This is the Grade 4 Mathematics self-learning module for Quarter 1, Module 11: “Dividing Mentally 2- to 4-Digit Numbers by 10, 100 or 1 000 Without and With Remainder.” It is an Alternative Delivery Mode (ADM) module from DepEd Region V, First Edition, 2020. It teaches learners to find a quotient and remainder in their head, without paper and pencil, by looking at the place value of the digits.
What learners will learn
After going through this module, learners are expected to:
- divide mentally 2- to 4-digit numbers by 10, 100 or 1 000 without and with remainder.
The three rules for dividing mentally
The module gives one simple rule for each divisor. The trick is to “cover” the last one, two, or three digits of the number.
| Divisor | The quotient is… | The remainder is… |
|---|---|---|
| 10 | all the digits except the ones place | the digit in the ones place |
| 100 | all the digits except the tens and ones places | the number formed by the tens and ones digits |
| 1 000 | all the digits except the hundreds, tens, and ones places | the number formed by the hundreds, tens, and ones digits |
If the covered digits are all 0, there is no remainder.
Dividing without remainder
The module opens with a story problem. Andrea wants to give boxes of oranges to COVID-19 frontliners. She has 5 000 oranges. How many boxes can she make?
- 10 oranges per box: 5 000 ÷ 10 = 500 boxes
- 100 oranges per box: 5 000 ÷ 100 = 50 boxes
- 1 000 oranges per box: 5 000 ÷ 1 000 = 5 boxes
There is no remainder in each case because the covered digits are all 0. A short practice table follows. For example, 8 000 ÷ 10 = 800, 8 000 ÷ 100 = 80, and 8 000 ÷ 1 000 = 8.
Dividing with remainder
Next, the module divides 3 472 by each divisor:
- 3 472 ÷ 10 = 347 r. 2
- 3 472 ÷ 100 = 34 r. 72
- 3 472 ÷ 1 000 = 3 r. 472
More worked examples include 1 205 ÷ 10 = 120 r. 5, 1 205 ÷ 100 = 12 r. 5, and 9 081 ÷ 1 000 = 9 r. 81.
Parts and activities in the module
- What I Know (pretest): 10 items such as 35 ÷ 10 and 8 734 ÷ 100.
- What’s In: a review cross-number puzzle using division learned earlier, such as 340 ÷ 10 and 65 ÷ 5.
- What’s New: Andrea’s story problem about boxes of oranges.
- What is It: the rules and worked examples above.
- What’s More: three sets of five items, one set each for dividing by 10, by 100, and by 1 000.
- What I Have Learned: a summary of the three rules.
- What I Can Do: a word problem. John has a 112-meter piece of rope. How many 10-meter pieces can he cut? (112 ÷ 10 gives 11 ropes.)
- Assessment: a 10-item test of mental division.
- Additional Activities: two money problems. One asks how many 100-peso bills are in ₱7 654. The other asks how Mrs. Dela Cruz can share ₱9 095 among 10 families affected by the ECQ.
How to use this module
- Learners: Start with the pretest to see what you already know. Then work through the parts in order. Write your answers on a separate sheet or in your notebook, not on the module. Check your work using the answer key at the end, and be honest when you use it.
- Parents and facilitators: Help your child read the story problems. Ask them to explain which digits they “covered” to get each answer. If they find a task hard, consult the teacher.
- Teachers: The Notes to the Teacher suggest adding games that make learners divide mentally. The answer key covers every activity, the assessment, and the additional activities.
Frequently asked questions
What grade and quarter is this module for?
It is for Grade 4 Mathematics, Quarter 1. It is Module 11 of the series.
How do you divide a number by 100 mentally?
Cover the digits in the tens and ones places. The remaining digits are the quotient, and the covered two-digit number is the remainder. For example, 3 472 ÷ 100 = 34 r. 72.
When is there no remainder?
There is no remainder when the covered digits are all 0. Examples are the ones digit when dividing by 10, or the last three digits when dividing by 1 000, as in 5 000 ÷ 1 000 = 5.
Does the module have an answer key?
Yes. The answer key covers the pretest, the review puzzle, the three What’s More activities, What I Can Do, the assessment, and the additional activities.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 1 – Module 11: Dividing Mentally 2- to 4-Digit Numbers by 10, 100 or 1 000 Without and With Remainder
CO_Q1_Mathematics4_Module11
[illustration: learners studying outdoors and at home, a teacher helping a learner at a desk, a child writing by lamp light, and learners with a globe]
Mathematics – Grade 4 Alternative Delivery Mode Quarter 1 – Module 11: Dividing Mentally 2- to 4-Digit Numbers by 10, 100 or 1000 Without and With Remainder 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
Development Team of the Module
Writer: Michael L. Delgado
Editor: Elena D. Hubilla
Reviewers: Annavi M. Maravilla, Antonio M. Herrera, Jr.
Illustrator: Jason C. Borabo
Layout Artist: Teresa Vissia B. Suñga
Management Team: Regional Director: Gilbert T. Sadsad
CLMD Chief: Francisco B. Bulalacao Jr.
Regional EPS In Charge of LRMS: Grace U. Rabelas
Regional EPS In Charge of Math: Loyd H. Botor
Regional ADM Coordinator: Ma. Leilani R. Lorico
CID Chief: Monserat D. Guemo
Division EPS In Charge of LRMS: Florena M. Deuna
Printed in the Philippines by ________________________
Department of Education – Region V
Office Address: Regional Center Site, Rawis, Legazpi City 4500 Telefax: 0917-178-1288 E-mail Address: region5@deped.gov.ph
4
Mathematics
Quarter 1 – Module 11: Dividing Mentally 2- to 4-Digit Numbers by 10, 100 or 1 000 Without and With Remainder
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: target with arrow]
Have you ever wished you could divide numbers easily in your head without using paper and pencil? It may sound difficult, but would you believe that you can do it? This module will help you learn how to divide numbers mentally.
After going through this module, you are expected to:
- divide mentally 2- to 4-digit numbers by 10, 100 or 1 000 without and with remainder.
What I Know
[illustration: pencil]
Let us try to see what you know about dividing mentally 2- to 4-digit numbers by 10, 100 or 1 000 without and with remainder.
Remember to use a separate sheet for your answers.
Find each quotient mentally.
- 50 ÷ 10 = _____
- 300 ÷ 100 = _____
- 9 000 ÷ 1000 = _____
- 35 ÷ 10 = _____
- 205 ÷ 100 = _____
- 1 034 ÷ 1000 = _____
- 451 ÷ 10 = _____
- 792 ÷ 100 = _____
- 2 135 ÷ 10 = _____
- 8 734 ÷ 100 = _____
Are you done answering? If yes, time to check. Please go to page 12 for the Answer Key.
[illustration: girl with ponytail giving a thumbs-up]
What’s In
[illustration: puzzle pieces]
Let us review first some of the lessons that can help you understand the new concepts in this module.
Divide the following and fill each cross – number puzzle.
Across
b. 340 ÷ 10 d. 7 650 ÷ 15
Down
a. 65 ÷ 5 c. 4 631 ÷ 11 e. 48 ÷ 12
transcriber’s note: the puzzle grid is printed as a shaded grid; shaded cells are blocked and unshaded cells are answer cells. Letters a to e are printed in the cells shown below.
| a | ||||
| b | c | |||
| d | e | |||
Are you done answering? If yes, time to check. Please go to page 12 for the Answer Key.
Notes to the Teacher
[illustration: notepad and pencil]
The activities may be supplemented and enhanced with games that will require learners to mentally perform division.
What’s New
Let us start learning the new concept with the help of this story problem.
Read the story problem.
[illustration: girl beside stacked boxes and a pile of oranges]
Andrea wants to give boxes of oranges to the frontliners of COVID-19 pandemic. How many boxes of 10 oranges each can she make if there are 5 000 oranges?
What is asked in the problem?
- The number of boxes of oranges Andrea can make.
What are the given facts that can help you solve the problem?
- boxes of 10 oranges, 5 000 oranges
What can you say about Andrea? What kind of person is she?
- Andrea wanted to keep the frontliners healthy by giving them oranges. She is kind and generous.
Try to solve the problem mentally.
The next part of this module will help you check if your answer is correct.
What is It
[illustration: magnifying glass with question mark]
Dividing Mentally 2- to 4-Digit Numbers by 10, 100 or 1 000 Without Remainder
To find out how many boxes of oranges Andrea can make without using paper and pencil, remember the following:
➢ When a number is divided by 10, all its digits, except in the ones place, become the quotient. ➢ The digit at the ones place becomes the remainder, if there is any.
5 000 ÷ 10 = 500 quotient
transcriber’s note: in the original, the digits “5 0” of “5 000” are circled and an arrow points from them to the word “quotient” below.
So, 5 000 divided by 10 we get a quotient of 500.
Meaning, Andrea can make 500 boxes of 10 oranges each for the frontliners.
You will notice that there is no remainder since the digit at the ones place is 0.
Did you also get the same answer? Yes? Good job!
What if Andrea puts 100 oranges in each box? How many boxes of 100 oranges each can she make with 5 000 oranges?
Let us try to solve the problem mentally. But first, you have to remember the following:
➢ When a number is divided by 100, all its digits, except in the tens and ones places, become the quotient. ➢ The number formed by the digits in the tens and ones places becomes the remainder, if there is any.
5 000 ÷ 100 = 50 quotient
transcriber’s note: in the original, the digit “5” of “5 000” is circled and an arrow points from it to the word “quotient” below.
So, 5 000 divided by 100 we get a quotient of 50.
You will notice that there is no remainder since the digits in the tens and ones places are both 0.
Did you also get the same answer? Yes? Very good! You are now ready for the next one.
What if Andrea puts 1 000 oranges in each box? How many boxes of 1 000 oranges each can she make with 5 000 oranges?
Let us try to solve the problem mentally. Remember the following:
- ➢ When a number is divided by 1 000, all its digits, except in the hundreds, tens and ones places, become the quotient.
- ➢ The number formed by the digits in the hundreds, tens, and ones places becomes the remainder, if there is any.
5 000 ÷ 1 000 = 5 quotient
So, 5 000 divided by 1 000 we get a quotient of 5.
You will notice that there is no remainder since the digits in the hundreds, tens and ones places are all 0.
Did you also get the same answer? Yes? Great!
Before we go to the next lesson, let us try to solve the problems mentally.
| ÷ 10 | ÷ 100 | ÷ 1000 | |
|---|---|---|---|
| 2 000 | |||
| 8 000 |
If you are done answering, compare your answer to the answers given below.
| ÷ 10 | ÷ 100 | ÷ 1000 | |
|---|---|---|---|
| 2 000 | 200 | 20 | 2 |
| 8 000 | 800 | 80 | 8 |
Did you also get the same answer? Yes? Great! You are now ready to learn how to divide mentally numbers by 10, 100 or 1 000 with remainder.
Are you ready? Let us start.
Dividing Mentally 2- to 4-Digit Numbers by 10, 100 or 1 000 With Remainder
Let us try to divide 3 472 by 10.
Let us solve the problem mentally.
- ➢ When a number is divided by 10, all its digits, except in the ones place, become the quotient.
- ➢ The digit in the ones place becomes the remainder, if there is any.
3 472 ÷ 10 = 347 r. 2 quotient
So, 3 472 divided by 10 gives a quotient of 347 with a remainder of 2.
Did you also get the same answer? Yes? Good job!
Let us try to divide 3 472 by 100.
Let us solve the problem mentally.
- ➢ When a number is divided by 100, all its digits, except in the tens and ones places, become the quotient.
- ➢ The number formed by the digits in the tens and ones places becomes the remainder, if there is any.
3 472 ÷ 100 = 34 r. 72 quotient
So, 3 472 divided by 100 is equal to a quotient of 34 with a remainder of 72.
Did you also get the same answer? Yes? Very Good!
Let us try to divide 3 472 by 1 000.
Let us solve the problem mentally.
- ➢ When a number is divided by 1 000, all its digits, except in the hundreds, tens and ones places, become the quotient.
- ➢ The number formed by the digits in the hundreds, tens, and ones places becomes the remainder, if there is any.
3 472 ÷ 1 000 = 3 r. 472 quotient
So, 3 472 divided by 1 000 gives a quotient of 3 with a remainder of 472.
Did you also get the same answer? Yes? Great!
Before we go to the next exercise, let us try to solve the problems mentally.
| ÷ 10 | ÷ 100 | ÷ 1000 | |
|---|---|---|---|
| 1 205 | |||
| 9 081 |
If you are done answering, compare your answer to the answers given below.
| ÷ 10 | ÷ 100 | ÷ 1000 | |
|---|---|---|---|
| 1 205 | 120 r.5 | 12 r.5 | 1 r.205 |
| 9 081 | 908 r.1 | 90 r.81 | 9 r.81 |
Did you also get the same answer? Yes? Great! You are now ready to work with the problems independently.
Are you done answering? If yes, time to check. Please go to page 12 for the Answer Key.
What’s More
Activity 1. Divide the numbers mentally by 10 and write your answers in your notebook.
- 90 ÷ 10 =
- 611 ÷ 10 =
- 2 193 ÷ 10 =
- 65 ÷ 10 =
- 5 983 ÷ 10 =
Activity 2. Divide the numbers mentally by 100 and write your answers in your notebook.
- 800 ÷ 100 =
- 492 ÷ 100 =
- 7 242 ÷ 100 =
- 1 800 ÷ 100 =
- 9 001 ÷ 100 =
Activity 3. Divide the numbers mentally by 1 000 and write your answer in your notebook.
- 7 000 ÷ 1 000 =
- 8 924 ÷ 1 000 =
- 5 676 ÷ 1 000 =
- 3 002 ÷ 1 000 =
- 2 050 ÷ 1 000 =
Are you done answering? If yes, time to check. Please go to page 12 for the Answer Key.
What I Have Learned
Always remember:
- In dividing mentally 2- to 4-digit numbers by 10
- ➢ When a number is divided by 10, all its digits, except in the ones place, become the quotient.
- ➢ The digit in the ones place becomes the remainder, if there is any.
- In dividing mentally 2- to 4-digit numbers by 100
- ➢ When a number is divided by 100, all its digits, except in the tens and ones places, become the quotient.
- ➢ The number formed by the digits in the tens and ones places becomes the remainder, if there is any.
- In dividing mentally 2- to 4-digit numbers by 1 000
- ➢ When a number is divided by 1 000, all its digits, except in the hundreds, tens and ones places, become the quotient.
- ➢ The number formed by the digits in the hundreds, tens, and ones places becomes the remainder, if there is any.
What I Can Do
Let us see if you are now ready to solve this problem.
Read and understand the problem, then answer the questions that follow.
John has 112–meter extra piece of rope after fixing their deep well. How many 10-meter rope can he cut from it?
[illustration: John holding a rope beside a well]
Are you done answering? If yes, time to check. Please go to page 12 for the Answer Key.
- What is asked in the problem?
- What are the given facts that can help you solve the problem?
- How will you solve the problem?
- What is the answer to the problem?
Assessment
You are now ready for the next activity.
Divide the problems mentally and write your answers in your notebook.
- 50 ÷ 10
- 650 ÷ 100
- 8 040 ÷ 1 000
- 91 ÷ 10
- 121 ÷ 100
- 7 789 ÷ 1 000
- 43 ÷ 10
- 999 ÷ 100
- 3 110 ÷ 100
- 9 111 ÷ 10
Are you done answering? If yes, time to check. Please go to page 12 for the Answer Key.
Are you done answering? If yes, time to check. Please go to page 12 for the Answer Key.
Additional Activities
Let us try some more. Solve the following problems.
- How many 100-peso bill will there be in ₱ 7 654? How much will be the remainder?
- Mrs. Dela Cruz has ₱ 9 095. She wants to give it to the families affected by the Enhanced Community Quarantine (ECQ) in her community. How much will each of the family receive if she decides to give it to 10 families? How much money will be left?
Answer Key
[transcriber’s note: this page is printed upside down; the answers below are transcribed in the order they appear on the page, read with the page turned right side up]
What I Know
- 5
- 3
- 9
- 3 r. 5
- 2 r. 5
- 1 r. 34
- 45 r. 1
- 7 r. 92
- 213 r. 5
- 87 r. 34
What’s In
[transcriber’s note: this is a grid of letters a to e and numbers printed in cells, and the layout could not be read reliably; the visible entries are listed below]
- a. 1
- b. 3
- c. 4
- d. 5
- e. 0
Unlabeled entries: 2, 4
What’s More
| Activity 1 | Activity 2 | Activity 3 |
|---|---|---|
| 1. 9 | 1. 8 | 1. 7 |
| 2. 61 r. 1 | 2. 4 r. 92 | 2. 8 r. 924 |
| 3. 219 r. 3 | 3. 72 r. 42 | 3. 5 r. 676 |
| 4. 6 r. 5 | 4. 18 | 4. 3 r. 2 |
| 5. 598 r. 3 | 5. 90 r. 1 | 5. 2 r. 50 |
What I Can Do
- How many 10m can be cut from the remaining rope?
- 112m and 10m
- 112 ÷ 10 = ___
- 11 ropes
Assessment
- 5
- 6 r. 50
- 8 r. 40
- 9 r. 1
- 1 r. 21
- 7 r. 789
- 4 r. 3
- 9 r. 99
- 31 r. 10
- 911 r. 1
Additional Activities
- There will be 76 100-peso bills. The remainder is P54.
- Each family will receive P909. There will be P5 left.
[transcriber’s note: the supplied pages do not match the file name. They are the References page of CO_Q1_Mathematics4_Module11, not the Dividing Mentally module. The printed page number 13 and the footer are omitted as page furniture.]
References
K to 12 Mathematics Curriculum Guide, August 2016
Mathematics 4 Learner’s Material
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
Leave a Reply