Mathematics 6 Quarter 2 Module 4: Finding the Percentage, Base and Rate

Mathematics Quarter 2 – Module 4: Finding the Percentage, Base and Rate in a Given Problem

6

CO_Q2_Mathematics6_Module4

[illustration: group of students studying outdoors and indoors with a teacher, a globe, and a child writing by lamp light]

Mathematics– Grade 6 Alternative Delivery Mode Quarter 2 – Module 4: Finding the Percentage, Base and Rate in a Given Problem 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 book 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 VI Office Address: Duran Street, Iloilo City_________________________ Telefax: (033)336-2816, (033)509-7653___________________ E-mail Address: region6@deped.gov.ph_________________________

Development Team of the Module

Authors: Virgilio C. Failanza Jr., Rosemarie D. Aclan, Collin G. Sales, Marilou G. Dormis, Charlyn Joy A. Estimera, Lalyn G. Lumandog, Realyn F. Crispe, Rogilyn V. Nicolas, and Salvacion V. Emberga

Editors: Rebecca O. Billones, Ma. Portia Gencianeo Galanto and Collin G. Sales

Reviewers: Elleda Ebreo de la Cruz and Collin G. Sales

Illustrator: Virgilio C. Failanza Jr.

Layout Artist: Felizardo S. Valdez III

Management Team: Ramir B.Uytico, Pedro T. Escobarte, Jr., Elena P. Gonzaga, Donald T. Genine, Ma. Roselyn J. Palcat, Nordy D. Siason, Jr., Rowena S. Carillo, Rosemarie D. Aclan, Arthur J. Cotimo, Felizardo S. Valdez III, Marve E. Gelera

6

Mathematics

Quarter 2 – Module 4: Finding the Percentage, Base and Rate in a Given Problem

2

CO_Q2_Mathematics6_Module4

What I Need to Know

This module was designed and written with you in mind. It is here to help you master the lessons on Finding the Percentage, Base and Rate or Percent in given problems. The scope of this module permits it to be used in many different learning situations. The language used recognizes your diverse vocabulary level. 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.

The module is divided into three lessons, namely:

• Lesson 1 – Finding the Percentage in a Given Problem
• Lesson 2 – Finding the Rate in a Given Problem
• Lesson 3 – Finding the Base in a Given Problem

After going through this module, you are expected to:

1. identify the percentage, rate and base in a given problem;
2. find the base, percentage or rate or percent in a given problem; (M6NS-IId-142) and,
3. solve routine and non-routine problems involving the percentage, rate and base using appropriate strategies and tools. (M6NS-IId-143)

[illustration: target with arrow]

3

CO_Q2_Mathematics6_Module4

What I Know

[illustration: pencil]

A. Solve what is asked. Write the letter of the correct answer on your answer sheet.

1. What is 5% of 12?
   A. 60 B. 0.6 C. 0.7 D. 0.8

   
   

2. What is 10% of 25?
   A. 2.3 B. 2.4 C. 2.5 D. 25

   
   

3. Fifteen percent of 45 is what number?
   A. 6.70 B. 6.73 C. 6.74 D. 6.75

   
   

4. Twelve percent of 60 is what number?
   A. 7.2 B. 7.3 C. 7.4 D. 7.5

   
   

5. What number is 25% of 80?
   A. 20 B. 2.0 C. 21 D. 2.2

   
   

B. Read and solve the problems. Show your solutions on your answer sheet. Label your final answers.

1. Trexie Joy has 110 pieces of bond paper. She used 30% for her Portfolio. How many pieces did she use?

   
   

2. During the baseball practice, 50% out of 250 balls were used. How many balls were used during the baseball practice?

   
   

3. In a virtual meeting, there are 550 registrants. Due to unstable internet connection, only 80% were able to attend. How many participants were not able to make it?

   
   

4. Six hundred seventy persons were tested of RT-PCR. In a result, 80% were tested negative. How many were tested positive?

   
   

5. David Michael receives ₱135 from his sister as a help which is 10% of the money he gets from his mother. How much does his mother give him?

   
   

4

CO_Q2_Mathematics6_Module4

Lesson 1

Finding the Percentage in a Given Problem

In this lesson, you will apply your previous knowledge in changing percent to decimal as well as multiplying decimals. Finding the percentage is easy if you are good in multiplying numbers.

What’s In

[illustration: puzzle pieces]

A. Identify the base, rate, and percentage by completing the table below. The first one is done for you. Write your answers on your answer sheet.

Statement	Base	Rate	Percentage
1. 2% of 30 is 0.6	30	2%	0.6
2. 12 is 50% of 24
3. 15% of 100 = 15
4. 6% of 900 is 54
5. 90% of 50 = 45
6. 15 is 60% of 25

B. Find the percentage of a number.

1. What is 6% of 12?
2. What is 15% of 45?
3. Twenty percent of 80 is what number?
4. Sixteen percent of 68 is what number?
5. What number is 90% of 80?

5

CO_Q2_Mathematics6_Module4

What’s New

Read and study the following problem:

Twenty-five percent of Daisy’s 20 potted plants are peppers. How many potted plants are peppers?

What is It

[illustration: magnifying glass with question mark]

Use the four-step problem-solving approach to help you.

Understand

What information are given? We know that there are 20 potted plants and 25% of these are peppers.

What is asked? We need to find how many potted plants are peppers. This is a part of the total number of potted plants. So, we are looking for the percentage.

Plan

We can use different methods to solve the problem.

Solve

Method 1: Using a block model

[chart: block model; bar divided into four equal blocks labeled “20 potted plants” across the top, with the first block labeled “25% (? peppers)”]

100 % → 20

25% → 20 ÷ 4 = 5

6

CO_Q2_Mathematics6_Module4

Method 2: Expressing percent to fraction

25% of potted plants = 25% of 20 = 25/100 x 20 = 1/4 x 20 = 5

[illustration: thought bubble reading “Are there other ways to find the answer?”]

Method 3: Expressing percent as decimal

25% of potted plants = 25% of 20 = 0.25 x 20 = 5

Check Each method gives us the same answer.

Answer 5 potted plants are peppers.

Here are more examples.

In an elementary school, 30% of the 250 Grade Six pupils walk to school. How many Grade Six pupils walk to school?

Method 1: Using a block model

[chart: block model; bar divided into ten equal blocks labeled “100% (250 Grade Six pupils)”, with the first three blocks labeled “30% (? Grade Six pupils walk to school)”]

100% → 250 10% → 250 ÷ 10 = 25 30% → 25 x 3 = 75

Method 2: Using a formula

P = R x B = 30% x 250 = 30/100 x 250 = 3/10 x 250

[illustration: thought bubble “Think: What number is 30% of 250?” with arrows labeled Percentage = Rate x Base]

Answer: 75 Grade Six pupils walk to school.

[chart: bar model; unnumbered, illustrates “Two books cost ₱225. The cost of Book A is 80% of the cost of Book B.”; labels: Book A (8 units, bracket 80%), Book B (10 units, bracket 100%), ₱225]

Two books cost ₱225. The cost of Book A is 80% of the cost of Book B. How much does Book A cost?

18 units = ₱ 225 1 unit = 225 ÷ 18 1 unit = 12.5 Book A = 8 units Book A = 8 x 12.5 Book A = ₱ 100

Harvey’s weekly salary is ₱4500. He sets aside 40% of this for his daily expenses and 25% of the remaining as savings. How much does he save?

[chart: bar model; unnumbered, illustrates Harvey’s salary problem; labels: 100% → ₱4500, 10 units with “1 unit = 10%”, dashed portion and ₱2700 bar]

100% → 4500 → 4500 ÷ 100 1% → 45

Since the remaining amount is 60% 60% → 60 x 45 = 2700 60% → 2700

To answer the second question, you may ask, what is 25% of 2700?

[chart: bar model; unnumbered, illustrates 25% of ₱2700; labels: 100% → ₱2700, 10 units with “1 unit = 27”]

100% → ₱2700 → 2700 ÷ 100 1% → 27 25% → 25 x 27 = 675 25% → 675

Answer: ₱675- Harvey’s savings

What’s More

A. Find what is asked. Write your solutions on your answer sheet.

1. What is 40% of 90?
2. Twenty-five percent of 120 is what number?
3. What number is 20% of 130?
4. Eighteen percent of 150 is what number?
5. What is 30% of 960?

B. Study the following problems. Show your complete answer on your answer sheet.

1. Genoveva answered 98% of a 50-item test correctly. If her friend Nenita made 4 more mistakes than Genoveva, how many points did Nenita get?

[chart: bar model; unnumbered, compares scores of Genoveva and Nenita on a 0% to 100% scale; labels: 0%, 98%, 100%, Genoveva, Nenita, 4 (difference between the two bars)]

100% = _____ 1% = _____ ÷ _____ 1% = _____ 98% = _____ x _____ 98% = _____ → Genoveva’s score _____ − _____ _____ → Nenita’s score

2. There are 450 pieces of pencils. Twelve percent of these are TW pencils. How many pencils are TW?

12% = 12% of 450 = _____ x 450 = _____ x 450 = _____

What I Have Learned

• Percentage is the actual amount that represents part of a whole. It can be found given the percent (rate) and the whole amount (base).
• Percentage can be calculated by using the formula, P = R x B.
• When solving problems that involve finding percentages, the four-step problem-solving approach (Understand, Plan, Solve and Check) can be helpful.

What I Can Do

A. Find out the hidden word by filling in the blanks with the letter of your answer. Choose your answer from the choices inside the box.

---

1. _____ is 20% of 20
2. What is 90% of 50?
3. Eighty percent of 150 is _____
4. The sum of 10% of 60 and 75% of 20 is _____.
5. The product of 5% of 40 and 8% of 50 is _____.

Choices	Choices	Choices
A. 50	I. 150	O. 21
B. 30	J. 120	R. 40
E. 4	N. 45	Y. 8

B. Read and solve the problems. Show your solutions on your answer sheet. Label your final answers.

1. The periodic test in Mathematics has 50 questions. If Joy got 90% correct answers, how many questions did she miss?

   
   

2. In school, 15% of the Math teachers are males. If there are 20 Math teachers in school, _____ of them are females?

   
   

3. Six percent of the fishes in the pond are Sword Fish. If there are 1400 fishes in the pond, how many are Sword Fish?

   
   

4. Hazel Joy gives 15% of her monthly salary to her mother. If her monthly salary is ₱25 500. How much will she give to her mother every month?

   
   

5. In a 75-item test, DM got a correct score of 96%. Is it true that DM missed 5 items of the test? Prove your answer.

   
   

Assessment

A. Find the percentage in the given problems below. Choose the letter of the correct answer and write it on your answer sheet.

1. What is 5% of 30?
   a. 0.15
   b. 1.05
   c. 1.5
   d. 15

   
   

2. What is 10% of 60?
   a. 10
   b. 6
   c. 0.6
   d. 1.0

   
   

3. Fifteen percent of 65 is what number?
   a. 9.75
   b. 97.5
   c. 9.57
   d. 95.7

   
   

4. Twenty percent of 80 is what number?
   a. 0.16
   b. 1.6
   c. 1.60
   d. 16

   
   

5. What number is 25% of 130?
   a. 32.5
   b. 35.2
   c. 23.5
   d. 25.3

   
   

B. Solve what is asked. Show your solutions on your answer sheet and label your final answers.

6. At Alcona Resort, 8% of the visitors are foreigners. If there are 225 visitors at the resort, how many visitors are foreigners?

   
   

7. Vic saves 9% of his salary each month. If Vic’s salary is ₱16 000, how much is Vic’s monthly savings?

   
   

8. In a fast food outlet, there are 50 service crew. Ninety-two percent of crew are men and the rest are women. How many service crew in a fast food outlet are men?

   
   

9. Fifteen percent of the 60 participants who attended the Mathematics Investigation Training were males and the rest are females. How many participants were females?

   
   

10. Vangie is a rice seller. She earns a profit of 15% for every kilogram at ₱45. She was able to sell 55 kilograms of rice. How much profit did she earn?

    
    

Additional Activities

A. Modified True or False: Write True if the statement is correct. If it is false, replace the italicized number/word to make the statement true. Write your answers on your answer sheet.

1. Fifteen percent of 25 is 1.25.
2. Ten percent of 90 is 9.
3. Twenty percent of 10 is 2.
4. 3.46 is 6% of 56?
5. Twelve is 18% of 80.
6. There are 45 students in a class. If 80% are present on that day, 9 of the students are absent.
7. In a class of 40 students, 55% are boys. Therefore, there are 22 boys and 16 girls.

B. Solve what is asked. Show your solutions on your answer sheet. Label your final answers.

8. The school successfully implemented 85% of their planned activities in the School Improvement Plan. If there were 20 planned activities, how many activities were successfully implemented?

   
   

9. In a 35-kilogram of mixed nuts, 23.15% were cashew nuts. How many kilograms of cashew nuts were there in the mixed nuts?

   
   

10. A fruit basket contains 25 different kinds of fruits. Sixty-four percent of which are mangoes and 16% are avocados. How many of the fruits are mangoes and avocados?

    
    

Answer Key

[transcriber’s note: this page is printed rotated 180 degrees; the answer key is transcribed upright in reading order]

What I Know

[transcriber’s note: letters A, B, C, D, A, A, B are visible in this column, but their item numbers are not clearly legible [?]]

A, B, C, D, A, A, B [?]

What’s In

A. Base Rate Percentage

Base	Rate	Percentage
30	2%	0.6
24	50%	12
100	15%	15
900	6%	54
50	90%	45
25	60%	15

B.

1. 0.72
2. 6.25
3. 16
4. 10.88
5. 72

What’s More

A.

1. 36
2. 30
3. 26
4. 27
5. 288

B.

1. 45 = 90%
   100% = 50
   98% = 98 x 0.5
   1% = 50 ÷ 100
   98% = 49 Genoveva’s score
   1% = 0.5
   49 − 4
   45 Nenita’s score
2. 12/100 x 450
   = 3/25 x 450
   = 54

What I Can Do

A.

1. E
2. N
3. J
4. O
5. Y

B.

1. 5 [?]
2. 17
3. 84
4. ₱3 825
5. False. Answers may vary.

Assessment

1. C
2. B
3. A
4. D
5. A
6. 18 foreigners
7. ₱1 440 savings
8. 46 men
9. 51 females
10. ₱371.25 profit

Additional Activities

A.

1. 5%
2. True
3. True
4. 3.36
5. 15%
6. True
7. 18 girls

B. 8) 17 planned activities 9) 8.1025 kilograms 10) 16 mangoes, 4 avocados

What I Know

A. Match column A with column B. Write the letter of the correct answer on your answer sheet.

Column A	Column B
1) What percent of 40 is 5?	A. 6%
2) Twenty-seven is N% of 180. What is N?	B. 12%
3) Thirty is what percent of 120?	C. 12.5%
4) What percent of 400 is 24?	D. 8%
5) Forty-two is what percent of 350.	E. 25%
	F. 15%

B. Analyze and solve the problems below. Do it on your answer sheet.

1. Roman knocks 9 cans out of 15. What percent of cans did he knock? Draw a model to solve this problem.

   
   

2. Forty-three out of 86 rubber band are red. What percent are red? Use equivalent fraction method to solve the problem.

   
   

3. The original price of a bike is ₱ 6 500. Carlo pays ₱ 5 525. What is the percent sale?

   
   

4. At the party, there are 400 balloons used. One hundred of the balloons are blue. What percent are blue?

   
   

5. Mrs. Cruz called for a P.T.A. meeting. Eighteen were absent. If there are 120 parents in all, what percent were present?

   
   

Lesson 2: Finding the Rate or Percent in a Given Problem

In this lesson, you are expected to apply carefully your knowledge in division especially on division of decimals. A step-by-step process on how to find the rate or percent in a given problem will be illustrated to you. You have to analyze each step very well in order to be guided on how to go about the whole procedures.

What’s In

A) Find what is asked. You can use any methods in solving for the percentage. Write your solutions on your answer sheet.

1. What is 25% of 700?
2. Forty-five percent of 325 is what number?
3. What number is 20% of 130?
4. In a class of 52 children, 75% are boys. How many girls are there in the class?
5. What is 32% of 137?

What’s New

Read and study the following problems:

A school chess club has 50 members. Twenty-nine of them are girls. What percent of the chess club are girls?

What Is It

Use the four-step problem-solving approach to help you.

Understand

What information are given?

We know that 29 out of 50 members of the school’s chess club are girls.

What is asked?

We need to find how many how many percent of the chess club are girls.

This means that we are looking for the rate.

Plan

We can use different methods to solve the problem.

Solve

Method 1: Using a block model

[chart: block model; Method 1: Using a block model]

• Top bracket label: 100 % (50 members)
• Shaded block label: 29
• Bottom bracket label: ?
• Callout: The total number of members in the chess club is equal to 100%.

50 members → 100% 1 member → 100% ÷ 50 = 2% 29 members → 2% x 29 = 58%

Method 2: Using equivalent fractions

29 out of 50 members are girls

29/50 = ?/100 = 58/100 = 58%

Method 3: Using a formula

Rate (R) = Percentage (P) / Base (B) x 100 = 29/50 x 100% = 0.58 x 100% = 58%

[chart: formula diagram; callout]

• What percent of 50 is 29
• Rate x Base = Percentage

Check Each method gives us the same answer.

Answer 58% of the chess club are girls.

What’s More

Read and analyze the problems below. Show the complete answer on your answer sheet.

1. What percent of 30 is 6?

   
   

2. Fifteen is what percent of 25?

   
   

3. One hundred twenty-five is what percent of 500?

   
   

4. Twenty is what percent of 200?

   
   

5. What percent of 120 is 30?

   
   

6. There are 40 Grade 6 pupils in a class. If 30 are boys, what percent are girls?

   
   

100% = 40 Grade 6 pupils

[chart: bar model; two parts, pink and dark blue, with bracket labels and blank boxes] _____ → _____ Girls _____ = 30 boys

100% → _____ 25% → _____ x _____ 1% → _____ ÷ _____ 25% → _____ → number of girls. 1% → _____

7. There are 25 questions in a summative test. Three points are added for every correct answer and two points are deducted for every wrong answer. Joy gets a total score of 45. How many correct answers did she get? What percent of the total number of questions did she miss?

What I Have Learned

• Rate is the ratio of the percentage to the base. It is written in percent.
• Rate can be calculated by using the formula, R = P/B x 100.
• When solving problems that involve finding rates, the four-step problem-solving approach (Understand, Plan, Solve and Check) can be helpful.

What I Can Do

A. Match column A with the correct answer in column B. Write the letter of the correct answer on your answer sheet.

Column A	Column B
1) What percent of 64 is 8?	A. 10%
2) Twenty-five is what percent of 250?	B. 5%
3) What percent of 400 is 80?	C. 20%
4) Sixteen is what percent of 40?	D. 50%
5) What percent of 40 is 2?	E. 12.5%
	F. 40%

B. Solve what is asked. Show your solutions on your answer sheet and label your final answers.

6. What percent of 300 is 75?
7. Nick is a factory worker. He worked 9 months in a year. What percent of the year did he work?
8. David Michael hits 12 out of 15 throws of the pitcher in baseball game. What percent of the throws did he miss?
9. In a basketball game, Rex shoots 54 goals out of 72 shots. What is the percent of goals?
10. On October 27, 2020 data on COVID-19, out of 54 confirmed cases, there were 49 recoveries. How many percent were recovered from COVID-19? Round your answer to the nearest tenths.

Assessment

A. Match Column A with Column B. Write the letter of the correct answer on your answer sheet.

Column A	Column B
1) What percent of 40 is 10?	A. 30%
2) Thirty-six is what percent of 120?	B. 25%
3) What percent of 375 is 75?	C. 85%
4) Fifty is what percent of 1000?	D. 31%
5) Seven hundred thirty-two and seven tenths is what percent of 862?	E. 5%
	F. 20%

B. Solve the following problems. Show your solutions on your answer sheet and label your final answers.

6. Reoiux James bought 50 noodles for his sari-sari store. Forty-two of which are beef. What percent of noodles are beef? Use equivalent fraction method to solve this problem.
7. Ivy paid ₱880.00 for her purchased groceries. Looking at her Official Receipt, she found out that there was a discount of ₱39.60. What was the percent of discount?
8. Christine Joy got a score of 47 out of 50 items in a Mathematics 6 test. What percent of the test did she answer incorrectly?
9. What is the shooting percentage of Joshua if he shoots 18 out of 20 free throws? Draw a model to solve this problem.
   10.) In a Primary school, there are 45 parents. On a rainy day, 36 were present to get the modules. What percent of parents were able to get the modules?

Additional Activities

Answer questions A and B for each given situation below. Do it on your answer sheet.

1. Tony bought an item in a department store with 10% discount and another 20% after the first discount.
   A. Is it right to say that he received 30% discount in the item he bought? Why?
   B. How much should he pay for the item he bought that cost ₱200?

   
   

2. Forty percent of 30 is ____ % of 60.
   A. Is the missing number greater than or less than 40%? Why?
   B. What is the missing rate?

   
   

3. Thirty percent of 60 is 20% of what number?
   A. Illustrate this problem using models.
   B. Are we looking for the rate in this problem? Why or why not?

   
   

Answer Key

[transcriber’s note: this page is printed upside down, and parts of the key were hard to read. The answers below were checked against the questions; any unclear entry is marked [?].]

What I Know

A.

1. C
2. F
3. E
4. A
5. B

What’s More

1. 20%
2. 60%
3. 25%
4. 10%
5. 25%
6. 25%
   • 100% = 40
   • 75% = 30
   • 25% = 10
   • 1% = 0.4
   • 25% x 40 = 10
7. 19 – correct answers
   24% – questions missed

Assessment

A.

1. B
2. A
3. F
4. E
5. C

B. 6) 84% 7) 4.5% 8) 6% 9) 90% 10) 80%

What’s In

1. 175
2. 146.25
3. 26
4. 13 girls
5. 43.84

What I Can Do

A.

1. E
2. A
3. C
4. F
5. B

B. 6) 25% 7) 75% 8) 20% 9) 75% 10) 90.7%

Additional Activities

A. No. (Possible reason) It should be less than 30% for additional discount is made after discount. B. ₱144

A. Less than, because the second amount is bigger than the first amount. B. 20%

A. [illustration: model drawing for the problem] B. No, because the rate is already given. (Base is missing)

What I Know

A. Solve what is asked. Write the letter of the correct answer on your answer sheet.

1. Forty percent of what number is 18?
   A. 72
   B. 222
   C. 45
   D. 720

   
   

2. Five percent of a number is 65. Find the number.
   A. 325
   B. 1 300
   C. 1 325
   D. 13

   
   

3. Twelve percent is 25% of what number?
   A. 45
   B. 480
   C. 300
   D. 48

   
   

4. Sixty is 3% of what number?
   A. 1 800
   B. 180
   C. 2000
   D. 200

   
   

5. One hundred-eight is 12% of a number. Find the number.
   A. 900
   B. 1 296
   C. 9
   D. 10

   
   

B. Read and solve the problems. Show your solutions on your answer sheet. Label your final answers.

6. Eight percent of the Grade 5 learners were absent in their virtual class. If 6 were absent, how many Grade 5 learners were there in all?

   
   

7. There was a Pre-Christmas sale of 15% on all items in a department store. Genie Rose pays ₱ 2 762.50 for a blouse. What is the original price?

   
   

8. Peter saves ₱ 17.50 which is 5% of the food he eats. How much is the total bill he paid?

   
   

9. Jonah bought a pair of socks at 35% less of the regular price. She paid ₱ 55.25 for a pair of socks. What was the original price?

   
   

10. Mr. Dell spends ₱ 3 000 in the Supermarket for their monthly consumption or 12% of his monthly family budget. How much is their family budget?

    
    

Lesson 3: Finding the Base in a Given Problem

In this lesson, you are expected to apply carefully your knowledge in division especially on division of decimals. A step-by-step process on how to find the base in a given problem will be illustrated to you. You have to analyze each step very well in order to be guided on how to go about the whole procedures.

What’s In

A. Modified True or False: Write True if the statement is correct. If it is false, replace the underlined number/word to make the statement true. Write your answers on your answer sheet.

1. Eight is 30 percent of 32?
2. Fifty percent of 60 is 30?
3. Sixty is 25% of 300?
4. N% of 130 = 10. N is 7.69%.
5. Forty-eight is 45% of 120?

What’s New

There are 72 Grade 6 pupils in a school. The Grade six pupils comprise 12% of the total enrolment. How many pupils are enrolled in a school?

In this lesson, you will learn on how to find the base in a given problem using the formula and different strategy.

What is It

We will use the four-step problem-solving approach to help you.

Understand

What information are given? We know that 12% of the total enrolment in the school is equal to 72 Grade Six pupils.

What is asked? We need to find the total number of pupils in the school. This means we are looking for the base.

Plan

We can use different methods to solve the problem.

Solve

Method 1: Using a block model

[chart: block model; labels: “100% ( ? pupils )” above the full bar, “72” in the small segment, “12%” below the small segment. Printed beneath the bar:]

12% of the enrolment → 72 1% of the enrolment → 72 ÷ 12 = 6 100% of the enrolment → 6 x 100 = 600

[illustration: thought bubble reading “The total number of members in the chess club is equal to…”]

Method 2: Using equivalent fractions

[chart: equivalent fractions; printed: “12 / 100 = 72 / ? = 72 / 600”, with “x 6” printed above and below the first two fractions]

[illustration: thought bubble reading “12% = 12/100”]

Method 3: Using a formula

Base (B) = Percentage (P) / Rate (R) = 72 / 12% = 72 / 0.12 = 600

[illustration: cloud reading “12% of what number is 72?” with “Rate x Base = Percentage” printed beneath it]

Check Each method gives us the same answer.

Answer 600 pupils are enrolled in the school.

Here is another example.

Percy thinks of a number. Thirty-seven percent of the number is 41.44. What is the number?

Use the four-step problem-solving approach to help you.

Understand

What information are given? We know that 37% of that number is 41.44.

What is asked? We need to find what is the original number which is the 100% of that number. This means we are looking for the base.

Plan

We can use different methods to solve the problem.

Solve

Method 1: Using a block model

[chart: block model; labels: “100% (?)” above the full bar, “41.44” in the small segment, “37% (41.44)” below the small segment. Printed beneath the bar:]

37% of the enrolment → 41.44 1% of the enrolment → 41.44 ÷ 37 = 1.12 100% of the enrolment → 1.12 x 100 = 112

[illustration: thought bubble reading “The original number or the 100% of the number is equal to…”]

Method 2: Using equivalent fractions

[chart: equivalent fractions; printed: “37 / 100 = 41.44 / ? = 41.44 / 112”, with “x 1.12” printed above and below the first two fractions]

[illustration: thought bubble reading “37% = 37/100”]

Method 3: Using a formula

Base (B) = Percentage (P) / Rate (R) = 41.44 / 37% = 41.44 / 0.37 = 112

[illustration: cloud reading “37% of what number is 41.11?” with “Rate x Base = Percentage” printed beneath it] [transcriber’s note: the cloud prints 41.11, although the problem states 41.44; transcribed as printed]

Check Each method gives us the same answer.

Answer 112 is the number

What’s More

Read and analyze the problems below. Show your complete answer on your answer sheet.

1. Twenty-five percent of ____ is 21.25?
2. Sixteen percent of what number is 8.96?
3. Find B when R = 25% and P = 125.
4. Forty-five percent of N is 54?
5. 25% (Twent-five percent) of a number is 30. Find the number.
6. Ten percent of the students in a Math class are absent. If there are 4 students who are absent, how many students are enrolled in a Math class?

[chart: bar model; a single bar labeled “100 %” above it, split into a 10% segment and a 90% segment. Printed below the bar: “10%” under the small segment and an empty box under the large segment. Printed working:]

10% = 4 | 100% = 100 x 0.4 1% = 4 ÷ 10 | 100% = 40 number of students 1% = 0.4 | enrolled in Math class

7. Mr. Catinan was able to save ₱ 27.75 on a pack of hotdogs. This amount is 15% of the original price. Find the original price of the pack of hotdogs.

[chart: bar model; a single bar labeled “100 %” above it, split into a 15% segment and an 85% segment. Printed below the bar: “15%” under the small segment and an empty box under the large segment. Printed working:]

15% = ₱27.75 | 100% = 100 x 1.85 1% = 27.75 ÷ 15 | 100% = 185 original price of the 1% = 1.85 | pack of hotdogs

8. Sixteen percent of Portia’s monthly salary is deducted for withholding tax. If the deducted amount is ₱11 000.00, how much is her monthly salary?

[chart: bar model; a single bar labeled “100 %” above it, split into a 16% segment and an 84% segment. Printed below the bar: “16 %” under the small segment and an empty box under the large segment. Printed working:]

16% = ₱11 000 | 100% = _____ x _____ 1% = _____ ÷ _____ | 1% = _____ | 100% = _____ monthly salary

What I Have Learned

• Base is the amount representing 100%. It is the whole from which a percent is taken from.
• Base can be calculated by using the formula, B = P / R.
• When solving problems that involve finding bases, the four-step problem approach (Understand, Plan, Solve and Check) can be helpful.

What I Can Do

Solve what is asked. Show your solutions on your answer sheet and label your final answers.

1. Twelve and five tenths percent of N is 8? What is N?
2. Twenty-five percent of a number is 63. Find the number.
3. Four hundred is 50% percent of what number?
4. Eighty percent of 240 is 25% of what number?
5. Seventy-two is 20% of what number?
6. Johnny bought a computer printer on sale at the store. The discount was 15% and he saved P1 350.00. What was the original price of the printer?
7. Forty-eight or 96% of the Grade 6 pupils joined the scouting activity. How many pupils were there in the Grade 6 class?

Assessment

A. Fill-in the blanks. Write the letter of the correct answer on your answer sheet.

1. 15 (fifteen) is 20% of ________. Find the number.

• A. 75
• B. 80
• C. 85
• D. 90

2. Five percent (5 %) of _________ is 75.

• A. 1 300
• B. 1 400
• C. 1 500
• D. 1 550

3. Seven percent of ________ is 34.3.

• A. 460
• B. 470
• C. 480
• D. 490

4. 180 is 15% of _______.

• A. 1 010
• B. 1 200
• C. 1 020
• D. 1 002

5. 22% _______ is 28.16. Find the number.

• A. 182
• B. 128
• C. 218
• D. 281

B. Solve the following problems below using any of the methods learned. Do it on your answer sheet.

6. Virgie grows her hair 3.75 cm in the last three months. If the length is 12.5% of her hair three months ago, how long is her hair now?

   
   

7. Sheila is engaged in an online business. She started with an investment of ₱10 000.00. Due to the COVID-19 pandemic, her business becomes in demand. In March, she gained 5% profit and added to her investment. She continuously adds her profit to her investment thereafter and gains 10%, 25%, and 40% in the succeeding months until June 2020. How much is her total investment by the end of June?

   
   

8. Sherwin recorded his monthly savings deposit in the bank. He started at ₱5 000.00 in January 2020. In the succeeding months, he consistently adds 25% of his monthly standing balance into his savings account. How much will be his total savings in April 2020? Round your answer to two decimal places.

   
   

9. Mr. Perez saves 5% of his monthly salary. If he saves ₱ 1338.20. How much is Mr. Reyes’ monthly salary?

   
   

10. Maricel had 15 red pony tail which is her favorite. The red pony tail is 15% of all the pony tail Maricel had. How many pony tail does Maricel had altogether?

    
    

Additional Activities

A. Create a problem using the given data below. Write your answer on your answer sheet.

[chart: diagram of data boxes with arrows; A. Create a problem using the given data]

1. ? → 2010 population of the Municipality of Jordan
   3% → increased from 2009 population
   45 → 2009 population of the Municipality of Jordan

   
   

2. ? → total number of pupils
   25% → boys
   3 → number of boys

   
   

3. ₱325 → sales tax
   5% → rate of sales tax
   ? → total sales

   
   

4. ? → total number of invited kids
   15% → did not show up
   45 → number of kids who did not show up

   
   

5. ? → total test item
   24% → wrong answers
   12 → number of wrong answers

   
   

Answer Key

[transcriber’s note: this page is printed upside down; it is transcribed in reading order from the upright layout, columns left to right]

What I Know

1. C
2. B
3. D
4. C
5. A
6. 75
7. ₱ 3250
8. ₱ 350
9. ₱ 85
10. ₱ 25 000

What’s In

1. 25%
2. True
3. 20%
4. True
5. 40%

What’s More

1. 85

   
   

2. 56

   
   

3. 500

   
   

4. 120

   
   

5. 120

   
   

90% 100 x 0.4 100% = 4 10% = number 40 100% = 10 ÷ 4 1% = of student 0.4 1% = enrolled in Math class

85% 100 x 1.85 100% = ₱27.25 15% = ₱185 100% = 15 ÷ ₱27.75 1% = original price 1.85 1% = of a pack of hotdog

84% 100 x ₱687.50 100% = ₱11 000 16% = ₱68 750 100% = 16 ÷ ₱11 000 1% = monthly salary 687.50 ₱ 1% =

What I Can Do

1. 64
2. 252
3. 800
4. 768
5. 360
6. ₱ 9000
7. 50

Assessment

A.

1. A
2. C
3. D
4. B
5. B

B. 6-10 [?]

Possible answer:

6. 30 cm
7. ₱ 20 212.50
8. ₱ 9 765.63
9. ₱ 26 764
10. 20

Additional Activities

Possible answer:

1. 1 500
2. 12
3. ₱ 6 500
4. 300
5. 50

References

• DepEd Most Essential Learning Competencies (MELC) in Mathematics for Grade 6

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