This document defines key terms related to percentages, rates, and bases. It explains that percentage is the part of a whole, rate is the number compared to 100, and base is the entire amount. A formula is provided to calculate percentage, rate, and base using a triangle method. Several examples are worked through step-by-step to demonstrate how to find the percentage, rate, or base when two values are given. Practice problems are also included for students to solve.

1. PERCENTAGE, BASE & RATE
Mr. Elmer B. Pascual
Master Teacher 1
Quarter2,Week3

2. What is a proportion?
Proportion is a statement of equality
between two ratios.
What are the types of proportion?
Direct proportion
Indirect/Inverse proportion
Partitive proportion
Percentage, Base & Rate

3. Definition of Terms
 Percentage (P) is the number or amount
that represents a part of a whole.
 Rate (R) is the number compared to 100.
Usually has either a percent sign (%) or the
word “percent” with it.
 Base (B) is the number that represents the
whole or entire amount.
Percentage, Base & Rate

4. Formula for Finding Percentage, Rate &
Base
Percentage
P = BR
Rate
R = P
B
Base
B = P
R
Techan’s Triangle
Percentage, Base & Rate
P
R B

5. Percentage, Base & Rate
Identify the P, R and B in each statement
below:
10 is 20% of 50
25% of 60 is 15
P B
R
P
B
R

6. Finding the percentage (P)
Example 1: Find 75% of 80.
Given:
R = 75%
B = 80
P = ? (n)
Percentage, Base & Rate
To find the percentage (P) or amount
of a number, change the rate/percent
(R) to decimal then multiply to the
base (B).

7. Finding the percentage (P)
Solution P = R x B
75% x 80
0.75 x 80
P = 60
Percentage, Base & Rate

8. Finding the percentage (P)
Example 2: There are 360 pupils in a school.
If 15% of them are Boy Scouts, how many Boy
Scouts does the school have?
Given:
R = 15%
B = 360 pupils
P = ? (n)
Percentage, Base & Rate

9. Finding the percentage (P)
Solution P = R x B
15% x 360
0.15 x 360
P = 54 Boy Scouts
Percentage, Base & Rate

10. Directions: Complete the table by solving
the percentage of the following items.
No. Rate Base Percentage
1. 25% 40
2 10% 120
3 15% 125
4 20% 300
5 50% 780
Percentage
10
12
18.75
60
390
Percentage, Base & Rate

11. Finding the rate (R)
Example 1: 36 is what percent of 60?
Given:
P = 36
B = 60
R = ? (n)
Percentage, Base & Rate
To compute for the rate (R), divide
the given percentage (P) by the base
(B).

12. Finding the rate (R)
Solution R = P
B
= 36
60
= 0.6
R = 60%
Percentage, Base & Rate

13. Finding the rate (R)
Example 2: There are 360 pupils in a school.
If 72 of the pupils are Girl Scouts, what
percent of the pupils are Girl Scouts?
Given:
P = 72
B = 360 pupils
R = ? (n)
Percentage, Base & Rate

14. Finding the rate (R)
Solution R = P
B
= 72
360
= 0.2
R = 20%
Percentage, Base & Rate

15. Directions: Solve for the rate (R) of each
word problem.
______ 1. 6 is what percent of 30?
______ 2. 24 is what percent of 96?
______ 3. What percent of 15 is 12?
______ 4. What percent of 10 is 4?
______ 5. What % of 80 is 30?
Percentage, Base & Rate
20%
25%
80%
40%
37.5%

16. Finding the base (B)
Example 1: 20% of what number is 44?
Given:
P = 44
R = 20%
B = ? (n)
Percentage, Base & Rate
To compute for the base (B), divide
the given percentage (P) by the
decimal form of the rate (R).

17. Finding the base (B)
Solution B = P
R
= 44
0.20
B = 220
Percentage, Base & Rate

18. Finding the base (B)
Example 2: In Ms. Aguilar’s class, 6 pupils
received an A on the last Math test. This is
20% of the number of pupils in her class.
How many pupils are there in Ms. Aguilar’s
class?
Given:
P = 6
R = 20%
B = ? (n)
Percentage, Base & Rate

19. Finding the base (B)
Solution B = P
R
= 6
0.20
B = 30
Percentage, Base & Rate

20. Directions: Solve for the base (B) of each
word problem.
______ 1. 60 percent of what number is 9?
______ 2. 18 is 24% of what number?
______ 3. 6 is 15% of what number?
______ 4. 25% of what number is 10
______ 5. 60% of n is 165
Percentage, Base & Rate
15
75
40
40
275

21. Generalization
Define the following:
percentage
rate
base
Types of proportion

22. Directions: Solve for the percentage, rate
or base
______ 1. 84 is 12 % of what number?
______ 2. 63 is 9% of n
______ 3. 16 is what percent of 16?
______ 4. What % of 40 is 20?
______ 5. What is 65% of 100?
Percentage, Base & Rate
700
700
100%
50%
65