PROPORTION
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Transcript of PROPORTION
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