Bus.-Math11-Module-4-W1.pdf

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
Learning Competency:
Solve problems involving direct,
inverse and partitive proportion
ABM_BM11rp-lf-4

Learning Module for Business Mathematics
https://www.examsbook.com/ratio-and-proportion-formulas
Quarter 1 Week 4 Module 4
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
2
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:
LESSON
4 Proportion
EXPECTATIONS

Solve problems involving direct, inverse and partitive proportion
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.78
82. Quezon City, Philippines. Phoenix Publishing House.
3
LOOKING BACK TO YOUR LESSON
PRETEST
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!
Great, you finished answering the
questions. You may request your
facilitator to check your work.
Congratulations and keep on learning!

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.
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 x same. proportionally; that is the ratio y
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 TERM

4
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.
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
BRIEF INTRODUCTION
Initial deposit

5

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 5.
=
840 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
6
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.
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.
Solution:
Number of 1 2 4 5 8 10 20
Number of
Winners
1 2 4 5 8 10 20
Prize for Each
Winner (in P)
1, 000,000 500,000 -
- -
-
-
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.

Winners (a)
Prize for Each
Winner (in P)
(b)
1, 000,000 500,000 t1 t2 t3 t4 t5
Since
ab=a1b1=a2b2=…=1X1 000 000=2X500 000=…1 000
000 so, a and b are said vary inversely.
Then, we have 1
= = P250,000
4 1 000 000
Similarly,
t2, P200,000; t3, P125,000; t4, P100,000; t5, P50,000.
7
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.
Solve for n: n+4
5
Solution: The cross products are equated as shown below.
5(n-2) =3(n+4)
5n-10=3n+12
t1
a
bd=
c
bd gives ad=bc. Cancelling same
b d

variables
= n-2
3
CROSS MULTIPLICATION

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 3
of P467, 500; the third child will receive
3
of
P467,500, and the fourth child will receiv11 e 4 of P467,500. 11
11
TIP!
When number is partitioned into different parts, we may use partitive proportion
to solve the given problem.
https://images.app.goo.gl/f3g6k4GCN6UsUruEA
8
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:
To get the
denominator, add
all the given
numbers in the
ratio.

Peter P56,000
54 Paul’s money X
P56,000=P70,000.
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
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
9
ACTIVITIES

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- 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
REMEMBER
https://images.app.goo.gl/2bGWjUFoKon4VN 1

3. x: 15 = 5 :24
1 x
4. 2=100
5. 2 12 : 6 = 3 : y
Chua, Simon L., et.al, 2018 Soaring 21st Century Mathematics Grade 11 Business Mathematics. p.75 Quezon
10

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
POSTTEST

11
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-and-
solve-proportions/v/find-an-unknown-in-a-proportion.
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/tussle over-
george-tys-fortune-erupts/. Retrieved June 25, 2020 Module Images:
https://images.app.goo.gl/2bGWjUFoKon4VNct5. Retrieved June 25, 2020
REFLECTIVE LEARNING SHEET
E-SITES
REFERENCES

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
12
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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