PROPORTION

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

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

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

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

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

SCALED DRAWINGS

DISTANCE ON THE

MAPTHE REAL DISTANCE

SCALE

SCALE =

THE REAL DISTANCE =

DISTANCE ON THE MAP

DISTANCE ON THE MAP

THE REAL DISTANCE

DISTANCE ON THE MAP

SCALE

= SCALE x THE REAL DISTANCE

EXAMPLES :

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

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

2. The distance Surabaya and jakarta

is 360 km, find the distance

on the map if the scale is

1 : 2,400,000 !

ANSWER : Real distance = 360 km = 36,000,000 cm Scale = 1 : 2,400,000

= Distance on the map = scale x real distance

2,400,000

1

= 360 : 24 = 15 Distance on the map = 15 cm

Distance on the map = 2,400,000

X 36,000,000

1

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

THE SOLUTION :

=

= 4 x = 3,000,000 = 30 km Distance between Depok and Bogor is 30 km

Distance on the map

ScaleReal distance =

750,00014

1750,000

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

x

w of small photow of big photo

l of small photol of big photo

89

12x8

34

= 12x = 72 x = 6 width of foto is 6 cm

X9812

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

108000

x3200

b. Scale =

=

=

So , Scale = 1 : 800

Real distance

Distance on the map

800010

8001

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 ?

ANSWER :

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

Book PRICE ( Rp )3 60,000.007 ?2 ?

x

60000

7

3

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

x60000

23 60000x

31

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

price pencil

2,000 61,500 x

6x

15002000