The document defines ratio and proportion. It provides examples of expressing ratios in different forms like 6:8 or 3:4. It explains that two ratios are in proportion if the product of their means equals the product of their extremes. Examples are given of solving proportions using cross multiplication or means-equals properties, including word problems involving ratios and rates.

5. RATIO
A comparison between two
quantities of the same units.
a to b a : b
𝒂
𝒃

6. EXAMPLE #1
Find the ratio of a to b if a = 6 cm
and b = 8 cm.
6 : 8 OR 3 : 4

7. EXAMPLE #2
Write the ratio of the number of female
presidents to the number of male presidents of
the Philippines in different forms.
2 to 15 2 : 15
𝟐
𝟏𝟓

8. Let’s Try!
Express each of the following ratios in simplest
form.
Php 6 to Php 72
1 hour to 40 minutes
2 weeks to 4 days
Eight out of 30 passengers are tourists.
Find the ratio of the number of tourists to
the number of other passengers.
Elmer has 42 marbles. Fourteen marbles are red
while the rest are green. What is the ratio of the
number of red marbles to the number of green
marbles?

9. PROPORTION
Equality between two ratios.
a:b = c:d or
𝒂
𝒃
=
𝒄
𝒅
Where, b≠0 and d ≠0

10. PROPORTION
a:b = c:d
Read as
“a is to b as c is to d”

11. PROPORTION
a:b = c:d
means
extremes

12. EXAMPLE:
1. 32:80
2. 27:72
3. 18:63
4. 34:85
2 : 5
3 : 8
2 : 7
2 : 5
This two
ratios are
proportion.

13. PROPORTIO
N
Two ratios are proportional if the
product of the means is equal to the
product of the extremes.
32 : 80 = 34 : 85

14. Example:

15. Is This Fair?

16. Properties of Proportion

17. EXAMPLE A:

18. EXAMPLE B:
Solve for the missing values in a proportion using the Cross
Multiplication Property or by Means-Extremes Property.

19. EXAMPLE B:

20. EXAMPLE B:

21. EXAMPLE B:

23. EXAMPLE C1: Word Problem
What is the fourth proportional to 3, 8,
and 6?

24. EXAMPLE C2: Word Problem
The ratio of three angles of a given
quadrilateral is 2:4:9. What is the
measure of the last angle?

25. EXAMPLE C3: Word Problem
The segment which measures 240 cm
long is divided into 3 parts in the ratio
2:3:5. How long is each part?

26. EXAMPLE C4: Word Problem
Jarred’s Carwash can washed 128 cars
in 3 hours. At that rate, how many cars
can they wash in 8 hours?

27. EXAMPLE C5: Word Problem
The length and width of a rectangle are
in the ratio 5:4. If its length is 80 cm, find
its width?

28. EXAMPLE C6: Word Problem
It takes 7 minutes for April to walk
around the gym track twice. At this rate,
how many times can April walk around
the track in half hour?