11
Business
Mathematics
Quarter 1 – Module 3:
Kinds of Proportion &
Solving Problems
Involving
Kinds of Pro ortion
Business Mathematics – Grade 11
Self-Learning Module (SLM)
Quarter 1 – Module 3: Kinds of Proportion & Solving Problems Involving Kinds of Proportion
First Edition, 2020
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Introductory Message
This Self-Learning Module (SLM) is prepared so that you, our dear learners,
can continue your studies and learn while at home. Activities, questions,
directions, exercises, and discussions are carefully stated for you to
understand each lesson.
Each SLM is composed of different parts. Each part shall guide you step-bystep as you discover and understand the lesson prepared for you.
Pre-test are provided to measure your prior knowledge on lessons in each
SLM. This will tell you if you need to proceed on completing this module, or if
you need to ask your facilitator or your teacher’s assistance for better
understanding of the lesson. At the end of each module, you need to answer
the post-test to self-check your learning. Answer keys are provided for each
activity and test. We trust that you will be honest in using these.
In addition to the material in the main text, Notes to the Teachers are also
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Please use this module with care. Do not put unnecessary marks on any part
of this SLM. Use a separate sheet of paper in answering the exercises and
tests. Read the instructions carefully before performing each task.
If you have any questions in using this SLM or any difficulty in answering the
tasks in this module, do not hesitate to consult your teacher or facilitator.
Thank you.
What I Need to Know
This module was designed and written with you in mind. It is here to help you
master the topic on kinds of proportion and solving problems involving kinds of
proportion. The scope of this module permits it to be used in many different learning
situations. The language used recognizes the diverse vocabulary level of students.
The lessons are arranged to follow the standard sequence of the course. But the order
in which you read them can be changed to correspond with the textbook you are now
using.
In this module, you will be able to:
• identify the kinds of proportion and write examples for each.
ABM_BM11RP-Ic-3
• solve problems involving direct, inverse and partitive proportion.
ABM_BM11RP-If-4
Specifically, you are expected to:
1. define ratio and proportion and apply it in real life situations and
2. identify the kinds of proportion and write examples for each.
3. translate verbal statements involving proportions into mathematical
statements;
4. describe direct, inverse and partitive proportions; and
5. solve problems involving direct, inverse and partitive proportion.
What I Know
Before we are going to proceed with our lesson, let me know first what you have
learned about kinds of proportion from your previous lessons by answering the
following questions.
Direction: Read and understand the following problems carefully. Encircle the letter
of the correct answer.
1. Which of the following is the relation between two numbers with the same kind?
a. rate
c. proportion
b. ratio
d. percentage
2. A basketball team won 15 games and lost 5 games. What is the ratio of the
games won to the total games played?
c. 3:4
a. 1:3
b. 3:1
d. 4:3
3. Which pair of ratios are proportional?
a. 3 T shi rts for ₱840; 6 T shir ts for ₱1400
b. 16 points scored in 4 games; 48 points scored in 8 games
c. 98 words typed in 3 minutes; 162 words typed in 5 minutes
d. 15 computers for 45 students; 45 computers for 135 students
4. What proportion states that as “one variable increases, the other variable
decreases”?
c. partitive
a. direct
d. negative
b. inverse
5. Which of the following is an example of direct variation?
-
a. 3:8 = 6:4
b. 4:3 = 40:30
-
2
c. 4:50 = 10:20
d. A:B:C = 2:3:5
6. Which
that is
a.
b.
c.
d.
concept is being involved when a whole portion is divided into parts
proportional to the given ratio?
direct
inverse
partitive
combined
7. What kind of proportion states that an increase of one variable will also
increase the other variable & the decrease in one will also decrease the other?
a. direct
b. inverse
c. partitive
d. combined
8. Which of the following is an example of indirect variation?
a. 2:3 = 20:30
b. 3:8 = 6:4
c. 3:12 = 5:20
d. 4:20 = 6:30
9. The verbal phrase “the ratio of a number (x) and four added to two” is
equivalent to which of the following mathematical statements?
a. 𝑥: 4 + 2
b.
𝑥 = 4+ 2
c.
d.
𝑥+2
4
𝑥
4
+2
10. Which is an example of an inverse proportion?
a.
1𝑔𝑢𝑖𝑑𝑒
3 𝑡𝑜𝑢𝑟𝑖𝑠𝑡𝑠
=
b.
3 𝑚𝑒𝑡𝑒𝑟𝑠
5 𝑓𝑟𝑎𝑚𝑒𝑠
= 20
c.
d.
𝐵
3 𝑏𝑜𝑦𝑠
=
1𝑥+ 2𝑥+3 𝑥
₱50 00
4 𝑔𝑢𝑖𝑑𝑒
𝑁
𝑀
𝑓𝑟𝑎𝑚𝑒𝑠
3 𝑤𝑒𝑒𝑘𝑠
1 𝑤𝑒𝑒𝑘
=
₱600.00
𝑥
11. Juanita spends her working hours (8 hours) in filing, typing, placing and
receiving calls. If she approximately performs these functio ns in the ratio of
1:3:4, which among the mathematical statements best represents the time
spent for each function?
a. 8𝑥 = 8
b.
1+3+ 4
𝑥
c.
1𝑥 + 3𝑥 + 4𝑥 =
d.
12. Which
a.
b.
=8
1
8
1𝑥 + 3𝑥 + 4𝑥 = 8
of the following problems DOES NOT belong to the group?
If 10 laptops cost ₱200,000.00, then how much do 8 laptops cost?
A basket of food is sufficient to feed 15 persons for 3 days. How
many days would it last for 10 persons?
boys sold garlands in the ratio of 2:3:4. Together they sold 225
Three
c.
garlands. How many garlands did each boy sell?
d. How many tea bags (B) are needed to make 15 liters o f iced tea when
eight tea bags are needed to make 5 liters of iced tea?
3
13. Carla will spend ₱ 3,920.00 for her birthday party if she will invite 14 guests.
If the cost is directly proportional to the number of invited guests, how much
will she spend if she will invite 56 guests?
a. ₱15,680.00
b. ₱15,685.00
c. ₱15,780.00
d. ₱15,880.00
14. If 3 men can do a portion of a job in 8 days, how many men can do the same
job in 6 days?
a. 4
b. 5
c. 6
d. 7
15. If Mang Gorio wants to give ₱5,000 to his four children in the ratio of 1:2:3:4
for their weekend allowance, how much will each of the four children receive?
a. ₱500: ₱1,000: ₱1,500: ₱2,000
b. ₱450: ₱1,050: ₱1,450: ₱2,050
c. ₱500: ₱1,000: ₱1,250: ₱2,250
d. ₱450: ₱1,000: ₱1,500: ₱2,050
Lesson
Kinds of Proportion
1
Hello! Do you know that the concept of proportion is very useful in every reallife situation especially in business? We can apply proportion to know and compare
the price of every item sold in the market, or a piece of share in an inheritance and
many others.
What’s In
To begin with, let us refresh your mind on the concept of ratio which is very
essential in your learning on different kinds of proportion. Let’s take a look on it.
Consider this example:
Mila, Brenda, and Pauline decided to invest ₱100,000.00 in a burger shop
business along Fil Am Avenue, Fatima, General Santos City. The table shows the
specific amount of their investment.
-
5
Business Partner
Amount of Investment
Mila
₱50 000
Brenda
₱20 000
Pauline
₱30 000
Questions:
1. What is the ratio of Mila’s investment to the whole investment?
2. What is the ratio of Brenda’s investment to the whole investment?
3. What is the ratio of Pauline’s investment to Mila’s investment?
Answers:
a. ₱50,000: ₱100,000 or 1:2
b. ₱20,000: ₱100,000 or 1:5
c. ₱30,000: ₱50,000 or 3:5
A RATIO is comparison of two numbers or measurement. The terms of the
ratio are the numbers or measurements being compared. The expression 1:2 (read as
“one is to two”), ½, 1÷2, indicate ratios. We are comparing the relationship between
1 and 2. When we are asked to give the ratio of Mila’s investment to the
whole investment, the answer is ₱50,000: ₱100,000. Expressing it in simplified form,
we get 1:2, where 1 represents her investment and 2 refers to the total investment.
Examples:
Express the following in terms of ratio:
a. A certain store serves three flavors of ice cream: 4 parts strawberry, 6
parts mango, and 11 parts chocolate.
Solution:
The ratio of ice cream flavors is 4:6:11.
b. A small merchandise has 12 female and 20 male employees. What is the
ratio of female employees to male employees?
Solution:
The ratio of female employees to male employees is 3:5. Since
there are 12 female employees and 20 male employees, we
3
12
4 3
have = · = .
20
4
5
5
Wow! You are already refreshed. Let us now proceed to the next part of this
module.
6
What’s New
This module focuses on the kinds of proportions and how these are applied into
real life situations. But before we proceed, let us ponder first on the given activity
below.
Activity 1: Know Me First!
Direction: State if the following equations and situations illustrates direct, inverse or
partitive proportion. Write your answer under the kinds of proportion
column.
Situation
Kinds of Proportion
1. 2:1 = 24:12
2. Girl : Boy = 4:5
3. The number of workers and the
number of days to work
Very good! You are now ready to discover more about proportion.
What is It
In this part of the module, you will learn about proportion and its kinds. Let us
take a look on it.
What is proportion?
An equation showing two ratios that are equal is called a proportion. It can
be written in two ways:
1. As Two Equal Fractions
𝑎: 𝑏 = 𝑐: 𝑑
2. Using a Colon
𝑚𝑒𝑎𝑛𝑠
𝐸𝑥𝑡𝑟𝑒𝑚𝑒𝑠
Since the two ratios are equal, the product of the means is equal to the product
of the extremes.
Illustrative Example 1: In the proportion 15:35 = x:70, what is x?
7
Solution:
15
35
=
x
70
15 (70) = 35x
1050 = 35x
35
35
𝒙 = 𝟑𝟎
Cross multiply 15 and 70 then 35 and x
The product is divided by 35 to find x:
Thus, 𝒙 equals 30 .
Illustrative Example 2:
One (1) dozen of apples costs ₱240. How much does three (3) dozens cost?
Solution:
1 dozen of apples: cost of one dozen = 3 dozens of apples: cost of 3 dozens
1 dozen of apples = 3 dozens of apples
₱240 per dozen
𝑥
1𝑥 = 3(240)
x = 720
Thus, ₱720 is the cost of 3 dozens of apple.
Kinds of Proportion
1. Direct Proportion. It is the relationship between two variables when their ratio is
equal to a constant value. Say, 𝑦 is directly proportional to 𝑥 when the
equation takes the form: 𝑦 = 𝑘𝑥, where k is the constant term. In this
proportion, an increase of one variable will also an increase of the other
variable, and a decrease in one variable will also the decrease of the
other.
“Situations 1. The number of computers to the number of students.
that illustrates 2. The number of plants to the total cost.
direct 3. Your score in examination to your grade.
proportion:”
15 computers for 45 students; 45 computers for 135
students. This can be written as
Sample equation:
𝟏𝟓: 𝟒𝟓 = 𝟒𝟓: 𝟏𝟑𝟓.
The number of computers is directly proportional to the number of students
since as the number of computer increases, the number of students also increases
with the constant value of 3.
Sample word problem:
If 10 cactus plants cost ₱2,000.00 then how much do 8 cactus plants cost?
The total amount of sales is directly proportional to the number of cactus sold.
We see that the greater the number of cactus, the higher is the total cost.
Take a look on this ratio:
Cactus: cost = cactus: cost
10:2000 = 8:𝒙
8
If 10 cactus plants cost ₱2,000.00, it is expected that the cost of 8 cactus plants
will be lesser than ₱2,000.00. In the problem, the number of cactus plants and total
cost are directly proportional hence the more cactus you buy, the higher the cost will
be or the lesser cactus you buy, the lower the cost.
2. Inverse or Indirect Proportion. It is the relationship between two variables when
their product is equal to a constant value. Say, 𝑦 is inversely
proportional to x when the equation takes the form: 𝑦 = 𝑘/𝑥, where k is
the constant term, or k=x*y. This means that the two values x and y are
inversely or indirectly proportional to each other, such that if x
increases then y decreases orif x decreases, y increases.
“Situations that 1. The number of workers and the number of days to work
Illustrate 2. The speed of a vehicle and the time of travel in a uniform
distance
Indirect
proportion” 3. The pressure exerted in a confined as and its pressure
Sample equation: 3 persons vs 6 persons: 1 day vs 2 days. This can be written as
3:6 = 1:2.
The number of persons needed to do the work is inversely proportional to the
number of days needed to finish the work. Since the number of persons needed to
do the job increases, the number of working days should decrease.
Sample word problem:
In a Top Spray Bottle factory, 2 employees can manufacture 20 bottles of spray
in one hour. How long will it take 5 people to manufacture 20 bottles?
Take a look on this ratio:
employee: employee = hour: hour
2:5 = 𝒙:1
If 2 employees can finish 20 bottles in one hour, then five employees will take
less than an hour to manufacture 20 bottles. We see that more workers on a job
would reduce the time to complete the task.
3. Partitive Proportion. A whole is divided into parts that is proportioned into equal
or unequal ratios.
‘Situations that 1. Dividing inheritance to children.
illustrates 2. The number of men and women who attended a
partitive
seminar.
proportion’ 3. Allotment of salary into different expenses.
Sample equation:
child A: child B: child C = 2:3:3
9
Sample word problem:
Karen wants to donate her collection of figurines to her four friends in the ratio
of 1:3:3:5. She has a total of 96 figurines. If her best friend wants the most number of
figurines, how many figurines will she get?
Take a look on this ratio:
Friend A: Friend B: Friend C: Friend D = 1:3:3:5
In the problem, the total number of figurines is partitioned or divided into
unequal ratio of 1:3:3:5, thus making use of partitive proportions.
Amazing! You did very well.
What’s More
Let us try to answer more challenging sets of problems and activities about ratio
and kinds of proportion.
Activity 2: Find Me!
Direction: Give what is being asked in the following problem. All answers must be in
simplified form.
1. Express the sentence into ratio: In selling personalized cakes, the cost of
packaging is ₱60.00 and the cost of ingredients is ₱340.00.
Answer:
2. Cheska participates in a baking contest. During the competition, Cheska made
sure she put 2 cups of sugar and 4 eggs on every cake. What would be the
ratio of the cups of sugar to the number of eggs if she baked 4 cakes?
Answer:
3. Liza, Kathryn and Nadine are partners. Their capital balances are ₱20,000.00
₱40,000.00 and ₱30,000.00 respectively. What is their capital ratio?
Answer:
Activity 3: Tell Me More!
Direction: Identify if the given problem illustrates a direct proportion, inverse
proportion or partitive proportion.
1. An artisan bread maker uses 2,000 grams of flour to make 4 loaves of
handcrafted bread. How many grams of flour is needed to make 2 loaves of
bread?
Answer:
2. If Mang Gorio wants to give ₱5,000.00 to his four children in the ratio of 1:2:3:4
for their weekend allowance, how much will each of the four children receive?
Answer:
3. It takes 4 mechanics to repair a car for 6 hours. How long will it take for 7
mechanics to do the repair, if they work at the same rate?
Answer:
9
What I Have Learned
Now that you’ve learned a lot from the very start of our module, let’s summarize
our lesson from the very start by filling in the blanks with the correct statement.
Activity 4: Lets Wrap It Up!
1. A ratio is
between two numbers or measurement.
2. In the proportion
.
3:5 =
6:10, the means
are
and
3. In direct proportion, if one variable increases the other variable
4. A number is inverse proportionate to another when one variable decreases, the
other variable
.
5. Speaking of partitive proportion, we are talking about a whole divided into
.
What I Can Do
Here is another activity that will help you apply what you have learned about
kinds of proportion.
Activity 5: Choose Me Please!
Direction: Choose the letter of the following real life situations and problems that
illustrates direct, inverse and partitive proportion. Write your answer on
the second column.
-
a. A school buys 4 gallons of juice for 50 kids. How many gallons do they need
for 75 kids?
b. Assuming they work at the same rate, how long will it take 2 housekeepers to
clean an entire house if it takes 4 days for 8 housekeepers to clean it?
c. If one US dollar is equivalent to ₱49 pesos, how much is 50 US dollars if
converted to peso?
d. Amidst the community quarantine, Richard wants to donate 400 sacks of
rice to the residents of barangay San Jose, Fatima and Calumpang in the
ratio of ____________________________.
How can
many
sacks
of rice
barangay
Fatima
e. 1:3:2.
receive?
Three men
finish
doing
thewill
interior
designing
of a
house in 3 weeks. How
many men are needed to finish the interior designing in a week?
Kinds of Proportion
Answer
Direct Proportion
Inverse Proportion
Partitive Proportion
10
.
Lesson
2
Solving Problems Involving
Kinds of Proportion
Hello! Do you still remember these lines, “if two ratios are equal, then their
reciprocals are also equal” or “the product of the extremes is equal to the product of
the means”? Right now, let us deal with these statements more in-depth as go
through with this module.
What’s In
Let us review on the following terms using a concept map for you to better
understand the lessons in this module.
Activity 1: Refresh Your Mind
Direction: Fill in the blanks with right word/s to make each statement correct. Base
your answer on the illustrations below.
11
1. It is comparison of two numbers or measurement known as
.
2. A relationship between two variables when their ratio is equal to a constant
value is called
3.
.
represents a relationship of two values x and y such when
x increases, then y decreases or vice versa.
4. A/an
i s a ratio in which the two terms are different in units.
5. A whole is divided into parts that is proportioned into equal or unequal ratios
refers to the
Alright! You are now ready to explore kinds of proportion and solve real life
problems.
-
What’s New
How are you coping with our lesson? I hope you are curious about the following
activities that we will discuss ing in this module. The next activity will test your
readiness on pre requisite skills on translating verbal statements involving
proportions into mathematical statements
-
Activity 2: Match It, Translate It!
Direction: In this activity, you will:
A. Match the following phrases translated into mathematical expressions or
statements by connecting it through lines:
Mathematical
Expressions/Statements
Verbal Sentences/Phrases
1. There are twice as many partners ( P)
as corporations (L).
A. 𝟏/𝟐(𝑳 - 𝑷 ) + 𝟐
2. There are half as many profit ( P) as
loss ( L).
B. 𝟐𝑷 = 𝑳
3. The number of Php100 bills (L) is
twice as many as Php500 bills ( P).
4. One less than twice the salaries of
Pedro (P) & Lito (L)
C. L =
𝟏P
𝟐
D. 𝟐(𝑷 + 𝑳) - 𝟏
-----
5. Two more than half the difference of
certain mobile phones sales (L) and
power bank sales (P)
E. 𝑷 = 𝟐𝑳
12
B. Translate the following problems to mathematical statement:
Given Problem
Mathematical Statement
6. It takes Andy 30 minutes to burn 200
calories in jogging. How long (T) will it take
Andy to burn 400 calories?
7.How many tea bags (B) are needed to make
15 liters of iced tea when eight tea bags are
needed to make 5 liters of iced tea?
8. Assuming they work at the same rate, how
long (S) will it take 2 housekeepers to clean
an entire house if it takes 4 days for 8
housekeepers to clean it?
9.Four machines can recopy 25000 books in
6 days. How many machines (M) are needed
to copy 25000 books in 3 days?
10. Mr. Covito donated ₱5,000.00 as a club
fund for the upcoming ABM strand fair.
The Accountancy Club, Business Club
and Management Club will share the
amount in the ratio of 2:3:5. How much
(x) will each group receive?
Great Job! Keep the fire burning! Let’s unlock some difficulties.
What is It
You are already knowledgeable in translating worded problems to mathematical
statements.
Now, let us process and classify those translated problems to the three (3) kinds
of proportions. How do we recognize whether a given proportion problem involves a
direct proportion, an inverse proportion, or a partitive proportion? The definitions
below determine the kinds of proportion considering the following problem:
13
1.) If 10 laptops cost the number of ₱200,000.00, then
how much do 8 laptops cost?
We see that the greater the number of laptops, the
higher is the total cost (x). Setting up the ratio, we
obtain:
Given:
Number of laptops:
a=
Total cost:
10 laptops
b = ₱200,000.00
c= 8 laptops
d= x
* 10 laptops for ₱ 200,000.00
Mathematical Statement:
∗ 𝐿𝑎𝑝𝑡𝑜𝑝𝑠 ∶ 𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡 = 𝐿𝑎𝑝𝑡𝑜𝑝𝑠 ∶ 𝑡𝑜𝑡𝑎𝑙 𝑐𝑜𝑠𝑡
10 𝑙𝑎𝑝𝑡𝑜𝑝𝑠
8 𝑙𝑎𝑝𝑡𝑜𝑝𝑠
=
₱200,000.00
𝑥
Solution:
10
200,000
=
8
𝑥
10𝑥 = 8(200,000)
10𝑥
10
=
1,600,000
10
𝒙 = ₱𝟏𝟔𝟎, 𝟎𝟎𝟎
In the problem, the number of laptops and total cost are directly proportional
since the more laptops you buy, the higher is the cost or the lesser laptops you buy,
the lower is the cost. Thus, the problem involves Direct Proportion.
2.) In a T-shirt factory, 5 employees can finish designing
20 T-shirts in two hours. How long will it take 10 people
to design 20 T-shirts?
We see that the more employees on a job, the lesser time
(x) needed to finish the job. Setting up the ratio, we obtain:
Given:
No. of employees:
Time spent:
a=
5 employees
b = 2 hrs.
c = 10 employees
d = x hrs.
* 5 employees for 2 hours
Mathematical Statement:
* less 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒𝑠 ∶ more 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒𝑠 = 𝑚𝑜𝑟𝑒 𝑡𝑖𝑚𝑒 ∶ 𝑙𝑒𝑠𝑠 𝑡𝑖𝑚𝑒
5 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒𝑠
x
10 𝑒𝑚𝑝𝑙𝑜𝑦𝑒𝑒𝑠 2 hours
14
=
Solution:
5
10
=
x
2
5(2) = 10(x)
10
10x
____ = _____
10
10
10
𝑥=
10
𝒙 = 𝟏 𝒉𝒓.
In the problem, the number of employees and time to finish the job are
inversely/indirectly proportional since the more employees you hired, the lesser the
time to spend to finish the job. Thus, the said problem involves Inverse/Indirect
Proportion.
3.) Quarantina wants to donate her collection of figurines to
her four friends in the ratio of 1:3:3:5. She has a total of 96
figurines. If her best friend wants the most number of
figurines, how many figurines will she get?
We see that the whole collection of figurines is being divided
into parts (x) and distributed to them with specified ratio.
Setting up the partition, we obtain:
Given:
Let x be the constant number of figurines
1x = number of figurines for her 1st friend
3x = number of figurines for her 2nd friend
3x = number of figurines for her 3rd friend
5x = number of figurines for her best friend (the most)
96 = total number of figurines
Mathematical Statement:
1𝑥 + 3𝑥 + 3𝑥 + 5𝑥 = 96
Solution:
12𝑥 = 96
12𝑥 96
=
12
12
𝒙 = 𝟖 𝒇𝒊𝒈𝒖𝒓𝒊𝒏𝒆𝒔
5x = number of figurines for her 4th friend (the most)
5x = 5(8) = 40 figurines for her best friend
When a whole is partitioned into equal or unequal ratios, such concept involves
Partitive Proportion. In the problem, the total number of figurines is partitioned
into the ratio of 1:3:3:5, thus making use of partitive proportions.
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What’s More
Alright! We have already unlocked your difficulties in classifying, differentiating
and defining kinds of proportions. At this moment, be ready for our next activity.
Here, your will be able to use what you have learned from our previous discussions.
You can do this!
Activity 3: Answer Me: Where do I belong?
Direction: Solve the following problems and identify the kind of proportion involved.
1. An artisan bread maker uses 2,000 grams of flour to make 4 loaves of
handcrafted bread. How many grams of flour is needed to make 2 loaves of
bread?
Solution
Kind of Proportion:
2. It takes 4 mechanics to repair a car for 6 hours. How long will it take 7
mechanics to do the repair if they work at the same rate?
Solution
Kind of Proportion:
3. If Mang Orly wants to give ₱5,000.00 to his four children in the ratio of 1:2:3:4
for their weekend allowance, how much is the least amount of allowance?
Solution
Kind of Proportion:
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4. A box of pencil costs ₱30 pesos. How much do 4 boxes cost?
Solution
Kind of Proportion:
5. Three men can finish doing the interior designing of a house in 3 weeks. How
many men are needed to finish the interior designing in a week?
Solution
Kind of Proportion:
What I Have Learned
Now, let us summarize what you have learned. Let’s do this activity!
Activity 4: Write About Me
Direction: Write an essay briefly and concisely to process your knowledge on how to
solve problems involving kinds of proportions.
1. What are the steps in solving problems involving direct proportions?
__ __ __ __ __ __ __ __ __ __ _________________ _________________________________________ __
________________________________________________________________________________
2. What are the steps in solving problems involving indirect/inverse proportion
__ __ __ __ __ __ __ __ __ __ __ __ __ __________ ____________________________________________
________________________________________________________________________________
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3. What are the steps in solving problems involving partitive proportions?
__________________________________________________________________________________
_ _ __ __ __ __ __ __ __ __ __ ____ ____ ___________ __________________________ _________________
What I Can Do
Let us now apply what you have learned in solving problems involving kinds
of proportion in real-life situations.
Activity 5: I am Being Solved!
Direction: Solve the following problems involving kinds of proportion.
1. The ratio of boys to girls in a badminton tournament game is 4:3. Mariel
counted that there are 12 more boys than girls. How many boys and
girls are there in the tournament?
2. It takes 3 salesmen 8 days to sell 5,000 boxes of soap. If 2 more
salesmen are added, how long will it take them to sell the same number
of boxes of soap?
3. Mr. Faustino allocates his monthly salary for bills, food, transportation,
and other expenses at the ratio of 3:6:7:9, respectively. If he receives
₱ 28,450.00 each month, how much is his budget for food?
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Assessment
Now that we are about to end this module, let us assess your learnings by
answering the following questions. Do your best in this test. Goodluck!
Direction: Read and understand the following problems carefully. Encircle the letter
of the correct answer.
1. A couple went out for a date and spent ₱1,500 on dinner and ₱400 at the movie
theater. What is the ratio of peso spent on dinner and the total amount spent
for a movie?
a. 4:15
b. 15:4
c. 15:19
d. 19:15
2. A basketball team won 15 games and lost 5 games. What is the ratio of games
lost to the total games won?
a. 1:3
b. 1:4
c. 3:4
d. 4:3
3. Which
a.
b.
c.
d.
pair of ratios are proportional?
3 laptops for ₱66; 6 laptops for ₱132
16 points scored in 3 games; 48 points scored in 6 games
98 words typed in 3 minutes; 162 words typed in 5 minutes
20 computers for 60 students; 40 computers for 130 students
4. What proportion states that as one variable increases, the other variable
decreases?
a. direct
b. inverse
c. partitive
d. negative
5. Which
a.
b.
c.
d.
of the following is an example of direct proportion?
3:18 = 9:6
6:30 = 5:25
10:3 = 15:2
15:5 = 6:18
6. What kind of proportion is involved between the time taken for a journey and
the speed of the car at a uniform distance?
a. direct
b.
c.
d.
inverse
partitive
combined
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7. Which of the following is an example of partitive proportion?
a. 6:9 = 18:3
b. 9:45 = 5:25
c. 20:4 = 40:80
d. Divide 200 into 1:4:5
8. What kind of proportion is involved when a whole portion is divided into parts
that is proportional to the given ratio?
a. direct
b. inverse
c. partitive
d. combined
9. Which of the following problems represent an inverse proportion?
a. Divide a 75 m rope into 4 with the ratio 1:2:5 :7. What is the measure
of each rope?
b. The exchange rate of peso to a dollar in 2019 is ₱51.20 to $1. How
much will you get for $8.50?
c. Three men can complete a project in 6 weeks. How many men will be
needed if the project is to be completed in a week?
d. When Mrs. Reyes went to abroad for an educational tour, she noticed
that each guide goes along with five tourists. If there are 5 guides, how
many tourists would they bring around?
-
10. Which of the following problems DOES NOT belong to the group?
a. A government-donated food pack is sufficient to feed 15 persons for
3 days. How many days would it last for 10 persons?
b. If 10 tablet-PC cost he number of ₱100,000.00, then how much do 8
tablet-PCs cost?
c. How many tea bags (B) are needed to make 10 liters of iced tea when
eight tea bags are needed to make 5 liters of iced tea?
d. Three boys sold rosary necklaces in the ratio of 2:3:4. Together they
sold 225 rosary necklaces. How many rosary necklaces did each boy
sell?
11. The verbal phrase “the ratio of a three and number (x) added to four” is
equivalent to which of the following mathematical statements?
𝑥+4
a.
3
b. 3: 𝑥 + 4
c. 𝑥 = 3 + 4
d. 3 + 4
𝑥
12. Mr. Ramon allocates his monthly salary for bills, food, transportation, and
other expenses at the ratio of 3:3:2:2. If he received ₱28,450.00 last month,
which among the mathematical statements represent an answer to solve the
various allocations for payment?
a. 10𝑥 = ₱28,450.00
b. 3𝑥 + 3𝑥 + 2𝑥 + 2𝑥 = 28,450.00
c.
3+3+2+2
𝑥
= ₱28,450.00
d. 3𝑥 + 3𝑥 + 2𝑥 + 2𝑥 =
28,450 00
1
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13. Junjun will spend ₱5,500.00 for his birthday party if he will invite 15 guests.
If the cost is directly proportional to the number of invited guests, how much
will it cost is he invites 30 guests?
a. ₱11,000.00
b. ₱11,100.00
c. ₱11,150.00
d. ₱11,190.00
14. If 4 men can do a portion of a job in 9 days, how many men can do the same
job in 6 days?
a. 5
b. 6
c. 7
d. 8
15. If Mang Inasal wants to give ₱10,000 to his four children in the ratio of 1:2:3:4
for their weekend allowance, how much will each of the four children receive?
a. ₱450: ₱1,050: ₱1,450: ₱2,050
b. ₱500: ₱1,000: ₱1,250: ₱2,250
c. ₱1,000: ₱2,000: ₱3,000: ₱4,000
d. ₱1,000: ₱2,000: ₱2,500: ₱4,500
Good Job! You did well on this module! Keep going!
Additional Activities
Congratulations! You’re done with this module. I know you’ve learned a lot from
different kinds of proportion. But for more additional activity, I want you to answer
the given problem below as a preparation for your next module.
Activity 1: Books Pa More!
1. Sean Matthew can read 10 books in 2 months. If he plans to read 30 books, how
many months will it take him to finish them all?
Activity 2: “My 3-2-1 Chart”
Direction: Complete the 3-2-1 chart below.
My 3-2-1 Chart
Three things I found out:
1.
2.
3.
Two interesting things:
1.
2.
One question I still have: :
1.
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Answer Key
Reference
Lopez, B.R., Lundag, L. Dagal, K.A. & Garces, I.J. (2016). Business Math Textbook.
Quezon City: Vibal Group, Inc. pp.53 -69
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DISCLAIMER
This Self-learning Module (SLM) was developed by DepEd SOCCSKSARGEN
with the primary objective of preparing for and addressing the new normal.
Contents of this module were based on DepEd’s Most Essential Learning
Competencies (MELC). This is a supplementary material to be used by all
learners of Region XII in all public schools beginning SY 2020-2021. The
process of LR development was observed in the production of this module.
This is version 1.0. We highly encourage feedback, comments, and
recommendations.
For inquiries or feedback, please write or call:
Department of Education – SOCCSKSARGEN
Learning Resource Management System (LRMS)
Regional Center, Brgy. Carpenter Hill, City of Koronadal
Telefax No.: (083) 2288825/ (083) 2281893
Email Address: region12@deped.gov.ph
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