ratio and proportion
TRANSCRIPT
Ratio and Proportion
Nurina AyuningtyasWahyu FajarYan AdityaYola Yaneta
Ratio and Proportion
1. Do they same?2. What’s the differ among them?
LET’S CHECK THIS OUT!!!!
Let’s us learn deeply aboutRatio & Proportion!!!
Ratio
We often encounter things ralated to ratios in daily life, for example:a.Tony’s age is greater than Rudy’sb.Rony’s weight is twice of Rino’sc. The area of Mr.Mike’s field is larger than
Mr.Samiden
Ratio
Comparing two quantities or more can be performed by two methods., nemely : through difference and division (quotient).
For example: Ryo’s age is 18 years and Tyo’s age is 6 years old. Their age can be compared in two methods, namely:
Ratio
A.ACCORDING TO THE DIFFERENCE
Ryo’s age is 12 years older than Tyo’s age, or Tyo’s age is 12 years younger than Ryo’s age.
In this case, the ratio of both children’s ages is done by finding the difference, namely: 18 – 6 = 12
Ratio
B. ACCORDING TO DIVISION
Ryo’s age is three times of Tyo’s age.
In this case, the ratio of both children’s ages is done by finding the quotient , namely:
18 : 6 = 3
RATIO
One day Rony and Rina go to shop to buy some pencils. They went at morning, the buy some pencils for a test tomorrow. Rony bought 8 pencils and Rina bought 5 pencils. Now they have 13 pencils to preparing test at tomorrow.
Comparing Two Quantities of the Same Kind
RATIO
From the story above ,answer the question below!!!
1. How many pencils does Rony have?2. How many pencils does Rina have?
Record the result on a table!
RATIO
Rony’s pencils Rina’s pencils
8 pencils 5 pencils
RATIO
From the table, we can say that the ratio of Rony’s book to Rina’s book is 8 : 5
From the table, we can say that the ratio of Rina’s book to Rony’s book is 5 : 8
RATIO
To make a cup of coffee, 2 teaspoons of coffee and 3 teaspoons of sugar are
needed. Find the ratio of the coffee to the sugar to make a cup of coffee.
The ratio is 2 : 3
RATIO
Find the amount of the coffee and the sugar to make
1. Two cups of coffee2. Five cups of coffee3. Eight cups of coffee
RATIO
Two cups of coffee
To make a cup of coffee, the ratio of coffee to sugar is 2 : 3
The sum of coffee and sugar that needed to make two cups of coffee is
Cups of coffee times the ratio.2 x 2 teaspoons of coffee = 4 teaspoons2 x 3 teaspoons of sugar = 6 teaspoons
It means that the sum of coffee is 4 teaspoons and the sum of sugar is 6 teaspoons
RATIO
Five cups of coffee
To make a cup of coffee, the ratio of coffee to sugar is 2 : 3
The sum of coffee and sugar that needed to make five cups of coffee is
Cups of coffee times the ratio.5 x 2 teaspoons of coffee = 10 teaspoons5 x 3 teaspoons of sugar = 15 teaspoons
It means that the sum of coffee is 10 teaspoons and the sum of sugar is 15 teaspoons
RATIO
Eight cups of coffee
To make a cup of coffee, the ratio of coffee to sugar is 2 : 3
The sum of coffee and sugar that needed to make eight cups of coffee is
Cups of coffee times the ratio.8 x 2 teaspoons of coffee = 16 teaspoons8 x 3 teaspoons of sugar = 24 teaspoons
It means that the sum of coffee is 16 teaspoons and the sum of sugar is 24 teaspoons
RATIO
We can conclude that RATIO is… two "things" (numbers or quantities in same unit) compared to each other.
SCALED DRAWING
SCALED DRAWING
We often find scaled pictures or models as maps, ground plan of a building house and a model of a car or plane in daily life. The following are several examples of scaled pictures and models.
SCALED DRAWING
Ilustration
• For example : a father ask his child to draw his rectangular land of 500m for long and 300 m wide. It’s imposibble to draw a piece of land in actual measurement, but congruent to its origin.
• 1 cm represent 100 m so that 500m represented by 5 cm and 300m represented by 3 cm
What is the definition of scaled picture?
A scaled picture is a picture made to represent a real object or situation in a certain measure.
With a scaled picture we know object or situation as a whole without watching the actual object.
• For example the piece of land in the form of a rectangle 500 m long and 300 m wide is represented by a figure of a rectangle of 5 cm long and 3 cm wide as the figure below.
5 cm
3 cm
Can you find the scale?
To find the scale we can compare between the model picture and the actual measurement.
Based on the explanation above, we can make the following ratio :
The Ratio between the measurement on the model picture and the actual measurement is called scale and formulated as follows
Exercises
A map is made to scale of 1 : 200.000, find :
a. The actual distance if the distance on the map is 5 cm.
b. The distance on the map if the actual distance is 120 km.
c. Given on the map that the distance of two towns is 4 cm, while the actual distance is 160 km, Find the scale of the map!
Exercises
Answer :a. 30 kmb. 60 cmc. 1 : 4.000.000
Factor of Enlargement and Reduction on Scaled Picture and
Model• What is the factor of Enlargement
and Reduction on Scaled Picture and
Model?
Factor of Enlargement and Reduction on Scaled Picture and
Model
• A very small object can be seen and learned easily if it is enlarged by picture using a certain scale.
• And the very big object can be reducted by picture using certain scale
What the purpose of this?
• For example :A rectangle have long 2 cm and width 1 cm. In order to be clearly seen, the componens is enlarged three times.
2 cm
1 cm
6 cm
3 cm
Length = 2 cm x 3 = 6 cm
Width = 1 cm x 3 = 3 cm
2 cm
1 cm
6 cm
3 cm
• The ratio before and after enlargement :
The enlargement in the example above has a factor of scale 3 orBoth have the ratio 3 : 1. It means that all measurement on the shape the product of enlargement represents 3 times of the actual shape.
2 cm
1 cm
6 cm
3 cm
Story
A photo have long 3 cm and width 2 cm.
• Because there are something, the photo’s size become 6 cm of length, 4 cm of width.
3 cm
2 cm
6 cm
4 cm
What is your
• What is the happen of before and after? • What is your conclution?
3 cm
2 cm
6 cm
4 cm
What is the enlargement of this picture?
Conclution
• Factor of scale where k>1 is called factor of enlargement
Story
A bus have long 6 m and width 2 m.If someone want to make a model of bus, so the model of bus made of 60 cm length and 20 cm width.
6 m
2 m
60 cm
20 cm
What you see?
• What is the reduction of bus and this model?• What is your conclution?
Conclution
• Factor of scale where 0<k<1 is called factor of reduction
ExercisesA photograph of 4 cm high and 3 cm wide is enlarged in such away that its width is 6 cm. Find :a. The factor of scaleb. The height after enlargmentc. Ratio of area before and after
enlargement
Exercisesa. Factor of scale =
So the factor of scale is 2 or 2:1b. The height after enlargement =
Factor of scale x the height of photograph= 2 x 4= 8 cm
Exercises
c. Ratio of the photograph area before and
after enlargement
Proportion
MILES 45 90 135 180 225
HOURS 1 2 3 4 5
Proportion
MILES 45 90 135 180 215
HOURS 1 2 3 4 5
Proportion
DOLLAR 9 18 27 36 45
HOURS 1 2 3 4 5
Proportion
DOLLAR 12 24 36 48 60
HOURS 1 2 3 4 5
Proportion
Olit buys 2 books that have cost $8. If she wants to buy 6 books, how much does it cost she must to pay?
So, Olit need to pay $ 24 for six books.
Then we can say it “8 dollars for 2 books" equals “24 dollars for 6 books".
Proportionis two ratios set to be equal to each other.
Ratio or Proportion?two out of five
This is a … proportionfour to every ten
This is a …ratio
ten to every four
This is a …ratiofour out of ten
This is a …proportion
4:10
This is a …ratio
Ratio, Proportion or Fraction?3 Aremania fans to every 2 Bonekmania fans
This is a … ratio
9 girls out of 10 use soap
This is a …proportion
3 boys out of 10 use deodorant
This is a …proportion
Direct Proportion
Andi buys a pair of shorts at the price of Rp 15.000,00. The price for two shorts, 3 shorts, and so on can be seen on the following table:
Number of Shorts (units) Price
One Shorts/1 Rp 15.000,00
Two Shorts/2 Rp 30.000,00
Three Shorts/3 Rp 45.000,00
Four Shorts/4 Rp 60.000,00
Five Shorts/x y
Direct Proportion
The table above indicates that the more shorts Andi buys the more money he has to spend. But, the amount of price for each shorts is always the same on each line:
Direct Proportion
Henceforth, the equation of the portion of the number of shorts and the portion of prices on two certain lines is always same.Example:
The quotient of the ratios on the other two line is:
So, the number of shorts and the price always increase or decrease at the same ratio, so that we say there is a direct proportion between the number of shorts and the price.
Direct Proportion
THERE’RE TWO METHODS TO CALCULATE A DIRECT PROPORTION:
1. CALCULATION BASED ON UNIT VALUE
2. CALCULATION BASED ON PROPORTION
Calculation Based on Unit Value
A car can travel 180 km in 3 hours. How long does the car need to travel 240 km?
The time for 180 km = 3 jam The time for 1 km =
The time to travel 240 km = x 240 = 4 hours
Calculation Based on Proportion
Number of shirts Price of shirt
3 75.0005 n
From table above, the proportion of the number of shits on this first line to the second is 3:5 or , while the proportion of the price is 75.000 : n or
Given:
Calculation based on Proportion
The calculation of the price of 5 shirts by using a proportion is as follows.
Side term and mid term
3n = 5 x 75.000
n=
or
Cross Multiplication
3n = 5 x 75.0000
3 : 5 = 75.000 : n
So, the price of 5 shirts is Rp 125.000,00
Calculation Based on Proportion
Based on the example above, on direct proportion, it is valid:
If a : b = c : d, hence ad = bc
If , hence ad = bc
PRACTICE
1. The price of three meters of cloth is Rp 54.000,00. How many maters of cloth is obtained by Rp 144.000,00?
2. The price of 3 kg of apples is Rp 36.000,00. What is the price of 15 kg of apples?
Solution
1. The price of 3 meters of cloth = Rp 54.000,00The price of 1 meter of cloth =
With Rp 144.000 we can obtain
So, we can obtain 8 meters of cloth.
2. If the number of apples increase, hence the price also increase. It means that the question above represent a direct proportion,Number of apples (kg) Price (rupiah)
3 36.000
15
So, the price of 15 kg of apples is Rp 180.000,00
The Graph of Direct Proportion
Number of chocolate Bar
1 2 3 4 5 6 7 8 9
Price 1.500 3.000 4.500 6.000 7.500 9.000 10.500 13.000 14.500
In order that you know the graph of a direct proportion, consider the following description. The table below indicates a relation between the number of chocolate and the price.
1 2 3 4 5 6 7 8 90
2000
4000
6000
8000
10000
12000
14000
16000
Price of chocolate Number of chocolate
The Graph of Direct Proportion
The Graph of Direct Proportion Practice
Times (hours) 1 2 3 4 5 6 7 8 9
Distance (km) 40 80
1. Complete the table above!2. Make its graph using the same scale!3. Based on the graph, calculate the distance taken in 2 and a half!
1 2 3 4 5 6 7 8 90
50
100
150
200
250
300
350
400
Distance (km
)
Times (hours)
The Graph of Direct Proportion
The Graph of Direct Proportion
Solution of c. The distance for 1 hour = 40 km The distance for 2 hour and a half = x 40 km = 100 km
Inverse Proportion
INVERSE PROPORTION
• Review : In direct proportions, when one row of a table shows that the proportion gets larger, the numbers in the other row or rows get "proportionally" larger.
• But, it’s different with inverse proportion. In these proportions, one row gets smaller at the same time that another gets larger.
Application of Inverse Proportion
The speed of Car A is 60 cm/sec. It needs 3 second to go until finish.
The speed of Car B is 30 cm/sec. It needs 6 second to go until finish.
So, which one the fastest???? Why???
1
2
30
60
CarBspeedAverage
CarAspeedAverage
2
1
carBtime
carAtime
2 is the inverse of ½
The proportional quotient of the average speed and time proportion on two certain lines always represent multiplication inverse of each.
Example• 12 workers build a wall in 10 hours. How long
do 5 worker build the wall?• Solution
If the number of workers decreases, then the time needed will increase, so that the question above represents an inverse proportion.
Number of worker Time12 10 5 n
24
51012105
12
n
n
n
Exercise
• Mother distributes cookies to 28 children and each of them gets 4 pieces of cookies. How many cookies does each child get if the cookies are divides to 16 children?