds to the larger fraction.
  • 29. Cross Multiplication Cross–Multiplication Test for Comparing Two Fractions When comparing two fractions to see which is larger and which is smaller. Cross–multiply them, the side with the larger product corresponds to the larger fraction. In particular, if the cross multiplication products are the same then the fraction are the same.
  • 30. Cross Multiplication Cross–Multiplication Test for Comparing Two Fractions When comparing two fractions to see which is larger and which is smaller. Cross–multiply them, the side with the larger product corresponds to the larger fraction. In particular, if the cross multiplication products are the same then the fraction are the same. Hence cross– multiply 3 5 9 15
  • 31. Cross Multiplication Cross–Multiplication Test for Comparing Two Fractions When comparing two fractions to see which is larger and which is smaller. Cross–multiply them, the side with the larger product corresponds to the larger fraction. In particular, if the cross multiplication products are the same then the fraction are the same. Hence cross– multiply 3 5 9 15 45 = 45 we get
  • 32. Cross Multiplication Cross–Multiplication Test for Comparing Two Fractions When comparing two fractions to see which is larger and which is smaller. Cross–multiply them, the side with the larger product corresponds to the larger fraction. In particular, if the cross multiplication products are the same then the fraction are the same. Hence cross– multiply 3 5 9 15 45 = 45 so 3 9 = 5 15 we get
  • 33. Cross Multiplication Cross–Multiplication Test for Comparing Two Fractions When comparing two fractions to see which is larger and which is smaller. Cross–multiply them, the side with the larger product corresponds to the larger fraction. In particular, if the cross multiplication products are the same then the fraction are the same. Hence cross– multiply 3 5 9 15 45 = 45 so 3 9 = 5 15 we get 3 5 5 8
  • 34. Cross Multiplication Cross–Multiplication Test for Comparing Two Fractions When comparing two fractions to see which is larger and which is smaller. Cross–multiply them, the side with the larger product corresponds to the larger fraction. In particular, if the cross multiplication products are the same then the fraction are the same. Hence cross– multiply 3 5 9 15 45 = 45 so 3 9 = 5 15 we get Cross– multiply 3 5 5 8
  • 35. Cross Multiplication Cross–Multiplication Test for Comparing Two Fractions When comparing two fractions to see which is larger and which is smaller. Cross–multiply them, the side with the larger product corresponds to the larger fraction. In particular, if the cross multiplication products are the same then the fraction are the same. Hence cross– multiply 3 5 9 15 45 = 45 so 3 9 = 5 15 we get Cross– multiply 3 5 5 8 24 25 we get
  • 36. Cross Multiplication Cross–Multiplication Test for Comparing Two Fractions When comparing two fractions to see which is larger and which is smaller. Cross–multiply them, the side with the larger product corresponds to the larger fraction. In particular, if the cross multiplication products are the same then the fraction are the same. Hence cross– multiply 3 5 9 15 45 = 45 so 3 9 = 5 15 we get Cross– multiply 3 5 5 8 24 25 we get less more
  • 37. Cross Multiplication Cross–Multiplication Test for Comparing Two Fractions When comparing two fractions to see which is larger and which is smaller. Cross–multiply them, the side with the larger product corresponds to the larger fraction. In particular, if the cross multiplication products are the same then the fraction are the same. Hence cross– multiply 3 5 9 15 45 = 45 so 3 9 = 5 15 we get Cross– multiply 3 5 5 8 24 25 Hence 3 5 5 8 is less than we get less more .
  • 38. Cross Multiplication Cross–Multiplication Test for Comparing Two Fractions When comparing two fractions to see which is larger and which is smaller. Cross–multiply them, the side with the larger product corresponds to the larger fraction. In particular, if the cross multiplication products are the same then the fraction are the same. Hence cross– multiply 3 5 9 15 45 = 45 so 3 9 = 5 15 we get Cross– multiply 3 5 5 8 24 25 Hence 3 5 5 8 is less than we get less more . (Which is more 7 11 9 14 or ? Do it by inspection.)
  • 39. Cross Multiplication Cross–Multiplication for Addition or Subtraction
  • 40. Cross Multiplication Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions
  • 41. Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions a b c d ± Cross Multiplication
  • 42. Cross Multiplication Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions a b c d ± = ad ±bc
  • 43. Cross Multiplication Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator. a b c d ± = ad ±bc
  • 44. Cross Multiplication Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator. a b c d ± = ad ±bc bd
  • 45. Cross Multiplication Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator. a ± c ad ±bc = b d bd Afterwards we reduce if necessary for the simplified answer.
  • 46. Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator. a ± c ad ±bc = b d bd Afterwards we reduce if necessary for the simplified answer. Example B. Calculate 3 5 5 6 a. – Cross Multiplication
  • 47. Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator. a ± c ad ±bc = b d bd Afterwards we reduce if necessary for the simplified answer. Example B. Calculate 3 5 5 6 a. – Cross Multiplication
  • 48. Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator. a ± c ad ±bc = b d bd Afterwards we reduce if necessary for the simplified answer. Example B. Calculate 3 5 5 6 – = 5*5 – 6*3 6*5 a. Cross Multiplication
  • 49. Cross Multiplication Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator. a ± c ad ±bc = b d bd Afterwards we reduce if necessary for the simplified answer. Example B. Calculate 3 5 5 6 – = 5*5 – 6*3 6*5 7 30 a. =
  • 50. Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator. a ± c ad ±bc = b d bd Afterwards we reduce if necessary for the simplified answer. Example B. Calculate 3 5 5 6 – = 5*5 – 6*3 6*5 7 30 a. = 5 12 5 9 b. – Cross Multiplication
  • 51. Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator. a ± c ad ±bc = b d bd Afterwards we reduce if necessary for the simplified answer. Example B. Calculate 3 5 5 6 – = 5*5 – 6*3 6*5 7 30 a. = 5 12 5 9 b. – Cross Multiplication
  • 52. Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator. a ± c ad ±bc = b d bd Afterwards we reduce if necessary for the simplified answer. Example B. Calculate 3 5 5 6 – = 5*5 – 6*3 6*5 7 30 a. = 5 12 5 9 – = 5*12 – 9*5 9*12 b. Cross Multiplication
  • 53. Cross Multiplication Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator. a ± c ad ±bc = b d bd Afterwards we reduce if necessary for the simplified answer. Example B. Calculate 3 5 5 6 – = 5*5 – 6*3 6*5 7 30 a. = 5 12 5 9 – = 5*12 – 9*5 9*12 15 108 b. =
  • 54. Cross Multiplication Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator. a ± c ad ±bc = b d bd Afterwards we reduce if necessary for the simplified answer. Example B. Calculate 3 5 5 6 – = 5*5 – 6*3 6*5 7 30 a. = b. = 5 5 12 5 9 – = 5*12 – 9*5 9*12 15 108 36 =
  • 55. Cross Multiplication Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator. a ± c ad ±bc = b d bd Afterwards we reduce if necessary for the simplified answer. Example B. Calculate 3 5 5 6 – = 5*5 – 6*3 6*5 7 30 a. = b. = 5 5 12 5 9 – = 5*12 – 9*5 9*12 15 108 36 = In a. the LCD = 30 = 6*5 so the crossing method is the same as the Multiplier Method.
  • 56. Cross Multiplication Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator. a ± c ad ±bc = b d bd Afterwards we reduce if necessary for the simplified answer. Example B. Calculate 3 5 5 6 – = 5*5 – 6*3 6*5 7 30 a. = b. = 5 5 12 5 9 – = 5*12 – 9*5 9*12 15 108 36 = In a. the LCD = 30 = 6*5 so the crossing method is the same as the Multiplier Method. However in b. the crossing method yielded an answer that needed to be reduced.
  • 57. Cross Multiplication Cross–Multiplication for Addition or Subtraction We may cross multiply to add or subtract two fractions with the product of the denominators as the common denominator. a ± c ad ±bc = b d bd Afterwards we reduce if necessary for the simplified answer. Example B. Calculate 3 5 5 6 – = 5*5 – 6*3 6*5 7 30 a. = b. = 5 5 12 5 9 – = 5*12 – 9*5 9*12 15 108 36 = In a. the LCD = 30 = 6*5 so the crossing method is the same as the Multiplier Method. However in b. the crossing method yielded an answer that needed to be reduced. we need both methods.
  • 58. Cross Multiplication The Double Check Strategy
  • 59. Cross Multiplication The Double Check Strategy One of the most difficult thing to do in mathematics is to know that a mistake had taken place and to locate the mistake.
  • 60. Cross Multiplication The Double Check Strategy One of the most difficult thing to do in mathematics is to know that a mistake had taken place and to locate the mistake. The Double Check is to cross check an answer by doing a problem two different ways.
  • 61. Cross Multiplication The Double Check Strategy One of the most difficult thing to do in mathematics is to know that a mistake had taken place and to locate the mistake. The Double Check is to cross check an answer by doing a problem two different ways. If both methods yielded the same answer then the answer is likely to be correct.
  • 62. Cross Multiplication The Double Check Strategy One of the most difficult thing to do in mathematics is to know that a mistake had taken place and to locate the mistake. The Double Check is to cross check an answer by doing a problem two different ways. If both methods yielded the same answer then the answer is likely to be correct. If two answers are different then we have to clarify the mistake.
  • 63. Cross Multiplication The Double Check Strategy One of the most difficult thing to do in mathematics is to know that a mistake had taken place and to locate the mistake. The Double Check is to cross check an answer by doing a problem two different ways. If both methods yielded the same answer then the answer is likely to be correct. If two answers are different then we have to clarify the mistake. When we + or – fractions, we can use the above two methods to cross check an answer.
  • 64. Cross Multiplication The Double Check Strategy One of the most difficult thing to do in mathematics is to know that a mistake had taken place and to locate the mistake. The Double Check is to cross check an answer by doing a problem two different ways. If both methods yielded the same answer then the answer is likely to be correct. If two answers are different then we have to clarify the mistake. When we + or – fractions, we can use the above two methods to cross check an answer. For example, in part b. above, we obtain an answer via the crossing method.
  • 65. Cross Multiplication The Double Check Strategy One of the most difficult thing to do in mathematics is to know that a mistake had taken place and to locate the mistake. The Double Check is to cross check an answer by doing a problem two different ways. If both methods yielded the same answer then the answer is likely to be correct. If two answers are different then we have to clarify the mistake. When we + or – fractions, we can use the above two methods to cross check an answer. For example, in part b. above, we obtain an answer via the crossing method. Let’s cross check the first answer using the Multiplier Method. 5 12 5 9 –
  • 66. Cross Multiplication The Double Check Strategy One of the most difficult thing to do in mathematics is to know that a mistake had taken place and to locate the mistake. The Double Check is to cross check an answer by doing a problem two different ways. If both methods yielded the same answer then the answer is likely to be correct. If two answers are different then we have to clarify the mistake. When we + or – fractions, we can use the above two methods to cross check an answer. For example, in part b. above, we obtain an answer via the crossing method. Let’s cross check the first answer using the Multiplier Method. Since the LCD = 36, we multiply and divide by 36. 5 12 5 9 –
  • 67. Cross Multiplication The Double Check Strategy One of the most difficult thing to do in mathematics is to know that a mistake had taken place and to locate the mistake. The Double Check is to cross check an answer by doing a problem two different ways. If both methods yielded the same answer then the answer is likely to be correct. If two answers are different then we have to clarify the mistake. When we + or – fractions, we can use the above two methods to cross check an answer. For example, in part b. above, we obtain an answer via the crossing method. Let’s cross check the first answer using the Multiplier Method. Since the LCD = 36, we multiply and divide by 36. 5 12 5 9 ( – ( *36 / 36
  • 68. Cross Multiplication The Double Check Strategy One of the most difficult thing to do in mathematics is to know that a mistake had taken place and to locate the mistake. The Double Check is to cross check an answer by doing a problem two different ways. If both methods yielded the same answer then the answer is likely to be correct. If two answers are different then we have to clarify the mistake. When we + or – fractions, we can use the above two methods to cross check an answer. For example, in part b. above, we obtain an answer via the crossing method. Let’s cross check the first answer using the Multiplier Method. Since the LCD = 36, we multiply and divide by 36. 5 12 5 9 ( – ( *36 / 36 4 3
  • 69. Cross Multiplication The Double Check Strategy One of the most difficult thing to do in mathematics is to know that a mistake had taken place and to locate the mistake. The Double Check is to cross check an answer by doing a problem two different ways. If both methods yielded the same answer then the answer is likely to be correct. If two answers are different then we have to clarify the mistake. When we + or – fractions, we can use the above two methods to cross check an answer. For example, in part b. above, we obtain an answer via the crossing method. Let’s cross check the first answer using the Multiplier Method. Since the LCD = 36, we multiply and divide by 36. 4 3 5 12 5 9 ( – ( *36 / 36 = (5*4 – 5*3) / 36 = 5/36
  • 70. Cross Multiplication The Double Check Strategy One of the most difficult thing to do in mathematics is to know that a mistake had taken place and to locate the mistake. The Double Check is to cross check an answer by doing a problem two different ways. If both methods yielded the same answer then the answer is likely to be correct. If two answers are different then we have to clarify the mistake. When we + or – fractions, we can use the above two methods to cross check an answer. For example, in part b. above, we obtain an answer via the crossing method. Let’s cross check the first answer using the Multiplier Method. Since the LCD = 36, we multiply and divide by 36. 4 3 5 12 5 9 ( – ( *36 / 36 = (5*4 – 5*3) / 36 = 5/36 This is the same as before hence it’s very likely to be correct.
  • 71. Cross Multiplication Comments * The Double Check Strategy is an important tool for learning. It reassures us if we’re heading in the right direction. It warns us that a mistake had occurred so we should back track and locate the mistake.
  • 72. Cross Multiplication Comments * The Double Check Strategy is an important tool for learning. It reassures us if we’re heading in the right direction. It warns us that a mistake had occurred so we should back track and locate the mistake. Use this Double Check Strategy for learning!
  • 73. Cross Multiplication Comments * The Double Check Strategy is an important tool for learning. It reassures us if we’re heading in the right direction. It warns us that a mistake had occurred so we should back track and locate the mistake. Use this Double Check Strategy for learning! * The Multiplier Method and the Cross Multiplication Method are two methods to double check addition and subtraction of small number of fractions.
  • 74. Cross Multiplication Comments * The Double Check Strategy is an important tool for learning. It reassures us if we’re heading in the right direction. It warns us that a mistake had occurred so we should back track and locate the mistake. Use this Double Check Strategy for learning! * The Multiplier Method and the Cross Multiplication Method are two methods to double check addition and subtraction of small number of fractions. These two methods generalize to addition and subtraction of fractional (rational) formulas in later topics.
  • 75. Cross Multiplication Comments * The Double Check Strategy is an important tool for learning. It reassures us if we’re heading in the right direction. It warns us that a mistake had occurred so we should back track and locate the mistake. Use this Double Check Strategy for learning! * The Multiplier Method and the Cross Multiplication Method are two methods to double check addition and subtraction of small number of fractions. These two methods generalize to addition and subtraction of fractional (rational) formulas in later topics. Each method leads to various ways of handling various fractional algebra problems where each way has its own advantages and disadvantage.
  • 76. Cross Multiplication Comments * The Double Check Strategy is an important tool for learning. It reassures us if we’re heading in the right direction. It warns us that a mistake had occurred so we should back track and locate the mistake. Use this Double Check Strategy for learning! * The Multiplier Method and the Cross Multiplication Method are two methods to double check addition and subtraction of small number of fractions. These two methods generalize to addition and subtraction of fractional (rational) formulas in later topics. Each method leads to various ways of handling various fractional algebra problems where each way has its own advantages and disadvantage. We use both methods through out this database.
  • 77. Ex. Restate the following ratios in integers. 1 2 1 3 2 3 1 2 3 4 1 3 1. : 2. 3. 4. : : 2 3 3 4 : 3 5 1 2 1 6 1 7 3 5 4 7 5. : 6. 7. 8. : : 5 2 7 4 : 9. In a market, ¾ of an apple may be traded with ½ a pear. Restate this using integers. Determine which fraction is more and which is less. 2 3 3 4 4 5 3 4 10. , 11. 12. 13. , 4 7 3 5 , 5 6 4 5 , 5 9 4 7 7 10 2 3 14. , 15. 16. 17. , 5 12 3 7 , 13 8 8 5 , 1 2 1 3 1 2 1 3 18. + 19. 20. 21. – 2 3 3 2 + 3 4 2 5 + 5 6 4 7 7 10 2 5 22. – 23. 24. 25. – 5 11 3 4 + 5 9 7 15 – Cross Multiplication C. Use cross–multiplication to combine the fractions.