This is the Grade 5 Mathematics Self-Learning Module (SLM) for Quarter 3, Module 1: Visualizing Percent. It was developed by DepEd Region VIII as an Alternative Delivery Mode module (First Edition, 2020) for learners studying at home. After working through it, learners can use models to show how a percent relates to a fraction, a ratio, and a decimal, and can change one form into another.
On this page 7 sections
What learners will learn
At the end of the module, learners are expected to:
- visualize percent and its relationship to fractions, ratios, and decimal numbers using models;
- write percent in decimal numbers, ratios, and fractions; and
- appreciate the relationship of percent to decimal, ratio, and fractions.
What is inside the module
The module has one lesson, Lesson 1: Visualizing Percent, arranged in the usual SLM parts:
- What I Know: a 10-item multiple-choice pretest using shaded grids and a 10 by 10 grid of symbols.
- What’s In: a review of proportion from the previous module.
- What’s New and What is It: the main discussion of percent, with worked examples.
- What’s More: three practice activities.
- What I Have Learned: a fill-in-the-blanks summary of the conversion rules.
- What I Can Do: a word problem to solve and show with a model.
- Assessment: a 10-item multiple-choice post-test.
- Additional Activities: a table of missing ratios, fractions, decimals, and percents.
- Answer Key: answers for the tests and activities.
Key ideas: percent, ratio, fraction, and decimal
What a percent is
A percent is a number or ratio that represents a fraction of 100. It is written with the symbol %. For example, 35% is the same as the decimal 0.35 and the fraction 35/100.
When you read a model, the shaded part is the numerator and the total number of equal parts is the denominator. A fraction can also be written in colon form as a ratio. On a 10 by 10 grid, the number of shaded squares out of 100 gives the percent directly.
Review: proportion
A proportion says that two ratios are equal, such as a : b = c : d. The first and fourth terms are the extremes, and the second and third terms are the means. By the Fundamental Law of Proportion, the product of the extremes equals the product of the means, which is the same as cross multiplication.
The module’s empanada example shows this. A recipe uses 10 ounces of ground pork for 5 empanadas. Since 10 ÷ 5 = 2 ounces per empanada, 8 empanadas need 2 x 8 = 16 ounces. So 10 : 5 = 16 : 8, because 5 x 16 = 80 and 10 x 8 = 80.
Worked examples from the module
- Ratio from a model: Arthur travelled 32 km in 4 hours. The ratio of time to distance is 4:32, shown as 4 shaded squares out of 32. It simplifies to 1:8, so Arthur travels 8 km every hour.
- Percent from a score: Renan scored 89 out of 100 in a Math test. The ratio is 89:100, or the fraction 89/100. Dividing, 89 ÷ 100 = 0.89. Moving the decimal point two places to the right gives 89%.
The conversion rules
The What I Have Learned section sums up these steps:
| To change | Do this |
|---|---|
| Ratio to fraction | Use the first quantity as the numerator and the second quantity as the denominator. |
| Fraction to decimal | Divide the numerator by the denominator. |
| Decimal to percent | Move the decimal point two places to the right and add the % sign, or multiply by 100 and add the % sign. |
| Percent to fraction | Write n% as n/100, then reduce it to lowest terms if needed. |
For example, the Additional Activities show that 2/5 = 2:5 = 0.4 = 40%, and 4:7 = 4/7 = 0.57 = 57% when rounded to the nearest hundredth.
Practice activities
- Activity 1: Equate Me! Write fractions such as 3/8, 8/12, and 4/20 as decimals and percents, rounding to the nearest hundredth.
- Activity 2: Express Me In! Write the shaded part of small grid models as a ratio and a fraction.
- Activity 3: A Part of Me! Write the shaded part of larger grids as a ratio, fraction, decimal, and percent.
- What I Can Do: A class of 60 students has 36 females and 24 males. Learners show each group as a ratio, fraction, decimal, and percent, and draw a model.
How to use this module
- Learners: Start with the What I Know pretest, then go through the parts in order. Write all answers on a separate sheet of paper and do not mark the module. Check your work with the answer key honestly. In the Assessment, a score of 8 to 10 means you are ready for the next module. If you score below 8, go over the lesson and exercises again.
- Parents and facilitators: Help your child read the directions before each task. Encourage them to draw or shade grids to see the percent, and to ask the teacher when a part is hard.
- Teachers: The pretest and post-test each have 10 items, and the answer key covers the tests and activities. Review the key before you check learners’ work (see the notes below).
Frequently asked questions
What grade and quarter is the Visualizing Percent module for?
It is Mathematics Grade 5, Quarter 3, Module 1. It was developed by DepEd Region VIII as a First Edition, 2020 self-learning module.
What is a percent, according to the module?
A percent is a number or ratio that represents a fraction of 100, written with the % symbol. For example, 35% equals 0.35 and 35/100.
How do you change a decimal to a percent?
Move the decimal point two places to the right and add the % sign, or multiply the decimal by 100 and add the % sign. For example, 0.89 becomes 89%.
Does the module have an answer key?
Yes. The answer key covers the pretest, the review, the three activities, What I Have Learned, What I Can Do, the assessment, and the additional activities.
What score should a learner get in the assessment?
The module says a score of 8 to 10 out of 10 means the learner can move on to the next module. Below 8, the learner should go over the lessons and exercises again.
Full text of the module
The text below is a transcription of the PDF above, as printed.
CO_Q3_Mathematics 5_Module 1
Mathematics Quarter 3 – Module 1: Visualizing Percent
Mathematics – Grade 5 Alternative Delivery Mode Quarter 3 – Module 1: Visualizing Percent 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.
Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio
Printed in the Philippines by ________________________
Department of Education – Region VIII
Office Address: DepEd Regional Office No. 8, Candahug, Palo, Leyte Telefax: (053)-832- 2997 E-mail Address: region8@deped.gpv.ph
Development Team of the Module
Writers: Nikolai S. Aralar, Nian L. Atis Editors: Christopher D. Salino Reviewers: Renato S. Cagomoc, Rolando Lacbo, Joshua Sherwin T. Lim Illustrator: Louie Mercader Layout Artist: Razle L. Jabelo, Jaycee B. Barcelona Management Team: Ma. Gemma M. Ledesma, Arnulfo R. Balane, Rosemarie M. Guino, Joy B. Bihag, Ryan R. Tiu, Sarah S. Cabaluna, Thelma Cabadsan-Quitalig, Elena S. De Luna, Renato S. Cagomoc, Noel E. Sagayap, Geraldine P. Sumbise, Joshua Sherwin T. Lim
Mathematics Quarter 3 – Module 1: Vizualizing Percent
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-by-step as you discover and understand the lesson prepared for you.
Pre-tests 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 Teacher are also provided to our facilitators and parents for strategies and reminders on how they can best help you on your home-based learning.
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. And 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
[illustration: bullseye target with arrow]
Hi, Mathletes! In this module, you will gain an understanding of percent and its relationship to fractions, ratios, and decimal numbers using models. In forming a fraction using a model, remember that the shaded part is the numerator, and the total number of equal parts is the denominator. A fraction can be also written in colon form to make it a ratio.
At the end of this module, you are expected to:
- visualize percent and its relationship to fractions, ratios, and decimal numbers using models;
- write percent in decimal numbers, ratios, and fractions; and
- appreciate the relationship of percent to decimal, ratio, and fractions.
What I Know
[illustration: pencil icon]
Directions: Choose the letter of the correct answer. Write your answers on a separate answer sheet.
What percent is the shaded portion?
[chart: 10 by 10 grid; shaded portion of grid]
A. 30%
B. 60%
C. 70%
D. 80%Which is the correct illustration for 8/12?
[illustration: four rectangular grid options labeled A, B, C, D]
A. [illustration] B. [illustration] C. [illustration] D. [illustration]Which decimal represents the shaded part?
[chart: 10 by 10 grid; shaded portion of grid]
A. 0.01
B. 0.10
C. 0.90
D. 00.09What percent is shaded in the figure in number 3?
A. 9% C. 90%
B. 10% D. 100%What fraction is the shaded portion?
[chart: 5 by 7 grid; shaded portion of grid]
A. 25/35 C. 20/35
B. 25/40 D. 20/40
Use the given figure to answer numbers 6 to 10.
What fraction is represented by the stars (★)?
[chart: 10 by 10 grid with stars, smileys, suns, diamonds, and hearts]
A. 1/3 C. 20/100
B. 2/3 D. 20/20If smileys (☺) has a fraction of 24/100, what is its equivalent in decimal form?
A. 0.12 C. 0.25
B. 0.24 D. 0.48What fraction is being illustrated by the sun (☼)?
A. 20/100 C. 22/100
B. 21/100 D. 25/100What percent is the diamond (◆) in the figure?
A. 13% B. 15% C. 20% D. 25%What fraction is equivalent for the blue hearts (♥)?
A. 2/10 B. 20/100 C. 22/100 D. 78/100
Please check your answers against the answer key on page 14.
Lesson 1: Visualizing Percent
In this module, you will learn how to visualize percent and its relationship to fractions, ratios and decimals using models. So, let’s get started.
A percent is a number or ratio that represents a fraction of 100. It is often denoted by the symbol “%”. For example, 35% is equivalent to the decimal 0.35, or the fraction 35/100.
What’s In
In the previous module, you have learned about two quantities in direct proportion.
A proportion is a statement that two ratios are equal. Proportion can be expressed through colon (:) and fraction. The first and the fourth terms are called extremes, and the second and third terms, are called the means.
[chart: proportion diagram; a : b = c : d, with “means” over b and c and “extremes” under a and d]
Recall the Fundamental Law of Proportion.
In a proportion, the product of the extremes is equal to the product of the means.
[chart: a : b = c : d, ad = bc, with arrows marking extremes and means]
This is equivalent to cross multiplication of equivalent fractions as shown below.
[chart: cross multiplication of a/b and c/d; ad = bc]
Example 1:
The ratio of ground pork in ounces to number of empanadas in its original recipe is 10:5. As the amount of ground pork increases, the number of empanadas also increases.
Suppose that the given ratio of ground pork to the number of empanadas is 20 : 8.
Let’s check if the two quantities are in proportion. Using cross multiplication,
10 x 8 = 80
[chart: cross multiplication; fractions 10/5 and 20/8 with crossing arrows]
5 x 20 = 100
Since the products are not the same, the two quantities are not in proportion.
Let’s make it a proportion.
First, calculate how much ground pork is needed for 1 serving. | 10 ÷ 5 = 2
1 serving needs 2 ounces. For 8 servings, multiply it by 8. | 2 x 8 = 16
Form the proportion. | 10: 5 = 16:8
To check if the answer is correct, use cross multiplication method or get the products of the means and extremes.
- Product of the means:
5 x 16 = 80 - Product of the extremes:
10 x 8 = 80 - The product of the means is equal to the product of the extremes. The two ratios are in proportion.
You should use 16 ounces of ground pork for 8 empanadas. Therefore, 10 : 5 and 16 : 8 is a proportion.
Answer the problem below. Show your solution.
Example 2:
For every 5 classes in the intermediate grades, there are 7 teachers. How many teachers are there for 20 classes?
What’s New
You will visualize percent and its relationships to fractions, ratios-and decimals.
Percent is a ratio of a number to 100. A ratio can be written as a fraction, and a fraction can be written as a decimal. So, visualizing percent using models and decimals would be very easy for you.
What is It
Let us solve the given problem.
Example #1:
Arthur travelled 32 km in 4 hours. What is the ratio of his travel time in hours to the distance in kilometers?
The ratio of time to distance can be written as 4:32 or 4/32.
[illustration: 4 by 8 grid of squares with the first four squares of the top row shaded]
This is illustrated in the given figure. There are 4 shaded squares out of 32 squares.
Note that the fraction form of 4:32 is 4/32 or 1:8.
To find the ratio of time to distance: 4:32 = 1:8 meaning for every hour, Arthur travels 8 km.
To find the ratio of distance to time: 32:4 or 8:1 meaning Arthur travels 8 km every hour.
Example #2:
Renan took the entrance exam at Calbayog City National High School for the STEM Curriculum. He scored 89 out of a 100-item test in Math. What percent of the test did he answer correctly?
Form the ratio 89:100 or the fraction 89/100
Note that 89/100 = 89 per hundred = 32% by definition of percent.
[transcriber’s note: the printed note reads “32%”; this is as printed]
Change it to decimal: divide numerator by the denominator.
89 ÷ 100 = 0.89
Change it to percent: multiply by 100 or move the decimal point two places to the right and attach the % sign.
0.89 = 89%
Therefore, Renan answered 89% of the math test correctly.
What’s More
Activity 1: Equate Me!
Directions: Write each fraction in decimal form and in percent. Round off the decimals to the nearest hundredth.
| Fraction | Decimal | Percent | |
|---|---|---|---|
| 1. | 3/8 | ||
| 2. | 8/12 | ||
| 3. | 5/15 | ||
| 4. | 2/8 | ||
| 5. | 4/20 |
Activity 2: Express Me In!
Directions: Write the shaded part in each illustration as a ratio and a fraction.
| Ratio | Fraction | |
|---|---|---|
| 1) [illustration: 2 by 3 grid of rectangles, one square shaded] | ________ | ________ |
| 2) [illustration: 3 by 2 grid of squares, two squares shaded] | ________ | ________ |
| 3) [illustration: 2 by 2 grid of squares, three squares shaded] | ________ | ________ |
| 4) [illustration: row of five squares, four squares shaded] | ________ | ________ |
| 5) [illustration: two rows of five squares, four squares shaded in the top row] | ________ | ________ |
Activity 3: A Part of Me!
Directions: Write the shaded part in each model as a ratio, fraction, decimal, and percent.
- [illustration: square grid of cells with the upper rows and left-hand cells shaded]
Ratio: ___________
Fraction: _____
Decimal: ___________
Percent: ___________
- [illustration: square grid of cells with the upper rows and a block of left-hand cells shaded]
Ratio: ___________
Fraction: _____
Decimal: ___________
Percent: ___________
- [illustration: square grid of cells with the upper rows and left-hand cells shaded]
Ratio: ___________
Fraction: _____
Decimal: ___________
Percent: ___________
- [illustration: grid of cells with two cells shaded at the lower left]
Ratio: ___________
Fraction: _____
Decimal: ___________
Percent: ___________
- [illustration: grid of cells with three left-hand columns shaded in the upper rows and two left-hand columns shaded in the lower rows]
Ratio: ___________
Fraction: _____
Decimal: ___________
Percent: ___________
What I Have Learned
Fill in the blanks.
- To change the _____ to fraction, use the first quantity as the _____ and the _____ quantity as denominator.
- To change a fraction to _____, divide the numerator by the _____.
- To convert decimal to a _____, simply move the decimal point two places to the right and add the % sign. Or, _____ the decimal by _____ and add a percent sign.
- To write n% as a , use the ratio n/100. Then, reduce it term if needed.
Good job! You are almost done with this module.
What I Can Do
Directions: Solve the word problem. Write your answer in ratio, fraction, decimal and percent. Show your answer using models.
A class of sixty (60) students is comprised of thirty-six (36) females and twenty-four (24) males. We can see that thirty-six out of sixty (36/60) students are females and twenty-four out of sixty (24/60) are males. The two fractions can be read as thirty-six sixtieths and twenty-four sixtieths. Represent this part-whole concept in a model with ratio, percent, decimal, and fraction.
Assessment
Directions: Choose the letter of the correct answer.
- What fraction is the shaded portion?
[illustration: 10 by 10 grid with an irregular block of cells shaded in the upper left]
- A. 12/100
- B. 10/25
- C. 12/12
- D. 10/10
- Which is the correct illustration for 7/10?
- A. [illustration: two-row bar model]
- B. [illustration: two-row bar model]
- C. [illustration: two-row bar model]
- D. [illustration: two-row bar model]
- Which illustration shows 27/50?
- A. [illustration: green-shaded grid]
- B. [illustration: green-shaded grid]
- C. [illustration: green-shaded grid]
- D. [illustration: green-shaded grid]
- Which is fraction shows the shaded portion of the illustration?
[illustration: grid of cells with a shaded block at the upper left]
A. 6/6 C. 6/20 B. 6/24 D. 24/6
- What fraction is the shaded portion?
[illustration: 10 by 10 grid with the upper rows and left-hand part shaded]
A. 81/50 C. 31/81 B. 81/31 D. 50/81
For numbers 6 to 10, use the figure below.
[illustration: 10 by 10 grid of symbols showing apple, swirl, music note, smiley and diamond symbols]
[transcriber’s note: counted from the image: apples 24, swirls 48, music notes 15, smileys 5, diamonds 8]
- What is the equivalent of 48/100 in decimal form?
A. 0.48 C. 0.408 B. 0.048 D. 00.048
- What fraction is illustrated by the iphone logo ([illustration: apple symbol])?
A. 24/100 B. 24/24 C. 48/14 D. 24/10
- What fraction is illustrated by the musical notes ([illustration: music note symbol])?
A. 15/15 B. 16/100 C. 15/100 D. 14/100
- What fraction is represented by the smileys ([illustration: smiley symbol])?
A. 5/5 B. 95/100 C. 5/10 D. 5/100
- What percent is the diamond ([illustration: diamond symbol]) in the figure?
A. 12% B. 11% C. 10% D. 8%
Please check your answers with the ANSWER KEY on page 14.
Got a score of 8-10? CONGRATULATIONS! Job well done. See you in the next module. If below 8, you may have to go over the lessons and the exercises again.
Additional Activities
Directions: Find the missing quantities. Round off decimals to the nearest hundredth.
| Ratio | Fraction | Decimal | Percent | |
|---|---|---|---|---|
| 1. | 2/5 | |||
| 2. | 0.08 | |||
| 3. | 78% | |||
| 4. | 4:7 | |||
| 5. | 1/6 |
Answer Key
Assessment
- A
- A
- C
- B
- D
- A
- A
- C
- D
- D
Additional Activity
| Ratio | Fraction | Decimal | Percent | |
|---|---|---|---|---|
| 1. | 2:5 | 2/5 | 0.4 | 40% |
| 2. | 8:100 | 8/100 | 0.08 | 8% |
| 3. | 78:100 | 78/100 | 0.78 | 78% |
| 4. | 4:7 | 4/7 | 0.57 | 57% |
| 5. | 1:6 | 1/6 | 0.17 | 17% |
What I Have Learned
- ratio
- numerator
- second
- decimal
- denominator
- percentage
- multiply
- 100
- fraction
- lowest
What I Can Do
| Ratio | Fraction | Decimal | Percent | |
|---|---|---|---|---|
| Females | 32:60 | 32/60 or 3/5 | 0.6 | 60% |
| Male | 24:60 | 24/60 or 2/5 | 0.4 | 40% |
What’s More
Activity 2
| Ratio | Fraction | |
|---|---|---|
| 1. | 1 : 6 | 1/6 |
| 2. | 2 : 6 | 2/6 |
| 3. | 3 : 4 | 3/4 |
| 4. | 4 : 5 | 4/5 |
| 5. | 4 : 10 | 4/10 |
What’s More
Activity 3
| Ratio | Fraction | Decimal | Percent | |
|---|---|---|---|---|
| 1. | 32:100 | 32/100 | 0.32 | 32% |
| 2. | 40:100 | 40/100 | 0.40 | 40% |
| 3. | 54:100 | 54/100 | 0.54 | 54% |
| 4. | 4:100 | 4/100 | 0.04 | 4% |
| 5. | 26:100 | 26/100 | 0.26 | 26% |
What I Know
- C
- D
- C
- C
- A
- C
- B
- B
- A
- C
What’s In
5/7 = 20/n
5 x n = 7 x 20
5n/5 = 140/5
n = 28
5 : 7 = 20 : 28
What’s More
Activity 1
| Decimal | Percent | |
|---|---|---|
| 1. | 0.38 | 38% |
| 2. | 0.67 | 67% |
| 3. | 0.33 | 33% |
| 4. | 0.25 | 25% |
| 5. | 0.20 | 20% |
References
Burgos, Jaime R., Markjoseph H. Perez and Donnel P. Placer. 2016. 21st Century Mathletes. Quezon City, Viral Group Inc.
Coronel, Carmelita C. and Nelia D. Bamba. 2010. Mathematics for a Better Life Textbook. Quezon City, SD Publication, Inc.,
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Email Address: blr.lrqad@deped.gov.ph * blr.lrpd@deped.gov.ph
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