The document discusses ratios, proportions, and scale drawings. It begins by defining a ratio as a comparison of two or more quantities without units. Ratios can be written in different forms such as a:b or a to b. A proportion is an equation stating that one ratio is equal to another. Direct proportion means that as one quantity increases, the other also increases by the same factor. Inverse proportion means that as one quantity increases, the other decreases. Scale drawings use a scale ratio to show the relationship between an object's depicted size and its actual size. Examples are provided to demonstrate calculating ratios, proportions, direct and inverse proportions, and using scale ratios.

1. RATIO &
PROPORTION
SMPK PENABUR GS

2. DO NOW (not later):
• Compare the number of boys to
girls in the class.

3. • The number of boys =
• The number of girls =
• If we compare boys to girls we get
___ boys to _____ girls.

4. What do we call a comparison
between two or more quantities?
We just found the
RATIO RATIO of boys to girls.
Is the ratio of
girls to boys the
same ?
No, when writing a ratio, ORDER matters.

5. AIM:
What is a ratio?

6. DEFINITION OF RATIO
A ratio is the comparison
of two or more numbers
(quantities).
A ratio has no units

7. Which ratio shows the ratio of 3
butterflies to 1 apple?

8. Three Ways to write a Ratio

9. Three ways to write a ratio
•

10. Write A Ratio
 Rewrite into a ratio :
a) 15 metre to 2 km
15 m : 2 km ( ratio no units, and km change to m )
15 : 2000 ( write into simplest form )
3 : 400
b) 135 seconds : 1.5 minutes ( minute change to
second )
135 : 90 ( write into simplest form )
3:2

11. Write A Ratio
 If
P : Q = 3 : 5, and Q : R = 2 : 1, find the ratio P : R !
P : Q : R
(1) 3 : 5
(2) 2 : 1
The value of Q are 5 and 2.
So, we need to make it equal .
Find LCM of 2 and 5 ! It is 10
Ratio becomes :
P : Q : R
(1) 6 : 10
(2) 10 : 5
So, the ratio of P : R = 6 : 5

12. WRITE A RATIO
 In a new car dealer’s lot, there were 23 silver, 18 white, 2
maroon, 8 red, and 12 blue vehicles.
 Write the ratio of silver vehicles to total vehicles.
silver 23
total 63
 Write the ratio of white to blue vehicles.
white 18 3
blue 12 2

13. Decrease and Increase in Ratio
If the number of teachers in a college is increased from 50 to 60.
Then the ratio of new staff and old staff is :
Numbers of new staff Number of old staff
60 50
6 5
We say that,
number of teachers
has been
increased in ratio 6 : 5

14. RULE TO INCREASE OR DECREASE

Improper
fraction
Proper
fraction

15. PROPORTION

16. Definition of Proportion
• A proportion is an equation that says
one ratio is equal to another.
3 39
ratio = ratio
4 52

17. DIRECT PROPORTION
 Two quantities x and y are said to
be in direct proportion if they
increase (decrease) together in
such a manner that the ratio of
their corresponding values
remains constant.

18. Understanding Direct Proportion
Question :
Price of 8 oranges Rp 2600. What is the price of 6
oranges ? based on units
Calculation
Price 8 oranges = Rp 2600
Price 1 orange = Rp 2600 : 8
= Rp 325
Price 6 oranges = 6 x Rp 325
= Rp 1950

19. Understanding Direct Proportion
Price of 8 oranges Rp 2600. What is the price of 6
oranges ?
Calculation Based on ratio
Number of oranges Price ( Rp )
8 2600
6 X

20. Understanding Direct Proportion
 If you drive 90 miles in 2.5 hrs, how long should it
take for you to complete the final 200 miles of a trip?
mile hour
90 2,5
200 X

21. Understanding Direct Proportion
 Six identical CNC machines can produce 768
pistons in one day. If two of the CNC machines
break down, how many pistons can be produced in a
day? Piston
Machine
6 768
4 X

22. INVERSE PROPORTION
In the inverse proportion, if the
quantity x increases, the
quantity y decreases, or when
the quantity x decreases, the
quantity y increases.

23. Understanding Inverse Proportion
Some candies are distributed to 15 kids and each kid
gets 4 candies. If there are only 12 kids, how many
candies does each kid get
Calculation based on the result of multiplication.
Kid candy
15 4
12 C
15 x 4 = 12 x C
60 = 12 C
C = 5 candies

24. Understanding Inverse
Proportion
 4 employees can complete a basic auto
interior restoration in 6 work days. If only two
employees are available for a similar project,
how long will it take?
Employee day
4 6
2 D
4x6 =2xD
24 =2D
C = 12 days

25. Understanding Inverse
Proportion
 6 childrens need 30 minutes time to tidy up
the books in their schools library. How many
children must be added so that the job could
be done in 20 minutes?
Children Minute
6 30
X 20
6 . 30 = X . 20 Children must be added
180 = 20 X :
X = 9 childrens 9 – 6 = 3 students

26. MAPS & SCALE
DRAWINGS

27. P
S R
P = Picture ( size on picture/map)
S = Scale ( in Ratio )
R = Real ( the real size of that object)

28. Example
•

30. EXERCISE 39
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