This is a Self-Learning Module (SLM) for Mathematics Grade 5, Quarter 1, Module 13. It teaches how to solve routine and non-routine word problems that use multiplication of fractions and whole numbers, alone or together with addition or subtraction. Learners use a four-step plan to work through real-life problems about money, time, length, and area.
The module is part of DepEd’s Alternative Delivery Mode (First Edition, 2020) and was developed by DepEd Region VIII. Its writer is Ivie C. Loayon.
What learners will learn
The module states one learning competency:
- Solve routine and non-routine problems involving multiplication without or with addition or subtraction of fractions and whole numbers, using appropriate problem-solving strategies and tools (M5NS-Ih-92.1).
Lessons in this module
The module has one lesson, with the same title as the module: Solving Routine and Non-Routine Problems Involving Multiplication without or with Addition or Subtraction of Fractions and Whole Numbers. It starts with a review of multiplying fractions. It then shows fully worked word problems and ends with practice activities and tests.
Key ideas: multiplying fractions quickly
The review part (“What’s In”) reminds learners how to find the product of fractions and of a fraction and a whole number. The module’s tip:
- Before multiplying, look for common factors in the numerators and denominators.
- Divide or cancel those common factors first, then multiply. For example, 2/5 x 5/7 = 2/7, because the 5 in the numerator and the 5 in the denominator cancel.
- To multiply a whole number by a fraction, write the whole number as a fraction over 1, such as 16 = 16/1.
Key ideas: the four-step plan
Every problem in the module is solved with four steps: Understand, Plan, Solve, and Check.
- Understand: What is asked? What are the given facts?
- Plan: Which operations are needed? Write a number sentence, using N or n for the unknown.
- Solve: Carry out the computation.
- Check: Verify the answer with another method, a block model, or a drawing.
Worked examples in the module
| Problem | Operations | Number sentence | Answer |
|---|---|---|---|
| Joey studied 16 years; 3/8 of that time was in college. | Multiplication | 3/8 x 16 = n | 6 years |
| Pedro is 144 cm tall; his sister Joan is 1/6 taller. | Multiplication and addition | (144 x 1/6) + 144 = n | 168 cm |
| A paper 8 1/2 in by 13 in has a 3/4-in border on all sides. Find the area inside the border. | Multiplication and subtraction | A = [13 − (2 x 3/4)] x [8 1/2 − (2 x 3/4)] | 80 1/2 square inches |
The height problem is checked with a block model: Pedro’s height is split into 6 blocks of 24 cm, and one more block is added to get Joan’s height (144 + 24 = 168). The border problem is checked with a drawing. The border is subtracted twice from each side, once on each edge, so the inside measures 23/2 inches by 7 inches.
Non-routine problems
Activity 3 shows problems that need more than one direct computation:
- The quiz scores of CJ, LV, and DJ: CJ got 1/2 of 10 items (5), LV got 3 more (8), and DJ got 2 less than LV (6), for a total of 19 points.
- Little Enzo’s 90 animal toys: Each day he keeps a fraction of his toys, gives the rest to charity, and wraps one toy for a cousin. A table tracks each day. For example, on Monday 90 x 11/15 = 66, then 66 − 1 = 65. By Friday he has 5 toys left.
Practice activities and tests
- What I Know: a 10-item multiple-choice pretest, for example finding how much Jerick saves if he keeps 1/4 of a P32.00 allowance.
- Activity 1: Let us try!: five problems, with answers chosen from a box.
- Activity 2: The Color of My Heart: learners color a heart red if the answer is a whole number, yellow if it is a proper fraction, and blue if it is neither.
- What I Have Learned: naming the four steps and extending the non-routine problems.
- What I Can Do: five problems whose answers unlock a hidden word.
- Assessment: a 10-item matching test (Column A problems, Column B answers).
- Additional Activities: eight more problems for mastery.
How to use this module
- Learners: Answer the pretest first. It tells you whether you can go on or need help from your teacher or facilitator. Then work through the parts in order. Write all answers on a separate sheet or in your activity notebook, not on the module. Finish with the post-test (Assessment) to check your learning.
- Parents and facilitators: The module includes an answer key for each activity and test. Encourage your child to use it honestly, after answering, to check their own work. Help them follow the four-step plan.
- Teachers: The worked examples model the Understand-Plan-Solve-Check routine and the block model, and they can be used for class discussion. The Assessment and Additional Activities can serve as checks for the competency M5NS-Ih-92.1.
Frequently asked questions
What grade and quarter is this module for?
It is for Grade 5 Mathematics, Quarter 1, Module 13. Its competency code is M5NS-Ih-92.1.
What are the four steps in solving word problems in this module?
Understand, Plan, Solve, and Check. Learners find what is asked and what is given, write a number sentence, compute, and then verify the answer.
Does the module have an answer key?
Yes. The module has an answer key for the pretest, What’s In, the activities, What I Have Learned, What I Can Do, the Assessment, and the Additional Activities.
What is a non-routine problem in this module?
It is a problem that needs more than one direct computation or a special strategy. One example is Enzo’s toys, where a fraction is kept each day and one toy is removed, tracked in a table until 5 toys remain.
Where should learners write their answers?
The module asks learners to use a separate sheet of paper or their activity notebook and not to put marks on the module.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 1 – Module 13: Solving Routine and Non-Routine Problems Involving Multiplication without or with Addition or Subtraction of Fractions and Whole Numbers
[illustration: learners studying outdoors and at home, a teacher helping students at a table, a globe, and a child reading by lamplight]
CO_Q1_Math5_Module13
Mathematics – Grade 5 Alternative Delivery Mode Quarter 1 – Module 13: Solving Routine and Non-Routine Problems Involving Multiplication without or with Addition or Subtraction of Fractions and Whole Numbers 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 the exploitation of such work for a 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 VIII Office Address: Government Center, Candahug, Palo, Leyte Telefax: 053 – 832-2997 E-mail Address: region8@deped.gov.ph
Development Team of the Module
Writer: Ivie C. Loayon Editors: Zosimo M. Miñozo Jr., Catherine Cortez, Aida F. Bantiles, Lanie S. Fortaleza, John Michael C. Jalayajay, Ramil R. Magdua, Joseph Randolp Palattao, Lilia Martinez, Bernadeth Daran Reviewers: Renato S. Cagomoc, Rolando Lacbo, Joshua Sherwin T. Lim, Robirth Ornopia, and Aida F. Bantiles Illustrator: Angel L. Porlares Layout Artist: Modesto Y. Sapinit, Ryan R. Tiu Management Team: Ramir B. Uytico, Arnulfo M. 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
5
Mathematics
Quarter 1 – Module 13: Solving Routine and Non-Routine Problems Involving Multiplication without or with Addition or Subtraction of Fractions and Whole Numbers
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 SLMS 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 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
Hi, Mathlete!
In this module, you are going to gain understanding in solving routine and non-routine problems involving multiplication without or with addition or subtraction of fractions and whole numbers using appropriate problem-solving strategies and tools.
M5NS-Ih-92.1
What I Know
You need to answer this pre-test before you proceed to the lesson proper.
Directions: Solve the following problems. Write the letter of the correct answer on a separate sheet of paper.
Jerick’s daily allowance is P32.00. If he saves 1/4 of it, how much does he save daily?
a. P12.00 b. P5.00 c. P10.00 d. P8.00Three-fifths of a 10-item quiz were answered correctly by Lorenzo. How many points did he get if one item scored one point?
a. 3 b. 6 c. 7 d. 5There are 40 girls in a class. Three-eighths of them have long hair, while the rest have short hair. How many girls have short hair?
a. 13 b. 18 c. 25 d. 28In a graduating class of 164 students, 2/4 decided to take technical courses, 1/4 wanted to take education, and the rest decided to study nursing. How many students will enroll in nursing?
a. 41 b. 20 c. 26 d. 32A car travels at a speed of 2 1/4 kph. How far can it go in 3 1/3 hours?
a. 4 1/5 b. 5 1/3 c. 7 1/2 d. 10 3/4Rita has 10 guavas. She shared 3/5 of these guavas with her classmates. She then gave her brother 2 of the remaining guavas. How many guavas are left for Rita?
a. 2 b. 3 1/5 c. 4 d. 5 1/2Sam walks to school every day for 2/3 of an hour. Dana walks to school 5 more minutes than Sam. How many minutes does it take Dana to reach the school?
a. 50 b. 45 c. 40 d. 35Eight pupils have 5 marbles each. If they gave away 5/8 of these marbles, how many marbles are left?
a. 15 b. 20 c. 25 d. 30There are 45 books in a shelf. Three of these books were given to a child and 2/3 of the remaining books were donated to the barangay reading center. How many books were donated to the reading center?
a. 14 b. 16 c. 28 d. 32Cris wants to buy a mountain bike worth P5,463.00. He has saved only 5/9 of that amount so far. How much more money does Cris need?
a. P3,305.00 b. P3,035.00 c. P2,824.00 d. P2,428.00
Lesson 1: Solving Routine and Non-Routine Problems Involving Multiplication without or with Addition or Subtraction of Fractions and Whole Numbers
What’s In
Do you still remember how to get the product of the fractions? How about multiplying fractions and whole numbers? Recall the process by answering the exercise below. The first one is done for you.
Directions: Find the product of the following given fractions and whole number. Do this in your Activity Notebook.
1.) 2/5 x 5/7 = 2/7, Why? You may cross out or cancel the 5 (both in the numerator and denominator).
Start here!
2.) 6/9 x 1/6 = _____ 3.) 3/5 x 2/3 = _____ 4.) 2/6 x 3/4 = _____ 5) 4/5 x 1/3 = _____ 6) 2/6 x 3/9 = _____ 7) 6 x 2/3 = _____ 8) 5/6 x 3 = _____ 9) 5/6 x 4 = _____ 10) 2 x 2/3 = _____
Notes to the Learner
To multiply proper fractions mentally, simplify first the product expression before multiplying. If the numerators and denominators have common factors, divide the numerator and the denominator by their factor before multiplying.
Common factors appearing in the numerators and denominators of any two fractions being multiplied can already be cancelled even before actually multiplying.
What’s New
Directions: Solve the problem below.
Joey spent 16 years of his life studying from elementary to college. He spent 3/8 of this length of time in college. How many years did he spend in college?
Pedro is 144 cm tall, and his sister Joan is 1/6 taller than him. How tall is Joan?
A rectangular piece of paper is 8 1/2 inches wide and 13 inches long. If a border of 3/4 inch is to be drawn on all sides of the paper, what is the area enclosed by the border?
[illustration: a graduate in cap and gown]
What Is It
To solve the above problems, follow the four-step plan (Understand, Plan, Solve and Check).
Solution to Problem#1:
Understand
- a. What is asked?
- the total number of years Joey spent in college
- b. What are the given?
- Joey spent 16 years of his life studying
- 3/8 of Joey’s life studying is spent in college
Plan
a. What operation will be used?
- Multiplication
b. Write a number sentence.
- 3/8 x 16 = n (Note: N or n represent what is being asked)
Solve
3/8 x 16 = 3/8 x 16/1
= (3 x 16)/(8 x 1)
= 48/8
= 6Answer: n = 6,
Therefore, Joey spent 6 years in college.
Check
Verify if your answer is correct.
One way to check is to go back to your solution or try another method.
3/8 x 16 = 3/8 x 16/1
= (3 x 2)/(1 x 1)
= 6/1
n= 6The answer is correct.
Solution to Problem #2
Understand
- a) What is asked?
- The height of Joan
- b) What are given?
- Her brother Pedro is 144 cm tall
- Joan is 1/6 taller than his brother Pedro
- a) What is asked?
Plan
- a) What operation will be used?
- Multiplication and Addition
- b) Write a number sentence.
- (144 x 1/6) + 144 = n
- a) What operation will be used?
Solve
(144 x 1/6) + 144 = n
(144/1 x 1/6) + 144 = n
(144 x 1)/(1 x 6) + 144 = n
(144/6) + 144 = n
(24) + 144 = n
24 + 144 = n
168 = nAnswer: Joan is 168 cm tall
Check
a) You may use the Block Model approach to check if the answer is correct.
[chart: block model; Block model showing six blocks labeled 24 and a bracket, with the label “1/6 of Pedro’s height” pointing to one block]
Labels printed beside the bracket: “Height of Pedro divided into 6, that is 144 ÷ 6 = 24”
Since Joan is 1/6 taller than Pedro, add 24 cm to Pedro’s height to obtain Joan’s height.
[chart: block model; Seven blocks labeled 24 with a bracket]
Label printed beside the bracket: “144 + 24 = 168”
The answer is correct.
Solution to Problem #3
Understand
- a) What is asked?
- The area enclosed by the border
- b) What are given?
- The dimension of the paper which is 8 1/2 inches wide and 13 inches long
- The width of the border drawn on all sides of the paper which is 3/4 of an inch
- a) What is asked?
Plan
- a) How to find the area of a rectangle?
- Multiply length by its width (L x W)
- b) With the border, how does the length and width of the enclosed area differ from the width and length of the rectangular paper?
- Both the length and width of the enclosed area are shorter by 2 x 3/4 than the length and width of the rectangular paper?
- c) What operation will be used?
- Multiply and Subtraction
- d) Write the number sentence.
- Length; 13 − (2 x 3/4)
- Width; 8 1/2 − (2 x 3/4)
- Area enclosed by the border; A = l x w
- A = [13 − (2 x 3/4)] x [8 1/2 − (2 x 3/4)]
- a) How to find the area of a rectangle?
Solve
A = [13 − (2 x 3/4)] x [8 1/2 − (2 x 3/4)] — Rewrite the whole number to fraction
A = [13 − (2/1 x 3/4)] x [8 1/2 − (2/1 x 3/4)] — Multiply the fractions
A = [13 − (6/4)] x [8 1/2 − (6/4)] — Rewrite the mixed number to improper fraction and the whole number as a fraction with a denominator of 2.
A = [13 − (3/2)] x [8 1/2 − (3/2)] — Reduced the fraction 6/4 to lowest term
A = [26/2 − (3/2)] x [17/2 − (3/2)] — Remove the parentheses
A = [26/2 − 3/2] x [17/2 − 3/2] — Subtraction of Similar Fractions
A = [23/2] x [14/2] — Remove the bracket
A = [23/2] x [7] — Multiply
A = 23/2 x 7 — Simplify
A = 161/2
A = 80 1/2 square inches
Answer: The area enclosed by the border is 80 1/2 square inches.
- Check
a) You may show the problem by drawing to check if your answer is correct.
[illustration: rectangular piece of paper with length l and width w]
Rectangular piece of paper, 8-1/2 inches wide and 13 inches long[illustration: rectangle with a gray border of 3/4 inch on all sides, labeled w and l]
A border of 3/4 inch drawn on all sides of the paper
[chart: diagram; Bordered rectangle labeled “w” on top, “l” on the left, and “3/4” on each side of the border; inner labels “11-1/2 or 23/2” (vertical) and “7” (horizontal)]
Length = 23/2 inches ; width = 7 inches
Area enclosed by the border = l x w
A = 23/2 x 7
A = 161/2
A = 80-1/2 square inches
Therefore, the answer is correct.
[chart: diagram; Bordered rectangle with labels: “length of the area enclosed by the border; 23/2 inches” and “width of the area enclosed by the border; 7 inches”]
What’s More
Activity 1: Let us try!
Directions: Show your solution to solve the following problems. Choose the answer that will complete each statement from the box.
Box: 80 6 8 27 10 4 2
One rainy day, 1/5 of the 40 pupils in Miss Trigo’s class were absent. How many pupils were absent?
Answer: There are _____ pupils who were absent.
The school band has 36 members. Three-fourths of them are girls. How many girls are in the band?
Answer: There are _____ girls in the band.
The distance around the oval track is 160 m. If Kent ran around the track 1/2 times, how far did he run?
Answer: He run _____ meters around the oval track.
Joel made 10 garden plots. He planted pechay on 2/5 of these. Find the number of garden plots planted with pechay.
Answer: There are _____ garden plots planted with pechay.
A garden plot is 6/9 m wide and 9 m long. What is the area of the plot in square meters?
Answer: The area of the garden plot is _____ square meters.
Let us have another try! Use color pen or crayon to answer the activity below. Do this in your activity notebook.
Activity 2: The Color of My Heart
Directions: Rewrite the following in your worksheet. Use appropriate problem-solving strategies to solve the problems below. If the answer is a whole number, color the heart RED ; if the answer is a proper fraction, color the heart YELLOW and if the answer is neither a whole number nor a proper fraction, color it BLUE .
On Saturday, 24 people bought cars at Best Car Shoppe. Of the 24 customers, 3/4 bought new cars. How many people bought new cars?
Scarlet can pick 3/4 kg of berries in an hour. Rey can pick 1/6 kg more berries than Scarlet. How many kilograms of berries can Rey and Scarlet pick in an hour?
The store owner ordered 3/4 of a sack of sugar. Each sack of sugar contained 50 kilograms. The supplier sent only 2/3 of the order. How many more kilograms of sugar should the supplier send?
Donna can walk at a rate of 3 1/2 kilometers per hour. On a Saturday, she covers 1/5 kilometers more than her usual rate. How far can she walk in 2 hours on a Saturday?
Forty-two teachers attended the seminar. Two-thirds of them are Math teachers. Out of these Math teachers, 1/2 are Math majors. How many teachers are non-Math majors?
Activity 3:
Study carefully, the sample non-routine problem below:
A. CJ, LV and DJ are best friends and classmates in Math subject. Their teacher in Math gave a surprised quiz. CJ got 1/2 correct answers out 10 items, LV got 3 points higher of CJ’s scores while DJ got a scores of 2 less that the scores of LV. What is the score of DJ? What is the score of LV? If their scores will be sum up, what will be the total scores?
Note : Problem can be presented another strategy:
Problem: DJ and LV scores during their Math quiz Total scores : added together CJ, LV and DJ
Given : Math quiz = 10 items
CJ score = 1/2 (10) = 10/2 = 5
LV score = 1/2 (10) + 3 = N
DJ score = 1/2 (10) + 3 – 2 = N
Number sentence :
For LV : 5 + 3 = N
Solution: 5 + 3 → 8 (LV’s scores)
For DJ : 8 – 2 → 6 (DJ’s scores)
Total Score : CJ + LV + DJ= N 5 + 8 + 6 = 19 points/scores
B. Little Enzo has collected 90 pieces of animal toy last year. He would like to give part of his toys to a charity and keep one toy each day for his cousins.
On Monday, he kept 11/15 of his toys and gave the rest away. Then he wrapped one special toy for Justin.
On Tuesday, he kept 9/13 of his toys and gave the rest away. Then he wrapped one special toy for Kaori.
On Wednesday, he kept 7/11 of his toys and gave the rest away. Then he wrapped one special toy for Jenna.
On Thursday, he kept 5/9 of his toys and gave the rest away. Then he wrapped one special toy for Pzylx.
On Friday, he kept 3/7 of his toys and gave the rest away. Then he wrapped one special toy for Josh. How many pieces of animal toy did Enzo have in the end?
a) What is asked?
- Number of animal toy at the end of five days Enzo have
b) What are given? - 90= number of animal toy Enzo collected
- N= part his toys for charity
c) Consider the following conditions in finding the answer.
| Days | Mathematical Sentence | N=? | N- 1 =? | Number of toys that Enzo has at the end of the day |
|---|---|---|---|---|
| Monday | 90 x 11/15 = N | 66 | 66 -1 = | 65 |
| Tuesday | 65 x 9/13 = N | 45 | 45 -1 = | 44 |
| Wednesday | 44 x 7/11 = N | 28 | 28 –1 = | 27 |
| Thursday | 27 x 5/9 = N | 15 | 15- 1 = | 14 |
| Friday | 14 x 3/7 = N | 6 | 6 – 1 = | 5 |
Answer: Enzo has 5 pieces of animal toy at the end of 5 days.
What I Have Learned
A.
To solve routine and non-routine problems involving multiplication without or with the addition or subtraction of fractions and whole numbers using appropriate problem-solving strategies and tools, follow the four-step plan:
(a) _____, (b) _____, (c) _____, and (d) _____.
B. Refer to the non-routine problem in “Activity 3” to continue to answer below:
Again, their Math teacher double the items from the original of 10 items on the next quiz.
- b.1 What would be the score of CJ if he got 1/2 correct scores of the total items?
- b.2 But this time, LV got a score 5 points higher of his original scores. What will be his new score?
- b.3 What will be the score of DJ if he got 1/4 of the total items incorrect?
Janina, Enzo’s sister, has 65 dolls. Like Enzo, she kept a fraction of her dolls each day, gave the rest away to charity, but gave one of her dolls to her cousin Karla in exchange of a book. Find the order of fraction Janina used so that she has only one doll left at the end.
1/2, 2/3, 3/5, 4/6, 5/6, 5/9, 9/11, 11/13
What I Can Do
Directions: Solve the following problems to unlock the hidden word. Choose the letter of the correct answer from the big rectangle box then write it on the small square boxes below.
[illustration: row of five empty answer boxes numbered 1 to 5, with a heart shape in the second box]
| 4 = I | 13 1/4 = Y | 128 = T | 120 = M | 11 = K |
|---|---|---|---|---|
| 42 1/4 = H | 30 = E | 21 = U | 112 = C | 9 = A |
You may start now! Good luck and enjoy!
Janine had two 7-meter pieces of ribbon. She used 5/7 of the ribbon for her sash. How many meters of ribbon was left?
A man weighing 75 kg can pull a maximum load of 1 3/5 times his weight. How heavy is the maximum load that he can pull?
There are 50 pupils in Mr. Borela’s class. Three-fifths of them are girls. If 7/10 of the girls are members of Math Club, how many girls are not members of the club?
On average, a box turtle lives 1 3/5 times longer than a human being. If the average life span of a human being is 80 years, what is the average life span of a box turtle?
A square plot 6 1/2 m long is covered with Bermuda grass. The plot is surrounded by a cemented path 1/2 m wide. What is the area enclosed by the cemented path?
Assessment
Are you now ready to take the test below? If not, take your time to review the previous activities.
Directions: Solve the following problems using appropriate strategies and tool. The answers are provided in Column B.
| Column A | Column B |
|---|---|
| 1) Six pitchers each filled with 3/4 liter of juice was served to Jobelle’s visitors. Find the total amount of juice served. | A. 110 1/4 |
| 2) Mrs. Fuelas wants to cover the floor of her square living room with a red carpet. One side of the room is 10 2/4 meters long. Find the area of the carpet that will cover the floor of her living room. | B. 64 |
| 3) Christian has 20 prizes. He decided to give 1/2 to the winners of the relay game. How many of the prizes are for the relay game? | C. 18 |
| 4) In one parade, 3/4 of 24 girls wore skirts made of straw. How many girls wore straw skirts? | D. 10 |
| 5) Mr. Mendez had twenty pieces of lumber that were all of the same lengths. If each piece of lumber were 3 1/5 inches long and he put them side by side, what would be the total length of all pieces together? | E. 4 1/2 |
| 6) I spent 2/3 of my weekly allowance on food and save 1/2 of the remaining amount. If my weekly allowance is P165.00, how much money do I get to save every week? | F. 27 |
| 7) Consider that 2/5 of a group of children are girls. If there are 12 girls, how many children are in the group? | G. 180 |
[transcriber’s note: table continued from the previous page]
| Column A | Column B |
|---|---|
| 8) Aydz thought that travel from home to school would take 3/4 of an hour; but because of traffic, the travel took 1/5 hr. longer. How many minutes did the actual travel take? | H. 90 |
| 9) Ms. Fabi made 450 cookies. She sold 2/5 of the cookies and gave 1/3 of the remaining cookies to the frontliners. How many cookies are left? | I. 57 |
| 10) In a 30-item test, Gina answered 4/5 of the items correctly. Rafael got 3 more items correct than Gina. How many items did Rafael answer correctly? | J. 30 |
| K. 27.5 |
Additional Activities
For mastery, answer the problem below. Good luck!
Directions: Use separate sheet to answer the activity below. Show your solutions.
James’ house is 3/4 km from the school. He had already biked 2/3 of that distance when one of his tires went flat. What part of a kilometer had he biked?
A parking lot is equally divided into four areas. One-half of Area 1 is reserved for motorcycles. What part of the whole parking lot is reserved for motorcycles?
Lyra is given Php72.00 by her mother as her daily allowance. She spends 5/8 of her daily allowance on fare and 2/3 of the remaining money for food. How much does she spend from food?
Mark had 5/6 of a liter of paint. He used 4/5 of it to paint the door. How much paint did Mark use?
The length of a rectangle is 1200 cm and its width is 900 cm. If the length is decreased by 3/20 and the width is increased by 1/5. Find the area of the new rectangle.
Ana passed by Lani’s house and sell malagkit rice to Lani’s mother. She still had 4/5 of two kilograms of malagkit rice. Ana asked Lani’s mother, how much malagkit rice she would buy. Her mother said that she would like 1/3 of a kilogram of malagkit rice. How much malagkit rice does Ana have left?
Janet works every Saturday in her garden. She has a flower bed that measures 8 1/4 by 16 1/2 feet. A pathway of 2 3/4 feet wide surrounds the edge of the bed. Find the area enclosed by the pathway.
April puts 1/2 of her weekly allowance in savings and uses 2/3 of the remaining money for food. If she has P100 left at the end of the week, how much did she have at first?
[transcriber’s note: this page is printed upside down; its content is transcribed in upright reading order below]
Answer Key
Assessment
- E
- A
- D
- C
- B
- K
- J
- I
- G
- F
What’s More
| Activity 1 | Activity 2 | Activity 3 |
|---|---|---|
| 1) 8 | 1) Red | Part of the discussion w/ answer already. |
| 2) 27 | 2) Blue | |
| 3) 80 | 3) BLUE | |
| 4) 4 | 4) BLUE | |
| 5) 6 | 5) RED |
What I Know
- D
- B
- C
- A
- C
- A
- B
- A
- C
- D
What’s In
- 2/7
- 1/9
- 2/5
- 1/4
- 4/15
- 1/9
- 4
- 5/2
- 10/3
- 4/3
What I Have Learned
A. Answers
a. understand b. plan c. solve d. check
B. Non-routine problem:
No. of items = 20
b.1 CJ = (1/2)(20) = 10 scores
b.2 LV = 8 + 5 = 13 his new scores
b.3 DJ = (1/4)(20) = 5 incorrect 20 – 5 = 15 scores of DJ
A. Answer: 11/13, 5/6, 9/11, 5/9, 4/6, 3/5, 1/2, 2/3
This problem may be solved in different ways. Here is a hint:
To start, find a fraction whose denominator is a factor of 65.
In this case, we can choose between 3/5 and 11/13.
But since 11/13 will give a bigger number than 3/5 when multiplied with 65, then the first fraction is 11/13.
Finding 11/13 of 65 will result to 55. Subtracting 1 from 55 is 54.
Find again a fraction whose denominator is a factor 54… and so on.
What I Can Do
[illustration: row of six boxes holding the letters I, a heart, M, A, T, H, read left to right]
Additional Activities
- 1/2 km
- 1/8
- Php18
- 2/3 L
- 110,160 sq. cm [?]
- 4/5 x 2 = 8/5; 8/5 – 1/3 = 19/15 or 1 4/15
- 166 3/8 sq. ft.
- P600
References
Ursua, A. C. and A. P. Lumbre. 2016. 21st Century Mathletes Textbook. Quezon City: Vibal Group, Inc.
Coronel, C. C. and N.D. Bamba. 2010. Mathematics for a Better Life Textbook. Quezon City: SD Publications, Inc.
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
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