PROPORTION

PROPORTION AND SCALE DRAWING

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.

PROPORTIONTo 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= 10 : 4

2 2= 5 : 2So, the proportion of the number of Mila’s books to the

number of Ryan’s books is 5 : 2 or can be written

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

PROBLEM EXAMPLES:Express proportion in following problems!

1. The price of bag is Rp. 80.000,00 and the price of shoes is Rp. 120.000,00

Answer:the proportion of price of bag to the price of shoes isThe price of bag : the price of shoes

= 80.000 : 120.000= 80.000 : 120.000

40.000 40.000= 2 : 3So, the proportion of price of bag to the price of

shoes is 2 : 3

2. 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 iswidth rectangle : length rectangle

= 80 : 14020 20

= 4 : 7So, The proportion of width to length rectangle is 4 :

7

SCALE DRAWINGThe 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. 

PROBLEM EXAMPLES

1. 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).

2. 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). 

3. 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.

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4. 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.   

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. 

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PROBLEM EXAMPLES:1. 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 = 9 . 100  6x = 900  x = 150

So, The height of the door is 150 cm. 

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2. 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 = 4 . 600  12x = 2400  (simplified by dividing it by 12) x = 200

So, The real width of the car is 200 cm. 

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Enlargement Factor and Reduction Factor

in scale drawing

Poblem ExampleThe 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. o 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

EXERCISE1. State the following proportions in the simplest

forms !  a) 5 kg : 4 ounces b) 60 : one full rotation c) 1 hours : 30 minutes d) 3 m : 2,500 dm 

2. 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.

3. 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? 

4. A football field has a size of 75 m x 110 m. The distance from the penalty point to the goal is 11 metres.  a) Make a scale drawing of that field with

the scale 1 : 1,000.  b) Find the distance from the penalty point to the

goal in your scaled drawing.