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Republic of the Philippines
Department of Education
National Capital Region
DIVISION OF CITY SCHOOLS – MANILA
Manila Education Center Arroceros Forest Park
Antonio J. Villegas St. Ermita, Manila
Business Mathematics
Key Concepts of
Ratio and Proportion
https://www.examsbook.com/ratio-and-proportion-formulas
Quarter 1 Week 4 Module 4
Learning Competency:
Solve problems involving direct,
inverse and partitive proportion
ABM_BM11rp-lf-4
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Learning Module for Business Mathematics
HOW TO USE THIS MODULE?
Before starting the module, I want you to set aside other task/s that will
disturb you while enjoying the lessons. Read the simple instructions
below to successfully enjoy the objectives of this kit. Have fun!
1. Follow carefully all the contents and instructions indicated in
every page of this module.
2. Write on your notebook the concepts about the lessons.
Writing enhances learning, that is important to develop and
keep in mind.
3. Perform all the provided activities in the module.
4. Let your facilitator/guardian assess your answers using the
answer key card.
5. Analyze conceptually the posttest and apply what you
have learned.
6. Enjoy studying!
PARTS OF THE MODULE
•
Expectations - These are what you will be able to know
after completing the lessons in the module.
•
Pre-test - This will measure your prior knowledge and the concepts
to be mastered throughout the lesson.
•
Looking Back to your Lesson - This section will measure what
learnings and skills did you understand from the previous lesson.
•
Brief Introduction- This section will give you an overview of the
lesson.
• Activities - This is a set of activities you will perform with a partner.
•
Remember - This section summarizes the concepts and
applications of the lessons.
•
Check your Understanding - It will verify how you learned from the
lesson.
•
Post-test - This will measure how much you have learned from
the entire module
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Learning Module for Business Mathematics
Proportion
LESSON
4
EXPECTATIONS
As we study and immerse ourselves in “Business Mathematics” in the process,
it is necessary to know some Concepts, Principles and Formulas. The module is
subjected to discuss Module 4 – Proportion. You will represent real-life situations
different kinds of proportions.
Specifically, this module will help you to:
Solve problems involving direct, inverse and partitive proportion
Let us start your journey in
learning more on proportion. I am sure
you are ready and excited to answer
the Pretest. Smile and Enjoy!
PRETEST
MULTIPLE CHOICE.
Directions: Solve the following problems. Choose the letter of the best answer.
1. A machine in a fruit juice factory can fills 840 bottles in 6 hours. How
many bottles will it fill in 5 hours?
A. 5
C. 6
B. 700
D. 840
2. 168 men can do a piece of work in 14 days. How many men will do the
same work in 42 days?
A. 14
C. 42
B. 56
D. 168
3. Peter and Paul shared a sum of money in the ratio of 4:5. If Peter got
P56,000, what was the original amount of money?
A. P70,000
C. P14,000
B. P56,000
D. P126, 000
Chua, Simon L., et.al, 2018 Soaring 21st Century Mathematics Grade 11 Business Mathematics. pp.7882. Quezon City, Philippines. Phoenix Publishing House.
Great, you finished answering the
questions. You may request your
facilitator to
check
your
work.
Congratulations and keep on learning!
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Learning Module for Business Mathematics
LOOKING BACK TO YOUR LESSON
A PROPORTION is a statement that two
ratios are equal. Each of the four
numbers in a proportion is called a term
of the proportion. The first and fourth
terms are called the extremes. The second
and third are called the means.
proportionally; that is the ratio
x
Types of proportion (1) Direct proportiontwo variables say x and y, varying such
that as x increases, y also increases or as
x decreases, y also decreases always the
y
same.
y
The same holds true with the ratio x ; (2) Indirect/Inverse- two variables, s ay
x and y, varying such that as x increases, y decreases, or as x decreases, y
increases proportionally; that is, the product of x and y is always the same; (3)
Partitive proportion- a whole is divided into more than two parts.
https://www.edutopia.org/blog/restorative-justice-tips-for-schools-fania-dav
Let’s do this!
Identify the following by choosing your answers on the box provided.
________________ 1. It is a statement that two ratios are equal.
________________ 2. How do you call the four numbers in a proportion?
________________ 3. How do you call the second and third terms in proportion?
EXTREMES
MEANS
PROPORTION
4
TERM
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Learning Module for Business Mathematics
BRIEF INTRODUCTION
We come across many situations that unknowingly we apply either direct
or inverse proportions to our daily transactions.
Banks and other financial institutions give us interest along with the
principal (initial deposit of the depositor) at a certain rate for a specified period.
If you deposit your savings worth P1,000 to your chosen bank for 1 year
at the rate of 5% annually (per year), one will get back P1,050 after a year
because of the interest given by the bank.
Initial deposit
Here, P1,050 (Savings) =P1,000 (Principal) + P50 (interest).
In the presentation above, the money deposited in the bank and the
amount received back after a certain time and at a certain rate of interest are
in proportion (equal).
From the above example, we can say that if the values of two quantities
depend on each other in such a way that a change in one quantity results in a
corresponding change in the other, then the quantities are said to be in
proportion. (Chua, S., 2018)
A. DIRECT PROPORTION
Two quantities are said to be directly proportional if as the value of
one quantity increases (or decreases), the value of the other also increases
(or decreases) in such a way that the ratio of the value of the two
quantities remains the same. (Chua, S., 2018)
TIP!
When setting up a direct proportion in fraction form, the numerator of the
first ratio must correspond to the numerator of the second ratio. The
denominator of the first ratio must correspond to the denominator of the
second ratio.
https://images.app.goo.gl/DkpHHJTCn6a698F57
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Learning Module for Business Mathematics
Example:
A machine in a fruit juice factory fills 840 bottles in 6 hours. How many
bottles will it fill in 5 hours?
Solution:
Let the number of bottles filled in 5 hours be x. Then, the above data can
be presented in the following tabular form:
Time
6 5
Number of Bottles
840 x
We know that the time taken to fill the bottle is directly proportional to
the number of bottles filled.
Hence, 6:840=5:x
or
6
840
=
5.
x
Then 6x=5 840
X= 700.
Thus, 700 bottles will be filled in 5 hours.
Chua, Simon L., et.al, 2018 Soaring 21st Century Mathematics Grade 11 Business Mathematics. p.78. Quezon City,
Philippines. Phoenix Publishing House.
B. INVERSE PROPORTION
In direct proportion, we learned that two quantities may change in such a
manner that if one quantity increases (decreases), the other will increase
(decrease). Sometime, two quantities may change in such a manner that if one
quantity increases, the other quantity decreases and vice-versa. (Chua, S.,2018)
TIP!
Two quantities are inversely proportional if a change in one produces a change in
the other in the opposite direction, that is, an increase in one produces a
decrease in the other, or a decrease in one produces an increase in the other.
Example:
•
On increasing the number of workers to complete a work, the number
of days to complete the work will decrease.
•
On decreasing the speed of the car, the time needed to cover the
same distance will increase.
https://images.app.goo.gl/H4pRRzZiG4jMMjN2A
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Learning Module for Business Mathematics
Note: The word vary means change and the word rate means how a quantity
changes with another quantity. So, two quantities are said to be in variation
if the values of two quantities depend on each other in such a way that a
change in one causes a corresponding change in the other.
TIP!
When setting up an inverse proportion in a fraction form, the numerator of the first
ratio must correspond to the denominator of the second ratio. The numerator of the
second ratio must correspond to the denominator of the first ratio.
Example:
In a Supermarket raffle grand draw, the cash prize of P1,000,000 is to be
divided equally among the winners. Complete the following table and find
whether the prize money give to an individual winner is directly or inversely
proportional to the number of winners.
Number of
Winners
1
Prize for Each 1, 000,000
Winner (in P)
Solution:
Number of
1
Winners (a)
Prize for Each
Winner
(in P) 1, 000,000
(b)
Since
2
4
5
8
10
20
500,000
-
-
-
-
-
2
4
5
8
10
20
500,000
t1
t2
t3
t4
t5
ab=a1b1=a2b2=…=1X1 000 000=2X500 000=…1 000
000 so, a and b are said vary inversely.
Then, we have
Similarly,
1
4
=
t1
= P250,000
1 000 000
t2, P200,000; t3, P125,000; t4, P100,000; t5, P50,000.
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Learning Module for Business Mathematics
Also, the cash prize given to an individual winner is inversely
proportional to the number of winners.
Chua, Simon L., et.al, 2018 Soaring 21st Century Mathematics Grade 11 Business Mathematics. pp.80-81 Quezon
City, Philippines. Phoenix Publishing House.
a
c
If b = d , then ad=bc. Note that this is so because of the Multiplication
Property of Equality. That is, multiplying the whole equation by bd yields
the result as shown below.
a
b
bd=
Solve for n:
c
bd gives ad=bc.
d
n+4
5
Cancelling same
variables
= n-2

CROSS MULTIPLICATION
3
Solution: The cross products are equated as shown below.
5(n-2) =3(n+4)
5n-10=3n+12
2n=22
n=11
Licuanan, Patricia B., et.al, 2016 Teaching Guide for Senior High School Business Mathematics. p.52. Quezon City,
Philippines. CHED.
C. PARTITIVE PROPORTION
Partitive proportion involves identifying parts of a whole based on
given ratios of these parts. (Chua, S., 2018)
Example:
A father wants to leave P467,500 to his four children in the ratio of
1 : 3 : 3 : 4, so the first child will receive 1
of P467,500; the second child
11
will receive
of P467, 500; the third child will receive
11
4 of P467,500.
the fourth child will receive
11
3
TIP!
3
11
of P467,500, and
When number is partitioned into different parts, we may use partitive
proportion to solve the given problem.
https://images.app.goo.gl/f3g6k4GCN6UsUruEA
8
To get the
denominator, add
all the given
numbers in the
ratio.
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Learning Module for Business Mathematics
Example:
Peter and Paul shared a sum of money in the ratio of 4 :5. If Peter got
P56,000, what was the original amount of money?
Solution:
When we say that the ratio of Peter’s money to Paul’s money is 4:5, it
means that if Peter’s money is P4, then Paul’s money is P5. In other words,
4
5
Peter’s money is
times Paul’s money and Paul’s money are
times Peter’s
5 4 money. Now in this case, we can determine Paul’s money by:
Peter
Paul’s money
P56,000
4 X P56,000=P70,000.
5
Therefore, the original amount of money is
P56,000+P70,000=P126,000
Chua, Simon L., et.al, 2018 Soaring 21st Century Mathematics Grade 11 Business Mathematics. pp.81-82 Quezon
City, Philippines. Phoenix Publishing House.
ACTIVITIES
Individual Activity.
Directions: Solve the following problems. Write your answer in the yellow pad.
1. Eight tea bags are needed to make 5 liters of iced tea. How many tea bags
are needed to make 15 liters of iced tea?
2. A manufacturer knows that during an average production run, out of 1,000
items produced by a certain machine, 25 will be defective. If the machine
produces 2,030 items, how many can be expected to be defective?
3. If 1 out of 6 people buy a branded item, how many people can be expected to
buy this item in a community of 6,000 people?
Licuanan, Patricia B., et.al, 2016 Teaching Guide for Senior High School Business Mathematics. pp.54-55. Quezon
City, Philippines. CHED
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Learning Module for Business Mathematics
REMEMBER
Two quantities are said
to be directly proportional if as
the value of one quantity
increases (or decreases), the
value of the other also increase
(or decreases) in such a way
that the ratio of the value of
the two quantities
remains the same.
Two quantities may change
in such a manner that if one
quantity increases, the other
quantity decreases and vice-
https://images.app.goo.gl/2bGWjUFoKon4VN 1
versa and that is what we called
indirect or inverse proportion while partitive proportion involves
identifying parts of a whole based on given ratios of these parts.
CHECK YOUR UNDERSTANDING
Directions: Find the unknown terms in the following proportions.
1. A:9=7.5:6
3
6
2. 6 = x
3. x: 15 = 5 :24
1
4. 2=100
5. 2
x
12 : 6 = 3 : y
Chua, Simon L., et.al, 2018 Soaring 21st Century Mathematics Grade 11 Business Mathematics. p.75 Quezon
City, Philippines. Phoenix Publishing House.
10
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Learning Module for Business Mathematics
POSTTEST
Directions: Solve the problem below and write your answer in the
space provided below.
1. Two boxes of chocolates cost P180. How much do 7 boxes of chocolates cost?
2. Forty liters of water is transformed into 3 containers in the ratio 1:3:4. How
much water is in each container?
3. If Trina works 20 hours, she earns P600. How much does she earn if
she works 30 hours?
4. If nine men take 15 days to assemble 18 machines, how many days s will it
take to assemble 60 machines?
5. A deceased person stated in his testament that his 30-hectare land be
divided among his three children using 1:2:3 partition, the oldest getting the
biggest share. How much did the second child receive?
Licuanan, Patricia B., et.al, 2016 Teaching Guide for Senior High School Business Mathematics. pp.56-58. Quezon
City, Philippines. CHED
REFLECTIVE LEARNING SHEET
11
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Learning Module for Business Mathematics
E-SITES
To further explore the concept learned today and if it possible to connect
the internet, you may visit the link:
https://www.khanacademy.org/math/pre-algebra/pre-algebra-ratios-rates/pre-algebra-write-andsolve-proportions/v/find-an-unknown-in-a-proportion.
REFERENCES
Chua, Simon L., et.al, 2018 Soaring 21st Century Mathematics Grade 11 Business Mathematics.
pp. 72-85. Quezon City, Philippines. Phoenix Publishing House.
Licuanan, Patricia B., et.al, 2016 Teaching Guide for Senior High School Business
Mathematics.pp.51-58. Quezon City, Philippines. CHED.
Tussle
over George Ty’s fortune erupts. https://bilyonaryo.com.ph/2019/02/14/tussleover-george-tys-fortune-erupts/. Retrieved June 25, 2020
Module Images:
https://images.app.goo.gl/2bGWjUFoKon4VNct5. Retrieved June 25, 2020
https://images.app.goo.gl/f3g6k4GCN6UsUruEA. Retrieved June 25, 2020
https://images.app.goo.gl/H4pRRzZiG4jMMjN2A. Retrieved June 25, 2020
https://images.app.goo.gl/DkpHHJTCn6a698F57. Retrieved June 25, 2020
https://www.edutopia.org/blog/restorative-justice-tips-for-schools-fania-dav. Retrieved
June 25, 2020
Acknowledgements
Writers:
Clarabelle V. Dalimit, DEM
Jupiter Whiteside, MBA
Editor:
Isabel A. Gumaru, DBA
Evaluator:
Ellaine I. Dela Cruz, DBA
Validator & Reviewer:
Remylinda T. Soriano, EPS, Math
Angelita Z. Modesto, PSDS
George B. Borromeo, PSDS
Management Team:
Maria Magdalena M. Lim-Schools Division Superintendent-Manila
Aida H. Rondilla-Chief Education Supervisor
Lucky S. Carpio-EPS
Lady Hannah C Gillo, Librarian II-LRMS
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Learning Module for Business Mathematics
ANSWER KEY
PRE TEST
1. B
2. B
3. D
LOOKING BACK TO YOUR LESSON
1. Proportion
2. Term
3. Means
ACTIVITIES
1. 24 Tea bags
2. 50.75 or 51 defectives
3. 1,000 people
CHECK YOUR UNDERSTANDING
1. 11.25
2. 12
3. 3
4. 50
5. 7.2
POST TEST
1. P630
2. Container 1 (1 portion) = 5L
Container 2 (3 portions) = 15 L
Container 3 (4 portions) = 20 L
3. 900
4. 22 ½ days
5. 10
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