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Understanding Ratios: Examples and Applications in Geometry and Proportional Reasoning

This guide explores the concept of ratios through various practical examples, including the ratio of length to width in rectangles, calculating the perimeter and area ratios, and applying map scales to determine real-life distances. It covers direct and inverse proportion scenarios, highlighting the relationships between quantities. With detailed calculations and explanations, this resource is ideal for students and anyone interested in mastering ratios and proportions in geometry and everyday life.

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Understanding Ratios: Examples and Applications in Geometry and Proportional Reasoning

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  1. PROPORTION

  2. I. R A T I O EXAMPLES : 1. 40 cm 60 cm We can say that the ratio of length to width is 60 : 40 = 3 : 2

  3. 2. Given two rectangle the first has length 12 cm and width 9 cm the second has length 15 cm and width 12 cm. find the ratio of : a. Perimeter b. the area

  4. ANSWER : Perimeter = 2 ( length + width ) P = 2 ( l + w ) The area = length x width A = l x w

  5. So that : The ratio of perimeter is 2 ( 12 + 9 ) : 2 ( 15 + 12 ) 2 x 21 : 2 x 27 21 : 27 7 : 9

  6. The ratio of area is : 12 x 9 : 15 x 12 9 : 15 3 : 5

  7. SCALED DRAWINGS DISTANCE ON THE MAP SCALE THE REAL DISTANCE

  8. DISTANCE ON THE MAP THE REAL DISTANCE SCALE = THE REAL DISTANCE = DISTANCE ON THE MAP DISTANCE ON THE MAP SCALE = SCALE x THE REAL DISTANCE

  9. EXAMPLES : 1. The distance between Jakarta and Bandung is 180 km, if distance on the map is 12 cm find the scale !!

  10. ANSWER : Real distance = 180 km = 18,000,000 cm Scale = distance on the map : real distance = 12 : 18,000,000 = 1 : 1,500,000 The scale of the map is = 1 : 1,500,000

  11. 2. The distance Surabaya and jakarta is 360 km, find the distance on the map if the scale is 1 : 2,400,000 !

  12. ANSWER : Real distance = 360 km = 36,000,000 cm Scale = 1 : 2,400,000 = Distance on the map = scale x real distance 1 2,400,000

  13. 1 = 360 : 24 = 15 Distance on the map = 15 cm Distance on the map = X 36,000,000 2,400,000

  14. 3. Distance between Depok and Bogor on the map is 4 cm. find the real distance if the scale on the map is 1 : 750,000

  15. Distance on the map Real distance = Scale THE SOLUTION : = = 4 x = 3,000,000 = 30 km Distance between Depok and Bogor is 30 km 4 1 750,000 750,000 1

  16. PHOTOS AND SCALED MODELS Examples : 1. a photo has length 12 cm and width 8 cm if the length to be 9 cm find its width ! Answer : = 4x = 24 = = x = 6 l of big photo w of big photo l of small photo w of small photo 12 8 4 8 9 x 3 x

  17. 12 8 9 X = 12x = 72 x = 6 width of foto is 6 cm

  18. 2.A hotel has length 32 m and height 80 m if height on the photo is 10 cm, find : a. length hotel on the photo b. scaled. = answer : a. 32 m = 3200 cm 800x = 320 80 m = 8000 cm x = 4 so, length hotel on the photo is 4 cm 3200 8000 10 x

  19. Distance on the map Realdistance b. Scale = = = So , Scale = 1 : 800 10 8000 1 800

  20. DIRECT PROPORTION EXAMPLES : 1. the price of 3 mathematics books is Rp 60,000.00 , if Joko buys 7 books, how many rupiahs must Ali pays for ? and, how many rupiahs will Ali pay for if he buy only 2 books ?

  21. ANSWER : 3x = 7 x 60000 = 3x = 420000 x = 140000 So, The price of 7 books is Rp 140,000.00 3 60000 7 x

  22. 1 3 3 60000 x 60000 x Next : = 3x = 120000 x = 40000 So, the price of 2 books is Rp 40,000.00 or: find price of 1 book = 3x = 60000 x = 20000 7 books 7 x 20000 = 140000 3 books 2 x 20000 = 40000 2

  23. INVERSE PROPORTION Examples 1. Ita has some money she wants to buy pencils. If she wants to buy then the price is Rp 2,000.00 , she will get 6 pencil. How many pencils will Ita get, if she wants to buy that the price of pencil is Rp 1,500.00 ? answer = 15x = 120 x = 8 so, ita get 8 pencil 2000 x 6 1500

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