The document provides a tutorial on understanding base, rate, and percentage through various mathematical problems and examples. It includes pre-assessment questions and exercises to determine percentages, parts, and rates based on given data. Additionally, it demonstrates practical applications of percentages in real-life scenarios such as sales and employee statistics.

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BASE, RATE, AND
PERCENTAGE
by Sir Russell Ventura

2. PRE-ASSESSMENT
• What is 25% of 60?
• 300 is 50% of what?
• What percent of 400
is 50?

3. • PERCENTAGE
• BASE
• RATE
These questions involves...
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4. BASE
• Usually denoted as (B), it refers to the number
of which a certain number of hundredths is
taken
• It represents the whole or the total amount
that you are comparing the percentage to
• Generally preceded by keywords “of”, “as much
as”, “as large as”

5. RATE
• Usually denoted as (R), it refers to the number
of hundredths taken
• It tells you the proportion of the base that
makes up the part or percentage.
• Usually expressed in percent, but can also be
expressed in fraction and decimal

6. PERCENTAGE
• Usually denoted as (P), it is the part
considered; a part of the whole
• It is what you get when you apply the rate to
the base
• It is never expressed in percent, which is the
common mistake of some students

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8. Let’s answer the Pre-Assessment
What is 25% of 60?

9. What is 25% of 60?
Given:
Rate = 25%
Base = 60
Percentage = ?

10. Let’s answer the Pre-Assessment
300 is 50% of
what?

11. 300 is 50% of what?
Given:
P = 300
R = 50%
B = ?

12. Let’s answer the Pre-Assessment
What percent of
400 is 50?

13. What percent of 400 is 50?
Given:
B = 400, P = 50, R = ?

14. Let's Try

15. Let's Try
What is 50% of 24?

16. Let's Try
B = 24
R = 50%
P = ?
𝑃= 𝐵× 𝑅
(change percent to decimal)
𝑃=24× 0.5
𝑷=𝟏𝟐

17. Let's Try
66 is 66.5% of what?

18. Let's Try
P = 66
R = 66.5%
B = ?
𝐵=
𝑃
𝑅
𝐵=
66
66.5 %
(change percent
to decimal)
𝐵=
66
0.665
=𝟗𝟗.𝟐𝟓

19. Let's Try
72 is 20% of what?

20. Let's Try
P = 72
R = 20%
B = ?
𝐵=
𝑃
𝑅
𝐵=
72
20 %
(change percent
to decimal)
𝐵=
72
0.2
=𝟑𝟔𝟎

21. Let's Try
What part of ₱1200 is
₱400?

22. Let's Try
B = 1200
P = 400
R = ?
𝑅=
𝑃
𝐵
𝑅=
400
1200
=0.3333
(change decimal to percent)
𝑹=𝟑𝟑.𝟑𝟑%

23. Let's Try
In a class of 40, 30% are
girls, how many are boys?

24. Let's Try
B = 40
R(GIRLS) = 30%
P(GIRLS) = ?
𝑃= 𝐵× 𝑅
(change percent to decimal)
𝑃=40× 0.3
𝑃=12are girls
Since we are asked how
many are boys: are boys

25. Let's Try
In a stock of 120 blouses,
90 are sleeveless. How
many percent are blouses
with sleeves?

26. Let's Try
B = 120
P = 90
R = ?
𝑅=
𝑃
𝐵
=
90
120
=0.75
(change decimal to percent)
𝑅=75% are sleeveless
Since we are asked how many
percent are WITH SLEEVES: are with sleeves

27. Let's Try
Maria bought a dress that was
originally priced at ₱1750. She
got a 15% discount. How much
will she pay?

28. Let's Try
B = 1750
R = 15%
P = ?
𝑃= 𝐵× 𝑅
(change percent to decimal)
𝑃=1750× 0.15
𝑃=₱ 262.50is the discount
Since we are asked how
much will she pay: 1750−262.50=₱𝟏𝟒𝟖𝟕.𝟓𝟎

29. SEATWORK
1. A company’s gross sales for
the month is ₱58,642.75. If 45%
of the gross sales is the
company’s gross profit, how
much gross profit did the
company get?

30. SEATWORK
2. A department store has a total
stock of 750 shoes. Of this, 50% are
for ladies, 30% are for men, and
the rest are for children. Find the
number of shoes in each category.

31. SEATWORK
3. A basketball team won 8 out of
the total games that it played for
the current season. This represents
32% of the total games. How many
games did the team play in all?

32. SEATWORK
4. A retail store wants to determine
their increase in sales from the
previous month. If the sales last
month is ₱50,000, while this month is
₱65,000, what is the rate of the
increase?

33. SEATWORK
5. There are 240 male employees in
the company. This represents 30%
of the total number of employees.
How many female employees does
the company have in all?

35. SEATWORK
1. A company’s gross sales for
the month is ₱58,642.75. If 45%
of the gross sales is the
company’s gross profit, how
much gross profit did the
company get?

36. SEATWORK
B = 58642.75
R = 45%
P = ?
𝑃 = 𝐵 × 𝑅
𝑃=58642.75× 0. 45
𝑃 = ₱ 26,389.24

37. SEATWORK
2. A department store has a total
stock of 750 shoes. Of this, 50% are
for ladies, 30% are for men, and
the rest are for children. Find the
number of shoes in each category.

38. SEATWORK
B = 750
R = 50%, 30%, ?
P = ?
𝑃 = 𝐵 × 𝑅
𝑃 = 750× 0 .50
for ladies

39. SEATWORK
3. A basketball team won 8 out of
the total games that it played for
the current season. This represents
32% of the total games. How many
games did the team play in all?

40. SEATWORK
4. A retail store wants to determine
their increase in sales from the
previous month. If the sales last
month is ₱50,000, while this month is
₱65,000, what is the rate of the
increase?

41. SEATWORK
5. There are 240 male employees in
the company. This represents 30%
of the total number of employees.
How many female employees does
the company have in all?