7
Mathematics
Quarter 2 – Module 2:
Conversion of Measurements
in Metric and English Systems
Mathematics – 7
Self-Learning Module (SLM)
Quarter 2 – Module 2: Converting Measurements from One Unit to Another
First Edition, 2020
Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the
Government of the Philippines. However, prior approval of the government agency or office
wherein the work is created shall be necessary for exploitation of such work for profit. Such
agency or office may, among other things, impose as a condition the payment of royalties.
Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names,
trademarks, etc.) included in this module are owned by their respective copyright holders. Every
effort has been exerted to locate and seek permission to use these materials from their respective
copyright owners. The publisher and authors do not represent nor claim ownership over them.
Development Team of the Module
Writers: John Rey C. Baldestamon
Editors: Armi G. Samillano, Monaima P. Garcia
Reviewers: Freddie V. Noble, Evelyn Q. Neral and Marrissa L. Noble
Illustrator: John Rey C. Baldestamon
Layout Artist: John Rey C. Baldestamon
Cover Art Designer: Reggie D. Galindez
Management Team: Allan G. Farnazo, CESO IV – Regional Director
Fiel Y. Almendra, CESO V – Assistant Regional Director
Name of Schools Division Superintendent
Name of Assistant Schools Division Superintendent
Gilbert B. Barrera – Chief, CLMD
Arturo D. Tingson Jr. – REPS, LRMS
Peter Van C. Ang-ug – REPS, ADM
Name of REPS – Subject Area Supervisor
Name of CID Chief
Name of Division EPS In Charge of LRMS
Name of Division ADM Coordinator
Name of EPS – Subject Area Supervisor
Printed in the Philippines by Department of Education – SOCCSKSARGEN Region
Office Address:
Telefax:
E-mail Address:
Regional Center, Brgy. Carpenter Hill, City of Koronadal
(083) 2288825/ (083) 2281893
region12@deped.gov.ph
7
Mathematics
Quarter 2 – Module 2:
Conversion of Measurements
in Metric and English Systems
Introductory Message
For the facilitator:
Welcome to the Mathematics 7
Self-Learning Module (SLM) on Converting
Measurements from One Units to Another!
This module was collaboratively designed, developed and reviewed by educators from
public institutions to assist you, the teacher or facilitator in helping the learners meet
the standards set by the K to 12 Curriculum while overcoming their personal, social,
and economic constraints in schooling.
This learning resource hopes to engage the learners into guided and independent
learning activities at their own pace and time. Furthermore, this also aims to help
learners acquire the needed 21st century skills while taking into consideration their
needs and circumstances.
In addition to the material in the main text, you will also see this box in the body of the
module:
Notes to the Teacher
This contains helpful tips or strategies that
will help you in guiding the learners.
As a facilitator you are expected to orient the learners on how to use this module. You
also need to keep track of the learners' progress while allowing them to manage their
own learning. Furthermore, you are expected to encourage and assist the learners as
they do the tasks included in the module.
2
For the learner:
Welcome to the Mathematics 7 Self-Learning Module (SLM) on Converting Units from
One Units to Another!
The hand is one of the most symbolized parts of the human body. It is often used to
depict skill, action and purpose. Through our hands we may learn, create and
accomplish. Hence, the hand in this learning resource signifies that you as a learner is
capable and empowered to successfully achieve the relevant competencies and skills at
your own pace and time. Your academic success lies in your own hands!
This module was designed to provide you with fun and meaningful opportunities for
guided and independent learning at your own pace and time. You will be enabled to
process the contents of the learning resource while being an active learner.
This module has the following parts and corresponding icons:
What I Need to Know
What I Know
What’s In
This will give you an idea of the skills or
competencies you are expected to learn in the
module.
This part includes an activity that aims to
check what you already know about the
lesson to take. If you get all the answers
correct (100%), you may decide to skip this
module.
This is a brief drill or review to help you link
the current lesson with the previous one.
What’s New
In this portion, the new lesson will be
introduced to you in various ways such as a
story, a song, a poem, a problem opener, an
activity or a situation.
What is It
This section provides a brief discussion of the
lesson. This aims to help you discover and
understand new concepts and skills.
What’s More
This comprises activities for independent
practice to solidify your understanding and
skills of the topic. You may check the
answers to the exercises using the Answer
Key at the end of the module.
What I Have Learned
This
includes
questions
or
blank
sentence/paragraph to be filled in to process
what you learned from the lesson.
What I Can Do
This section provides an activity which will
help you transfer your new knowledge or skill
into real life situations or concerns.
3
Assessment
Additional Activities
Answer Key
This is a task which aims to evaluate your
level of mastery in achieving the learning
competency.
In this portion, another activity will be given
to you to enrich your knowledge or skill of the
lesson learned. This also tends retention of
learned concepts.
This contains answers to all activities in the
module.
At the end of this module you will also find:
References
This is a list of all sources used in developing
this module.
The following are some reminders in using this module:
1. Use the module with care. Do not put unnecessary mark/s on any part of the
module. Use a separate sheet of paper in answering the exercises.
2. Don’t forget to answer What I Know before moving on to the other activities
included in the module.
3. Read the instruction carefully before doing each task.
4. Observe honesty and integrity in doing the tasks and checking your answers.
5. Finish the task at hand before proceeding to the next.
6. Return this module to your teacher/facilitator once you are through with it.
If you encounter any difficulty in answering the tasks in this module, do not hesitate
to consult your teacher or facilitator. Always bear in mind that you are not alone.
We hope that through this material, you will experience meaningful learning and
gain deep understanding of the relevant competencies. You can do it!
4
What I Need to Know
Good day, how are you? I hope you are safe and sound. How about we learn
something new today? Are you in for another mind-boggling challenge?
This module will help you find solutions on unit conversion which you may
encounter in real life. Sit back, relax and prepare yourself and materials. Let the
adventures begin.
After you go through the lessons, expect you will be able to:
1. convert measurement from one unit to another in both Metric and English
system;
What I Know
Before the challenges begin, find out how much you already know about the lesson you
will undertake. Answer the items below. Take note of the items that you were not able
to answer correctly and find the right answer as you go through this module.
1.
15 km is equal to?
a. 8.27 mi
b. 9.32 mi
c. 12.04 mi
d. 6.45 mi
2.
90 inches is equal to?
a. 5.8 ft
b. 8.5 ft
c. 5.7 ft
d. 7.5 ft
3.
5.5 ft is equivalent to?
a. 50 inches
b. 55 inches
c. 60 inches
d. 66 inches
4.
55 yd is equal to?
a. 0.08 km
b. 50.5 m
c. 1 980 in
d. 168 ft
5.
3.2 mi is equal to?
a. 5263 yd
b. 5362 yd
c. 5531 yd
d. 5631 yd
6.
10 lb is closest to?
a. 4.58 kg
b. 4.53 kg
c. 4.59 kg
d. 4.60 kg
7.
5 g = ______ mg
a. 50
b. 500
c. 1000
d. 5000
3.8 mm = ______ m
a. 0.0038 m
b. 0.038 m
c. 0.38 m
c. 38 m
8.
5
9.
10.5 ha = _____ acre
a. 2.6
b. 4.2
c. 26
d. 42
10.
How many hours are there in one week?
a. 120 hours
c. 200 hours
b. 168 hours
d. 218 hours
11.
The equivalent of 348 grams in centigrams is?
a. 3.48 cg
c. 34.8 cg
b. 348 cg
d. 34 800 cg
12.
The normal room temperature is 27℃. What is its equivalent in ℉?
a. 518℉
c. 800.60℉
b. 80.60℉
d. 8060℉
13.
Vani should spend 180 minutes in a remedial class. How many hours does she
need to complete the class?
a. 1.5 hour
c. 4.5 hours
b. 3 hours
d. 6 hours
14.
Arrange the following from shortest to longest measure of time:
I. 1 day
II. 25 hours
III. 640 minutes
IV. 2400 seconds
a. I-II-III-IV
b. IV-III-II-I
c. IV-III-I-II
d. I-II-IV-III
15. Convert 120 milliliters of alcohol into liters:
a. 0.012 L
c. 1.2 L
b. 0.12 L
d. 1.5 L
6
Lesson
1
Converting Measurements
from One Unit to Another
What’s In
Hey there! If you are now at this level, it means that you are now one step closer
to understanding new concepts.
To begin with, you need to arm yourself with pieces of information you have
acquired from the previous lesson. Recall also the different units of measure and when
to use each one. The following idea may be of help:
*Length is measured in centimeters, meters, kilometers, feet and miles.
*Weight can be measured in grams, kilograms and pound.
*Capacity is measured in liters and gallons.
*Temperature is measured in Celsius, Fahrenheit, and Kelvin.
*Time is measured in seconds, minutes, hours, days, weeks, months, and years.
Now, which unit of measure would you use to find the following?
1. length of a pencil
2. distance between two cities
3. Time it takes to write your name
4. Time it takes to complete a course in college
5. Weight of a sack of rice
7
What’s New
There you go! This is it. You are now equipped with necessary skills to face
upcoming challenges you may take. Take a breath and get ready to add something up
to your knowledge. Good Luck!
What’s the Pattern?
The lead researcher for the cure of covid-19 was
murdered. All of his researches are kept intact in his mobile
phone. Unfortunately, we need to unlock the phone using the
correct pattern to open it. The screen displays the series of
measurement under the number from 0 – 9.
If we are to draw the pattern base on the
measurements, what is sequence of the pattern?
Hint:
shortest to longest
1
1 meter
4
60 dm
7
23 ft
x
2
3
80 inches
3 yards
5
500 cm
6
1 km
0.004
8
9
0.005 miles
9 000 mm
0
√
33 ft
What is It
To begin our lesson, you will understand that in some time we encounter
converting number from one unit to another unit. For instance, did it happen to you
that your teacher asked your height in centimeters but you only knew it by feet? Or
the nurse
asked for your weight in pounds but you only knew it by kilograms? This is where
you realize the importance of learning the concept of conversions.
To “convert” means to change number’s unit into another unit but the value
remains the same. There are many methods of converting measurements but we will
only focus with the easiest – dimensional analysis method
The dimensional analysis method involves multiplying a series of fraction
which is equal to the value of one.
For example, if you want to convert 6 feet to inches:
6 ft x
12 𝑖𝑛
1 𝑓𝑡
By dimension analysis
= 6 x 12in
By multiplication and cancelling cm
= 72 in
By simplification
Thus, 6 feet is 72 inches.
8
Take this as the very important key to ponder:
Converting takes many forms, whether you convert time, length, width, distance, temperature, etc., the method we
will use is applicable to all except temperature. As long as you know the fraction to use, you can easily convert the
unit manually by dimensional analysis method. Although we have gadgets like mobile phones with application that
can easily converts units in just a blink of an eye, it is not right to rely on it all the time. Solving might be hard and
mind tiring for some, but it is a best way to upgrade our logical and critical thinking which you use to solve real life
Iproblems.
know that everything seems blurring at this point of time for you.
Now, let us go through the following examples for you to understand more.
Converting Length
Length is the longer dimension of an object as opposed to its width.
1. Convert 40 cm to mm.
Solution: In the conversion table given at the back of this module,
0.001 m = 0.1cm. Thus,
40 cm x
=
0.001 𝑚
0.1 𝑐𝑚
By dimension analysis
0.04 𝑚
By multiplication and cancelling cm
0.1
= 0.4 m
By simplification
2. Convert 1.4 km to mm.
Solution: in the conversion table
1km = 1 000 000 mm, thus:
1.4 km x
1 000 000 𝑚𝑚
1 𝑘𝑚
given at the
back of this module
By dimension analysis
= 1.4 x 1 000 000 mm
By multiplication and cancelling km
= 1 400 000 mm
By simplification
3. How many inches are in 1.6 miles?
Solution: in the
1mi = 63 360 in, thus:
1.6 mi x
conversion table
63 360 𝑖𝑛
1 𝑚𝑖
given at the
By dimension analysis
= 1. 6 x 63 360 in
By multiplication and cancelling mi
= 101 376 in
By simplification
9
back of this module
Converting Mass and Weight
Mass is the measure of the amount of matter in an object; Weight is the measure
of how heavy an object is.
1. Convert 1.8 kg to mg.
Solution: in the conversion table
1kg = 1 000 000 mg, thus:
1.8 kg x
1 000 000 mg
1 kg
given at the
back of this module
By dimension analysis
=1.4 x 1 000 000 mg
By multiplication and cancelling kg
= 1 800 000 mg
By simplification
2. What is 1.4 kg in mg
Solution: in the conversion table
1kg = 1 000 000 mg, thus:
1.4 kg x
1 000 000 mg
1 kg
given at the
back of this module
By dimension analysis
= 1.4 x 1 000 000 mg
By multiplication and cancelling km
= 1 400 000 mg
By simplification
3. How many 2.5 kg in lb?
Solution: in the
conversion table
thus:
given at the
back of this module
1kg is approximately 2.205 lb,
= 2.5 kg x
2.205 lb
1 kg
By dimension analysis
= 5.5125 lb
Converting Volume
Volume is the amount of space in an object and expressed in cubic units
1. Convert 4.5 L to ml.
Solution: in the
1 000 ml = 1 L, thus:
4.5 L x
conversion table
1 000 𝑚𝑙
1𝐿
= 4.5 x 1 000 ml
given at the
back of this module
By dimension analysis
= 4 500 ml
2. Convert 3.5 cm³ to mm³.
Solution: in the conversion table
1000 mm³ = 1 cm³ , thus:
10
given at the
back of this module
3.5 cm³ x
1 000 mm³
1 cm³
By dimension analysis
= 3 500 mm³
3. How many gallons are in 8 qt?
Solution: in the
1gallon = 4 qt, thus:
8 qt x
conversion table
given at the
back of this module
1 gallon
4 qt
= 2 gallons
Converting Time
Time is the interval between two or more events.
1. Convert 200 days to hours.
Solution:
200 days x
24 ℎ𝑟
1 𝐷𝑎𝑦
= 200 x 24 hr
= 4 800 hr
2. Convert 1.5 hours to seconds.
Solution :
1.5 hr x
60 min
1 hr
x
60 sec
1min
= (1.5)(60)(60) sec
= 5 400 sec
Converting Temperature
Temperature is the measure of how hot and cold a substance is. To convert temperature
a formula must be used. Below are the formulas use to convert temperature.
9
𝐹 = 5 ℃ + 32
5
𝐶 = 9 (℉ − 32)
Let us convert temperature using the formulas.
1. Convert 25 ℃ to ℉.
9
F = 5 ℃ + 32
9
5
(25) When simplified is equal to 45.
F = 45 + 32
F = 77
Thus 25 ℃ is equal to 77℉.
11
1. Convert 59 ℉ to 25 ℃.
5
C = 9 (℉ − 32)
5
C = 9 (59 − 32)
Substitute 25 to℃
5
5
C = 9 (27)
9
(27)When simplify is equal to 15.
C = 15
Thus 59℉ is equal to 15℃.
Follow up:
If it happened that you still don’t understand any of these examples, please feel free to
contact your teacher at this number _________________. We, from the mathematics
teachers’ department will be happier to assist your learning process.
What’s More
This time, perform the following exercises to strengthen your skill in converting.
Activity 1: My equivalent pair!
Direction: Fill in the blank with the correct number to make it equal.
1.
2.
3.
4.
5.
5.93 km
75 cm
650 cm
850 m
282 in
=
=
=
=
=
______________m
______________mm
______________m
______________km
______________ft
6. 95 g
7. 4200 oz
8. 150 000 mg
9. 400 oz
10. 45 mg
Activity2: Fill me up!
Direction: Convert the following temperatures.
1.
2.
3.
4.
5.
90 ℃
80 ℉
120℃
130℉
70 ℃
=_______________℉
=_______________℃
=_______________℉
=_______________℃
=_______________℉
12
=
=
=
=
=
______________kg
______________gr
______________kg
______________lb
______________g
What I Have Learned
In this section, let us summarize what you have learned from this module.
Complete each statement below by filling out the blanks.
1. Volume is the amount of ______ in an object and expressed in ____________.
2. Mass is the ____________ of the amount of ____________ in an object
3. ____________ is the measure of how ____________ an object is.
4. The dimensional ____________ method involves multiplying a series of ____________.
which is equal to the value of ____________.
5. ____________ is the measure of how ____________ or ____________ a substance is.
What I Can Do
This is it! Now that you have a deeper understanding of the topic, you are then
ready to do the task below.
Activity 3: Notice Me!
Directions: In your home, look around, cite an object and indicate its measurement in
the table below. Then, give its equivalent measurement by converting it to another unit.
Item number 1 is already given as an example for you.
Object
1. a window curtain
2.
3.
4
5.
Length
3 m = 300 cm = 3000 mm
_______ = _______ = _______
Mass and weight
_______ = ________ = _______
_______ = _______ = _______
Temperature
_______= _______ = _______
Assessment
Hey! Finally, we are done in this module. So, for us to determine how much you
have gained from our lesson, please answer the following items. Select the best answer
from the given choices.
1. Convert 5.77 ft to inches
a. 57.7 inches
b. 67.7 inches
c. 69.24 inches
d. 79.24 inches
13
2. Convert 6 cups to mL
a. 143 mL
b. 430 mL
c. 1240 mL
d. 1422 mL
3. 3.15 km is equal to?
a. 1.96 mi
b. 6.45 mi
c. 8.27 mi
d. 9.32 mi
4. What is the equivalent of 10 lb?
a. 4.5 kg
b. 5.3 kg
c. 5.5 kg
d. 5.9 kg
5. 4.53 kg when converted to dag is equal to?
a. 45.3dag
b. 453 dag
c. 653 dag
d. 6.53 dag
6. Viel bought 550 g of flour for their baking activity. Convert the weight of the flour
into kilograms.
a. 0.55 kg
c. 5.5 kg
b. 5 kg
d. 55 kg
7. How many gallons are in 12.5 qt?
a. 3.125 qt
b. 5.5 qt
8. What is 3.5 cm³ to mm³?
c. 9.25 qt
d. 10.5 qt
a. 3.125 qt
b. 5.5 qt
c. 9.25 qt
d. 10.5 qt
9. Which of the following would make the statement equal: 5.8 mi = _______
a. 6.33 km
c. 93.3 hm
b. 9.33 km
d. both b and c
10. The equivalent of 458 grams in centigrams is?
a. 4.58 cg
c. 45.8 cg
b. 458 cg
d. 45 800 cg
11. The normal room temperature is 27℃. What is its equivalent in ℉?
a. 518℉
c. 800.60℉
b. 80.60℉
d. 8060℉
12. Below are the distances travelled by the siblings who went on a road biking.
Determine the farthest:
a. 0.75 mi
c. 750 yd
b. 1.5 km
d. 1750 m
13. What is 45 ℃ when converted to ℉?
a. 81℉
b. 113 ℉
c. 32 ℉
d. 132 ℉
14. A girl carries her schoolbag weighing 2.48 kilograms. How much weight in grams
is she carrying?
a. 12.4 g
b. 124 g
c. 248 g
d. 2 480 g
14
15. A tank contains 15.6 liters of gasoline. How many cubic meters of
gasoline is in the tank?
a. 0.0156 cm3
b. 0.156 cm3
c. 1.56 cm3
d. 156 cm3
Additional Activities
Perhaps, you have now mastered converting measurements from unit to another.
To enrich your knowledge and skill on the lesson learned, convert the following by
using a series of fraction. Show your solutions.
1.
8 days
= ______________seconds
2.
2.58 km
= ________________inches
Arrange the following measurements from:
1. shortest to longest
20 dm, 0.004 km, 39.37 in, 16.40 ft, 300cm
______ ______ ______ ______ ______
2. lightest to heaviest
1 000 g, 0.005 T, 300 dag, 8. 81lb, 2kg
____
______ ______ ______ ______ ______
____
15
16
What's More
A.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
B.
1.
2.
3.
4.
5 930 m
750 cm
6.5 m
0.85 km
23.5 ft
0.095 kg
1 837 500 gr
0.15 kg
25 lb
0.01045 g
17
What I Do
*Student’s answer may
vary
Assessment
1. c
2. d
3. a
4. a
5. b
6. a
7. a
8. a
9. b
10. d
11. b
12. d
13. b
14. d
15. a
What I Know
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
b
d
d
b
d
b
d
a
c
b
d
b
b
c
b
What I Have
Learned
1. Volume is the amount of
space in an object and
expressed in cubic units
2. Mass is the measure of
the amount of matter in an
object
3. Weight is the measure of
how heavy an object is.
4.
dimensional
The
analysis method involves
multiplying a series of
fraction which is equal to
the value of one.
194 ℉
26.66 ℃
248 ℉
54.44 ℃
℉
5. Temperature is the
measure of how hot or cold
Answer Key
References
Aguiarlar, Isidro C., et. Al.(2013). Creative Mathematics 7. pp. 130 – 138. Quezon City,
Phillipines. MissionBook Publishing, Inc.
Orines, Fernando B. (2012). Next Century Mathematics 7. pp. 138 – 140. Quezon City,
Philippines. Phonex Publishing House, Inc.
18
19
20
For inquiries or feedback, please write or call:
Department of Education - Bureau of Learning Resources (DepEd-BLR)
Ground Floor, Bonifacio Bldg., DepEd Complex
Meralco Avenue, Pasig City, Philippines 1600
Telefax: (632) 8634-1072; 8634-1054; 8631-4985
Email Address: blr.lrqad@deped.gov.ph * blr.lrpd@deped.gov.ph