1. PROPORTION AND SCALE DRAWING

2. Explaining the concept of proportion
Learning Objectives: After implementing this lesson students will be able to:
Explaining the concept of proportion
Determine proportion of two number
Find a size in a map, actual measurement or scale
Find the size of a photo / model or real object
Calculate enlargement factor and reduction factor in scale drawing
The characters building: Discipline, respect, diligence and responsibility.

3. PROPORTION
To be easier in comprehending proportion, see following description.
Mila has 10 books, and Ryan has 4 books.
We can determine the proportion of the number of Mila’s books to the number of Ryan’s books in way follows:
The number of Mila’s books : The number of Ryan’s books
= 10 : 4
2 2
= 5 : 2
So, the proportion of the number of Mila’s books to the number of Ryan’s books is 5 : 2 or can be written

4. The concept of proportion:
If a and b are two quantities which unit the same (similar) then the comparison of a and b is written: a : b or can also be written , with a and b are positive rational numbers

5. PROBLEM EXAMPLES: Express proportion in following problems!
The price of bag is Rp ,00 and the price of shoes is Rp ,00
Answer:
the proportion of price of bag to the price of shoes is
The price of bag : the price of shoes
= :
= 2 : 3
So, the proportion of price of bag to the price of shoes is 2 : 3

6. A rectangle has a width of 80 cm and a length of 1,4 meters.
Express proportion in this problems!
Answer:
because the unit of length of rectangle isn’t similar with the unit of width’s, then we must equate the first unit.
length = 1,4 meters = 1,4 x 100 = 140 cm
The proportion of width to length rectangle is
width rectangle : length rectangle
= 80 : 140
= 4 : 7
So, The proportion of width to length rectangle is 4 : 7

7. Scale = Distance on the map : Real distance.
SCALE DRAWING
The figure behind is a map of the East Kalimantan Province with a scale of
1 : 8,000,000.
It means that 1 cm on the map represents 8,000,000 cm in the actual size. This scale is a ratio of the size on the map to the actual size. In other words 8,000,000 cm in reality will be drawn on the map as 1 cm. 
Scale 1 : 8,000,000
Scale = Distance on the map : Real distance. 

8. PROBLEM EXAMPLES
Look at the map of East Kalimantan. What is the real distance between Tanjung Redeb and Tanjung Selor ! 
Answer:
On the map, measure the distance between Tanjung Redeb and Tanjung Selor. The distance on the map is about 2.7 cm. 
Scale 1 : 8,000,000 
The real distance = 2.7 x 8,000,000 = 21,600,000 
Therefore, the distance between Tanjung Redeb and Tanjung Selor is 21,600,000 cm = 216 km (1 km = 100,000 cm).

9. On the same map, distance between Sengata and Bontang is 1,5 cm
On the same map, distance between Sengata and Bontang is 1,5 cm. What is the real distance between Sengata and Bontang? 
Answer: 
Scale 1 : 8,000,000 
The real distance = 1.5 x 8,000,000
= 12,000,000. 
Therefore, the real distance between Sengata and Bontang is  12,000,000 cm = 120 km (1 km = 100,000 cm). 

10. Let: The distance on the map = x cm.
The distance between Samarinda and Tarakan in East Kalimantan Province is 672 km. Find distance between the cities on the map with scale of 1 : 8,000,000. 
Answer: 
Scale 1 : 8,000,000
Real distance = 672 km = 67,200,000 cm 
Let: The distance on the map = x cm. 
Scale = distance on the map : real distance. 
8,000,000x = 67,200,000 
x =
x = = 8.4 
So, the distance between Samarinda and Tarakan on the map is about 8.4 cm. =

11. On another map, the distance between Surabaya and Banyuwangi is 3 cm
On another map, the distance between Surabaya and Banyuwangi is 3 cm. The real distance between those cities is 120 km. Find the scale of the map !
Answer: 
Distance on the map = 3 cm
Real distance = 120 km = 12,000,000 cm 
Scale = Distance on the map : Real distance. 
= 3 : 12,000,000  (simplified by dividing it by 3) 
= 1 : 4,000,000 
So, the scale of the map is 1 : 4,000,000.   

12. Photos and Scale Models
Before a car or house is constructed, usually a model of that car or house is made. Parts of the car or house have the same ratio as the corresponding parts (namely height, width, and length) of the model.  = =

13. PROBLEM EXAMPLES:
The heights of a door and a window model are 9 cm and 6 cm, respectively. The real height of window is 1 m. What is the real height of the door? 
Answer:
The height of the door model is 9 cm.
The height of the window model is 6 cm.
The real height of the window is 1 m = 100 cm.
The height of the door is x cm. 
6x =  
6x = 900 
x = 150
So, The height of the door is 150 cm.  = =

14. A car model has length 12 cm and width 4 cm
A car model has length 12 cm and width 4 cm. The real length of car is 6 m. What is the real width of the car? 
Answer:
The lengthof the car model is 12 cm.
The width of the car model is 4 cm.
The real length of the car is 6 m = 600 cm.
The real width of the car is x cm. 
12x =  
12x = 2400  (simplified by dividing it by 12)
x = 200
So, The real width of the car is 200 cm.  = =

15. Enlargement Factor and Reduction Factor in scale drawing

16. Poblem Example Answer:
The size of photo A is 4 x 6 and the size of photo B is 2 x 3. What is the ratio of photo A to photo B ? 
Answer:
The size of photo A is 4 x 6, which means 4 cm in width and 6 cm in length.
The size of photo B is 2 x 3, which means 2 cm in width and 3 cm in length.
The ratio of photo B to photo A is 1 : 2.
The size of photo B is as a result of the reduction of times of photo A. Coversely, the size of photo A is the enlargement of 2 times of photo B. 
Thus, the reduction factor of photo A to photo B is
Meanwhile, the enlargement factor of photo B to photo A is 2. = =
and = =

17. EXERCISE State the following proportions in the simplest forms !
5 kg : 4 ounces 
60 : one full rotation
1 hours : 30 minutes 
3 m : 2,500 dm 
A cupboard has a height of 200 cm, a length of 100 cm and a width of 60 cm. If that cupboard is modeled with the height of 20 cm, find the length and the width of the model.
A building which is seen on a television screen is 10 cm in height and 8 cm in width. If the width of building is 42 m, what is its height? 
A football field has a size of 75 m x 110 m. The distance from the penalty point to the goal is 11 metres. 
Make a scale drawing of that field with
the scale 1 : 1,000. 
Find the distance from the penalty point to the goal in your scaled drawing.