Ratio and proportion

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Ratio and proportion

  1. 1. Ratio and Proportion<br />NurinaAyuningtyas<br />WahyuFajar<br />Yan Aditya<br />Yola Yaneta<br />
  2. 2. Ratio and Proportion<br />Do they same?<br />What’s the differ among them?<br /> LET’S CHECK THIS OUT!!!!<br />
  3. 3. Let’s us learn deeply about<br />Ratio & Proportion!!!<br />
  4. 4. Ratio<br />We often encounter things ralated to ratios in daily life, for example:<br />Tony’s age is greater than Rudy’s<br />Rony’s weight is twice of Rino’s<br />The area of Mr.Mike’s field is larger than Mr.Samiden<br />
  5. 5. Ratio<br />Comparing two quantities or more can be performed by two methods., nemely : through difference and division (quotient). <br />For example: Ryo’s age is 18 years and Tyo’s age is 6 years old. Their age can be compared in two methods, namely: <br />
  6. 6. Ratio<br />ACCORDING TO THE DIFFERENCE<br /> Ryo’s age is 12 years older than Tyo’s age, or Tyo’s age is 12 years younger than Ryo’s age.<br /> In this case, the ratio of both children’s ages is done by finding the difference, namely: 18 – 6 = 12<br />
  7. 7. Ratio<br />B. ACCORDING TO DIVISION<br /> Ryo’s age is three times of Tyo’s age. <br /> In this case, the ratio of both children’s ages is done by finding the quotient , namely:<br /> 18 : 6 = 3<br />
  8. 8. RATIO<br />Comparing Two Quantities of the Same Kind<br /> One day Rony and Rina go to shop to buy some pencils. They went at morning, the buy some pencils for a test tomorrow. Rony bought 8 pencils and Rina bought 5 pencils. Now they have 13 pencils to preparing test at tomorrow.<br />
  9. 9. RATIO<br />From the story above ,answer the question below!!!<br />How many pencils does Rony have?<br />How many pencils does Rina have?<br />Record the result on a table!<br />
  10. 10. RATIO<br />
  11. 11. RATIO<br />From the table, we can say that the ratio of Rony’s book to Rina’s book is 8 : 5<br />From the table, we can say that the ratio of Rina’s book to Rony’s book is 5 : 8<br />
  12. 12. RATIO<br />To make a cup of coffee, 2 teaspoons of coffee and 3 teaspoons of sugar are needed. Find the ratio of the coffee to the sugar to make a cup of coffee.<br />The ratio is 2 : 3<br />
  13. 13. RATIO<br /> Find the amount of the coffee and the sugar to make <br />Two cups of coffee<br />Five cups of coffee<br />Eight cups of coffee<br />
  14. 14. RATIO<br />Two cups of coffee<br />To make a cup of coffee, the ratio of coffee to sugar is 2 : 3<br />The sum of coffee and sugar that needed to make two cups of coffee is<br />Cups of coffee times the ratio.<br />2 x 2 teaspoons of coffee = 4 teaspoons<br />2 x 3 teaspoons of sugar = 6 teaspoons<br /> It means that the sum of coffee is 4 teaspoons and the sum of sugar is 6 teaspoons<br />
  15. 15. RATIO<br />Five cups of coffee<br />To make a cup of coffee, the ratio of coffee to sugar is 2 : 3<br />The sum of coffee and sugar that needed to make five cups of coffee is<br />Cups of coffee times the ratio.<br />5 x 2 teaspoons of coffee = 10 teaspoons<br />5 x 3 teaspoons of sugar = 15 teaspoons<br /> It means that the sum of coffee is 10 teaspoons and the sum of sugar is 15 teaspoons<br />
  16. 16. RATIO<br />Eight cups of coffee<br />To make a cup of coffee, the ratio of coffee to sugar is 2 : 3<br />The sum of coffee and sugar that needed to make eight cups of coffee is<br />Cups of coffee times the ratio.<br />8 x 2 teaspoons of coffee = 16 teaspoons<br />8 x 3 teaspoons of sugar = 24 teaspoons<br /> It means that the sum of coffee is 16 teaspoons and the sum of sugar is 24 teaspoons<br />
  17. 17. RATIO<br />We can conclude that RATIO is…<br /> two "things" (numbers or quantities in same unit) compared to each other.<br />
  18. 18. SCALED DRAWING<br />
  19. 19. SCALED DRAWING<br />We often find scaled pictures or models as maps, ground plan of a building house and a model of a car or plane in daily life. The following are several examples of scaled pictures and models.<br />
  20. 20. SCALED DRAWING<br />
  21. 21. Ilustration<br />For example : a father ask his child to draw his rectangular land of 500m for long and 300 m wide. It’s imposibble to draw a piece of land in actual measurement, but congruent to its origin.<br />1 cm represent 100 m so that 500m represented by 5 cm and 300m represented by 3 cm<br />
  22. 22. What is the definition of scaled picture?<br />
  23. 23. A scaled picture is a picture made to represent a real object or situation in a certain measure.<br />With a scaled picture we know object or situation as a whole without watching the actual object.<br />
  24. 24. <ul><li>For example the piece of land in the form of a rectangle 500 m long and 300 m wide is represented by a figure of a rectangle of 5 cm long and 3 cm wide as the figure below.</li></ul>3 cm<br />5 cm<br />
  25. 25. Can you find the scale?<br />To find the scale we can compare between the model picture and the actual measurement.<br />
  26. 26. Based on the explanation above, we can make the following ratio :<br />
  27. 27. The Ratio between the measurement on the model picture and the actual measurement is called scale and formulated as follows<br />
  28. 28. Exercises<br />A map is made to scale of 1 : 200.000, find :<br />The actual distance if the distance on the map is 5 cm.<br />The distance on the map if the actual distance is 120 km.<br />Given on the map that the distance of two towns is 4 cm, while the actual distance is 160 km, Find the scale of the map!<br />
  29. 29. Exercises<br />Answer :<br />30 km<br />60 cm<br />1 : 4.000.000<br />
  30. 30. Factor of Enlargement and Reduction on Scaled Picture and Model<br />What is the factor of Enlargement and Reduction on Scaled Picture and Model?<br />
  31. 31. Factor of Enlargement and Reduction on Scaled Picture and Model<br />What the purpose of this?<br />A very small object can be seen and learned easily if it is enlarged by picture using a certain scale.<br />And the very big object can be reducted by picture using certain scale<br />
  32. 32. For example :A rectangle have long 2 cm and width 1 cm. In order to be clearly seen, the componens is enlarged three times. <br />Length = 2 cm x 3 = 6 cm<br />Width = 1 cm x 3 = 3 cm<br />1 cm<br />3 cm<br />2 cm<br />6 cm<br />
  33. 33. The ratio before and after enlargement :<br />1 cm<br />3 cm<br />2 cm<br />6 cm<br />
  34. 34. 1 cm<br />3 cm<br />2 cm<br />6 cm<br />The enlargement in the example above has a factor of scale 3 or<br />Both have the ratio 3 : 1. It means that all measurement on the shape the product of enlargement represents 3 times of the actual shape.<br />
  35. 35. Story<br />6 cm<br />2 cm<br />4 cm<br />3 cm<br /> A photo have long 3 cm and width 2 cm.<br />Because there are something, the photo’s size become 6 cm of length, 4 cm of width. <br />
  36. 36. What is your <br />6 cm<br />2 cm<br />4 cm<br />3 cm<br />What is the happen of before and after?<br />What is your conclution?<br />What is the enlargement of this picture?<br />
  37. 37. Conclution<br />Factor of scale where k>1 is called factor of enlargement<br />
  38. 38. Story<br />60 cm<br />20 cm<br />2 m<br />6 m<br /> A bus have long 6 m and width 2 m.<br /> If someone want to make a model of bus, so the model of bus made of 60 cm length and 20 cm width.<br />
  39. 39. What you see? <br />What is the reduction of bus and this model?<br />What is your conclution?<br />
  40. 40. Conclution<br />Factor of scale where 0<k<1 is called factor of reduction<br />
  41. 41. Exercises<br />A photograph of 4 cm high and 3 cm wide is enlarged in such away that its width is 6 cm. Find :<br />The factor of scale<br />The height after enlargment<br />Ratio of area before and after enlargement<br />
  42. 42. Exercises<br />Factor of scale =<br /> So the factor of scale is 2 or 2:1<br />The height after enlargement =<br /> Factor of scale x the height of photograph<br /> = 2 x 4<br /> = 8 cm<br />
  43. 43. Exercises<br />c. Ratio of the photograph area before and after enlargement <br />
  44. 44. Proportion<br />
  45. 45. Proportion<br />
  46. 46. Proportion<br />
  47. 47. Proportion<br />
  48. 48. Proportion<br />Olit buys 2 books that have cost $8. If she wants to buy 6 books, how much does it cost she must to pay? <br />So, Olit need to pay $ 24 for six books.<br />Then we can say it “8 dollars for 2 books" equals “24 dollars for 6 books".<br />
  49. 49. Proportion<br />is two ratios set to be equal to each other.<br />
  50. 50. Ratioor Proportion?<br />two out of five <br />This is a …<br />four to every ten <br />This is a …<br />proportion<br />ratio<br />ten to every four <br />This is a …<br />four out of ten<br />This is a …<br />ratio<br />proportion<br />4:10 <br />This is a …<br />ratio<br />
  51. 51. Ratio, Proportion or Fraction?<br />3 Aremaniafans to every 2 Bonekmaniafans <br />This is a …<br />ratio<br />9 girls out of 10 use soap <br />This is a …<br />proportion<br />3 boys out of 10 use deodorant <br />This is a …<br />proportion<br />
  52. 52. Direct Proportion<br />Andi buys a pair of shorts at the price of Rp 15.000,00. The price for two shorts, 3 shorts, and so on can be seen on the following table:<br />
  53. 53. Direct Proportion<br />The table above indicates that the more shorts Andi buys the more money he has to spend. But, the amount of price for each shorts is always the same on each line:<br />
  54. 54. Direct Proportion<br />Henceforth, the equation of the portion of the number of shorts and the portion of prices on two certain lines is always same.<br />Example:<br />The quotient of the ratios on the other two line is: <br />So, the number of shorts and the price always increase or decrease at the same ratio, so that we say there is a direct proportion between the number of shorts and the price.<br />
  55. 55. Direct Proportion<br />THERE’RE TWO METHODS TO CALCULATE A DIRECT PROPORTION:<br />CALCULATION BASED ON UNIT VALUE<br />CALCULATION BASED ON PROPORTION<br />
  56. 56. Calculation Based on Unit Value<br />A car can travel 180 km in 3 hours. How long does the car need to travel 240 km?<br /><ul><li> The time for 180 km = 3 jam
  57. 57. The time for 1 km =
  58. 58. The time to travel 240 km = x 240 = 4 hours</li></li></ul><li>Calculation Based on Proportion<br />Given:<br />From table above, the proportion of the number of shits on this first line to the second is 3:5 or , while the proportion of the price is 75.000 : n or <br />
  59. 59. Calculation based on Proportion <br />The calculation of the price of 5 shirts by using a proportion is as follows. <br />Side term and mid term<br />Cross Multiplication<br />3 : 5 = 75.000 : n<br />or<br />3n = 5 x 75.000<br />3n = 5 x 75.0000<br />n= <br />So, the price of 5 shirts is Rp 125.000,00<br />
  60. 60. Calculation Based on Proportion<br />Based on the example above, on direct proportion, it is valid:<br />If a : b = c : d, hence ad = bc<br />If , hence ad = bc<br />
  61. 61. practice<br />The price of three meters of cloth is Rp 54.000,00. How many maters of cloth is obtained by Rp 144.000,00?<br />The price of 3 kg of apples is Rp 36.000,00. What is the price of 15 kg of apples?<br />
  62. 62. Solution<br />The price of 3 meters of cloth = Rp 54.000,00<br /> The price of 1 meter of cloth =<br /> With Rp 144.000 we can obtain<br /> So, we can obtain 8 meters of cloth.<br />If the number of apples increase, hence the price also increase. It means that the question above represent a direct proportion,<br /> Number of apples (kg) Price (rupiah)<br /> 3 36.000<br /> 15 <br /> So, the price of 15 kg of apples is Rp 180.000,00 <br />
  63. 63. The Graph of Direct Proportion<br />In order that you know the graph of a direct proportion, consider the following description. The table below indicates a relation between the number of chocolate and the price.<br />
  64. 64. The Graph of Direct Proportion<br />
  65. 65. The Graph of Direct Proportion Practice<br />Complete the table above!<br />Make its graph using the same scale!<br />Based on the graph, calculate the distance taken in 2 and a half!<br />
  66. 66. The Graph of Direct Proportion<br />
  67. 67. The Graph of Direct Proportion<br />Solution of c.<br /><ul><li> The distance for 1 hour = 40 km
  68. 68. The distance for 2 hour and a half = x 40 km = 100 km</li></li></ul><li>Inverse Proportion<br />INVERSE PROPORTION<br />
  69. 69. Review : In direct proportions, when one row of a table shows that the proportion gets larger, the numbers in the other row or rows get "proportionally" larger.<br />But, it’s different with inverse proportion. In these proportions, one row gets smaller at the same time that another gets larger.  <br />
  70. 70. Application of Inverse Proportion<br />The speed of Car A is 60 cm/sec. It needs 3 second to go until finish.<br />The speed of Car B is 30 cm/sec. It needs 6 second to go until finish.<br />So, which one the fastest???? Why???<br />
  71. 71. The proportional quotient of the average speed and time proportion <br />on two certain lines always represent multiplication inverse of each.<br />2 is the inverse of ½ <br />
  72. 72. Example<br />12 workers build a wall in 10 hours. How long do 5 worker build the wall?<br />Solution<br />If the number of workers decreases, then the time needed will increase, so that the question above represents an inverse proportion.<br />Number of worker Time<br /> 12 10<br /> 5 n<br />
  73. 73. Exercise<br />Mother distributes cookies to 28 children and each of them gets 4 pieces of cookies. How many cookies does each child get if the cookies are divides to 16 children?<br />

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