This is a self-learning module (SLM) for Mathematics Grade 3, Quarter 1, Module 13: “Subtracting 3 to-4 Digit Numbers from 3 to-4 Digit Numbers.” It is written for Grade 3 learners studying at home or in class, with support from parents and teachers. By the end, learners should be able to subtract 3- and 4-digit numbers, with and without regrouping, and check their answers.
On this page 6 sections
What learners will learn
After going through this module, learners are expected to:
- Subtract 3- to 4-digit numbers from 3- to 4-digit numbers (M3NS-lg-32.6)
Lessons in this module
The module has one lesson: Lesson 1: Subtracting 3 to-4-Digit Numbers from 3 to-4-Digit Numbers without and with Regrouping. It opens by linking subtraction to daily life, such as counting the change a store gives you. It then reviews addition word problems, introduces subtraction using expanded form, and teaches the standard column method.
Key ideas in the module
Important terms
- Minuend: the number you subtract from. In 9 875 – 8 641, the minuend is 9 875.
- Subtrahend: the number being subtracted. Here it is 8 641.
- Difference: the answer. The difference between 9 875 and 8 641 is 1 234.
Subtracting with the expanded form
The module first shows subtraction by writing each number as thousands, hundreds, tens, and ones. For example, 9 452 becomes 9 000 + 400 + 50 + 2, and 7 231 becomes 7 000 + 200 + 30 + 1. Subtracting each place gives 2 000 + 200 + 20 + 1, or 2 221. The module calls this the long method for large numbers.
For regrouping in expanded form, learners follow a worked example with 9 451 minus 7 538:
- Ones: 8 cannot be taken from 1, so borrow 10 from the tens. The tens become 40 and the ones become 11. Then 11 – 8 = 3.
- Tens: 40 – 30 = 10.
- Hundreds: 500 cannot be taken from 400, so borrow 1 000 from the thousands. The thousands become 8 000 and the hundreds become 1 400. Then 1 400 – 500 = 900.
- Thousands: 8 000 – 7 000 = 1 000.
The answer is 1 000 + 900 + 10 + 3 = 1 913. The module reminds learners that you borrow 10 to the tens place, 100 to the hundreds place, and 1 000 to the thousands place.
Subtracting in columns
Without regrouping: When each digit of the subtrahend is less than the matching digit in the minuend, subtract the ones, then the tens, hundreds, and thousands. Example: 9 875 – 8 641 = 1 234.
With regrouping: When a digit in the subtrahend is greater than the matching digit in the minuend, regroup from the next place. Example: 9 547 – 658 = 8 889.
The module sums up the method in three steps:
- Align the ones, tens, hundreds, and thousands in their columns.
- Subtract from the rightmost place to the leftmost place.
- Regroup whenever the digit in the subtrahend is greater than the digit in the minuend.
Checking your answer
Add the difference and the subtrahend. If the sum equals the minuend, the difference is correct. For example, 1 234 + 8 641 = 9 875, so 9 875 – 8 641 = 1 234 is right.
How to use this module
The module is arranged in parts that build on each other:
- What I Know: a 5-item multiple-choice pretest to check what learners already know.
- What’s In: addition word problems to review the previous lesson.
- What’s New: Activity 1 (expanded form without regrouping) and Activity 2 (expanded form with regrouping).
- What is It: the worked examples and steps explained above.
- What’s More: five subtraction exercises, such as 8 537 – 3 154.
- What I Have Learned: a summary of the rules, including writing the larger number on top as the minuend.
- What I Can Do: word-style items, such as “What number is 320 less than 1 975?”
- Assessment: five items where learners find the difference and check it by adding.
- Additional Activities: questions based on a table of mangoes and bananas harvested on a farm.
For learners: Answer on a separate sheet of paper, not on the module. Read each direction carefully, and use the answer key honestly to check your work.
For parents: Sit with your child during the regrouping steps, since those are where most mistakes happen. Encourage them to check each answer by adding.
For teachers: An answer key for every activity and test is at the end of the module. Use the pretest result to decide which learners need extra help before moving on.
Frequently asked questions
What grade and quarter is this module for?
It is Mathematics Grade 3, Quarter 1, Module 13. It covers subtracting 3- to 4-digit numbers from 3- to 4-digit numbers.
What competency does the module cover?
The module states one objective: subtract 3 to-4 digit numbers from 3 to-4 digit numbers, printed with the code M3NS-lg-32.6.
Does the module have an answer key?
Yes. The answer key at the end covers the pretest, all activities, the assessment, and the additional activities.
What is the difference between subtracting with and without regrouping?
Without regrouping, each digit of the subtrahend is smaller than the matching digit of the minuend, so you subtract directly. With regrouping, you borrow from the next place when a subtrahend digit is larger, as in 9 547 – 658 = 8 889.
How can learners check their subtraction answers?
Add the difference and the subtrahend. If the sum equals the minuend, the answer is correct.
Full text of the module
The text below is a transcription of the PDF above, as printed.
Mathematics Quarter 1 – Module 13: Subtracting 3 to-4 Digit Numbers from 3 to-4 Digit Numbers
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Mathematics Quarter 1 – Module 13: Subtracting 3 to-4 Digit Numbers from 3 to-4 Digit Numbers
[illustration: students studying outdoors and at home, a teacher with students, a globe, and a lantern]
Mathematics – Grade 3 Alternative Delivery Mode Quarter 1 – Module 13: Subtracting 3 to-4 Digit Numbers from 3 to-4 Digit 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 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 _____
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Development Team of the Module
Author: Hepsheba C. Hinayon
Editors: Arnel S. Zaragosa, Jeremias C. Ceniza, Gina F. Silvestre, Elma C. Prudente, Annie Fel Lingatong, Edgardo Dondon S. Lorenzo, Ailyn V. Ponce
Reviewers: Helen C. Ugay, Divilyn M. Rodriguez, Edgardo D. Pamugas III, Melissa Keith A. Sarilla, Janette O. Caalim, Ana Lorma A. Dahiroc
Illustrators: Dennis Macaubos, Alfie Valenteros, Christian Loyd Alfuerto, Pit Ybanez
Layout Artist: Menard M. Arenas
Management Team: Allan G. Farnazo; Alona C. Uy; Mary Jeanne B. Aldeguer; Maria Gina F. Flores; Analiza C. Almazan; Arnel S. Zaragosa; Ma. Cielo D. Estrada; Jeremias C. Ceniza; Renato N. Pacpakin; Illuminado T. Boiser
3
Mathematics Quarter 1 – Module 13: Subtracting 3 to-4 Digit Numbers from 3 to-4 Digit 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 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 an arrow, icon beside the part title]
This module was designed and written with you in mind. The scope of this module permits it to be used in many different learning situations. 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 Mathematics Grade 3 learning materials you are using.
After going through this module, you are expected to:
- Subtract 3 to-4 Digit Numbers from 3 to-4 Digit Numbers. (M3NS-lg-32.6)
Enjoy your journey. Good luck!
What I Know
[illustration: pencil icon beside the part title]
Compute the following:
1.) 5 489 – 476
a. 5 310
b. 5 013
c. 5 130
d. 5 031
2.) 6 548 – 2 432
a. 4 110
b. 4 113
c. 4 110
d. 4 116
3.) 8 106 – 985
a. 7 121
b. 8 121
c. 7 131
d. 8 131
4.) 634 – 579
a. 53
b. 55
c. 61
d. 65
5.) 3 633 – 3 566
a. 56
b. 67
c. 78
d. 89
Lesson 1: Subtracting 3 to-4-Digit Numbers from 3 to-4-Digit Numbers without and with Regrouping
There are so many instances in life when you need to solve things involving subtraction of whole numbers. In playing, buying anything, paying debts and many other situations, we need to be aware on how to subtract numbers in order for us to get the right value of the thing we dealt with. If you intend to buy something, you count the money the store gave to you as change. Thus, in many circumstances in your day to day life, you applied your subtraction skills, may it be with or without regrouping.
What’s In
[illustration: puzzle-piece icon beside the part title]
Let us review the concept of problems involving addition including money that you have learned in the previous lessons by answering the following questions.
1.) Mario has 456 marbles and Roy has 231 chips. How many toys do the two boys have?
2.) Christine bought 315 pads of paper and Ana bought 120 pads of papers. How many pads of paper do the two girls have?
3.) Find the value of 479 added to 635?
4.) Francis combined his 500 toy cards to that of Mark which has 700 toy cards. How many toy cards do the two boys have?
5.) Mother bought 550 oranges, 750 apples and 1500 pineapples. How many fruits does mother have?
What’s New
[illustration: seedling icon beside the part title]
In the previous lesson, you performed addition operation through expanded form. In subtracting numbers, we can also apply the expanded form method.
Activity 1
Use expanded method to subtract the given numbers.
1.) 9 452 → 9 000 + 400 + 50 + 2 – 7 231 → – 7 000 + 200 + 30 + 1
_____ ← _____
2.) 5 356 → 5 000 + 300 + 50 + 6 – 2 143 → – 2 000 + 100 + 40 + 3
_____ ← _____
3.) 734 → 700 + 30 + 4 – 322 → – 300 + 20 + 2
_____ ← _____
4.) 6 467 → 6 000 + 400 + 60 + 7 – 465 → – 400 + 60 + 5
_____ ← _____
[transcriber’s note: in item 4, the original shows a dash followed by a blank space before “400 + 60 + 5”; no term is printed in that position on the page]
The expanded method in subtracting numbers is said to be the long method when we subtract numbers involving large digits.
The activity illustrates subtraction of numbers without regrouping using the expanded method. Do you know how to use this method in subtraction with regrouping?
Activity 2 — continued from earlier pages:
Fill in the missing numbers to complete the subtraction process with regrouping using the expanded form.
1.) Subtract 9 451 by 7 538.
| Thousands | hundreds | tens | ones | |
|---|---|---|---|---|
| 9 451 | 9 000 | + 400 | + 50 | + 1 (minuend) |
| – 7 238 | – 7 000 | + 500 | + 30 | + 8 (subtrahend) |
[transcriber’s note: an arrow printed between the standard form and the expanded form is omitted]
Remember that we do the subtraction starting at the ones place.
Is it possible to subtract 8 from 1? _____ What will you do to the minuend so that you can subtract the normal way? _____ Yes, do the regrouping!
We can borrow from the number at the tens place value which is 50. We will now borrow 10 from the tens place.
| Thousands | hundreds | tens | ones | |
|---|---|---|---|---|
| 9 451 | 9 000 | + 400 | + | + (1 + 10) |
| – 7 538 | – 7 000 | + 500 | + 30 | + 8 |
[transcriber’s note: in the original, the 50 is struck through and 40 is printed above it]
Again, we borrow 10 at the tens place. So, 50 -10 = 40. Then we add 10 to the ones place. So, 1 + 10 = 11. Can you now subtract at the ones place?
| Thousands | hundreds | tens | ones | |
|---|---|---|---|---|
| 9 451 | 9 000 | + 400 | + | + 11 |
| – 7 538 | – 7 000 | + 500 | + 30 | + 8 |
| _____ |
[transcriber’s note: the 50 is struck through and 40 is printed above it; the empty box is under the ones column]
11 – 8 = ? If your answer is 3, then you are correct! Now that you are done in the ones place, kindly proceed to the tens place.
| Thousands | hundreds | tens | ones | |
|---|---|---|---|---|
| 9 451 | 9 000 | + 400 | + | + 11 |
| – 7 538 | – 7 000 | + 500 | + 30 | + 8 |
| _____ | 3 |
[transcriber’s note: the 50 is struck through and 40 is printed above it]
40 – 30 = ? If your answer is 10, then you are correct! Now that you are done in the tens place, then proceed to the hundreds place.
| Thousands | hundreds | tens | ones | |
|---|---|---|---|---|
| 9 451 | 9 000 | + 400 | + | + 11 |
| – 7 538 | – 7 000 | + 500 | + 30 | + 8 |
| _____ | 10 | 3 |
[transcriber’s note: the 50 is struck through and 40 is printed above it]
Can you subtract 500 from 400? _____ What will you do to make subtraction possible? _____ Yes, do the regrouping again! This time, hundreds place will borrow 1 000 from thousands place. Can you show the solution below?
| Thousands | hundreds | tens | ones | |
|---|---|---|---|---|
| 9 451 | 9 000 | + 400 | + | + 11 |
| – 7 538 | – 7 000 | + 500 | + 30 | + 8 |
| _____ | _____ | 10 | 3 |
[transcriber’s note: the 50 is struck through and 40 is printed above it]
If you borrow 1 000 to thousands place then add that 1 000 to hundreds place, then congratulations! You got it right!
| Thousands | hundreds | tens | ones | |
|---|---|---|---|---|
| 9 451 | + | + | + 11 | |
| – 7 538 | – 7 000 | + 500 | + 30 | + 8 |
| 1 000 | 900 | 10 | 3 |
[transcriber’s note: in the original, 9 000, 400 and 50 are struck through, with 8 000, 1 400 and 40 printed above or beside them]
Can you now write the final answer to the empty cell?
| Thousands | hundreds | tens | ones | |
|---|---|---|---|---|
| 9 451 | + | + | + 11 | |
| – 7 538 | – 7 000 | + 500 | + 30 | + 8 |
| _____ | 1 000 | 900 | 10 | 3 |
For the next two items, fill in the empty cells by subtracting numbers with regrouping using the expanded form.
Remember that you can only borrow:
- ✓ 10 to the tens place
- ✓ 100 to the hundreds place
- ✓ 1 000 to the thousands place
2.) Subtract 2 718 from 5 346
| Thousands | hundreds | tens | ones | |
|---|---|---|---|---|
| 5 346 | 5 000 | + 300 | + 40 | + 6 |
| – 2 718 | – 2 000 | + 700 | + 10 | + 8 |
| _____ | _____ |
[transcriber’s note: the answer boxes are empty; the loose numbers printed beside them in the original are 40, 900, 10, 3, 8 000, 1 400 and 1 000, which belong to the item 3 layout]
3.) Subtract 1 352 from 6 334
| Thousands | hundreds | tens | ones | |
|---|---|---|---|---|
| 6 334 | 6 000 | + 300 | + 30 | + 4 |
| – 1 352 | – 1 000 | + 300 | + 50 | + 2 |
| _____ | _____ |
[transcriber’s note: the answer boxes are empty]
What is It
For this lesson, you will focus in subtracting 3 to-4 digit numbers from 3 to-4 digit numbers with or without regrouping.
Example: 9 875 – 8 641 = ?
Study carefully the table below. Take note of how the answer is obtained. Remember that the process of obtaining the answer is as important as the answer itself.
| 1. Subtract the ones. | 2. Subtract the tens. | 3. Subtract the hundreds. | 4. Subtract the thousands. |
|---|---|---|---|
| 9 875 – 8 641 4 | 9 875 – 8 641 34 | 9 875 – 8 641 234 | 9 875 – 8 641 1 234 |
Checking:
In checking, try to add the difference and the subtrahend. If the sum will be the minuend, then your difference is correct. See example below.
| 9 875 | 1 234 |
|---|---|
| – 8 641 | + 8 641 |
| 1234 | 9 875 |
The minuend is 9 875 while the number to be subtracted or the subtrahend is 8 641. The answer is the difference. The difference between 9 875 and 8 641 is 1 234. The table above shows a systematic way of answering the equation. You indicate what you want to find, and what you need to do. You used subtraction in order to find the difference of the whole numbers.
Observe how the minuends and the subtrahends are properly aligned so that all the ones, tens, hundreds, and thousands digits are written in their respective columns.
The subtraction process in our previous example is a case in which each digit of the subtrahend is less than to its corresponding digit in the minuend. Such process is called subtracting numbers without regrouping.
In the next example, we will show a case where the digits of the subtrahend are greater than their corresponding digits in the minuend. Cases like this will undergo subtracting numbers with regrouping.
Example: 9 547 – 658 = ?
| Subtract the ones. Regroup. | Subtract the tens. Regroup. | Subtract the hundreds. Regroup. | Subtract the thousands. Regroup. |
|---|---|---|---|
| 3 17 9 5 4 7 – 6 5 8 9 | 13 4 17 9 5 4 7 – 6 5 8 8 9 | 14 13 8 17 9 5 4 7 – 6 5 8 8 8 9 | 14 13 8 17 9 5 4 7 – 6 5 8 8 8 8 9 |
[transcriber’s note: the regrouped digits are printed small above and beside the minuend, and some minuend digits are struck through in the original; the layout is flattened here]
The method above tells you how to subtract numbers with regrouping. The minuend is 9 547 and the subtrahend or the number to be subtracted is 658. The difference is 8 889.
In summary, when subtracting numbers, follow these simple steps:
Step 1. Align the digits properly by writing all the ones, tens, hundreds, and thousands in their respective columns.
Step 2. Start subtracting from the rightmost place to the leftmost place.
Step 3. Regroup whenever the digit in the subtrahend is greater than the digit in the minuend.
What’s More
Subtract the following.
| 1. 8 537 | 2. 7 642 | 3. 9 752 | 4. 6 430 | 5. 762 |
|---|---|---|---|---|
| – 3 154 | – 4 321 | – 3 863 | – 551 | – 673 |
What I Have Learned
In subtracting 3 to-4 digit numbers from 3 to-4 digit numbers, be sure to align all the ones, tens, hundreds, thousands properly so that it will not be difficult for you to subtract.
- The bigger or the larger number must be your minuend and be sure to write it on top or it must be written first.
- The smaller or the lesser number must be written next or at the bottom of the larger number as the subtrahend.
- Do not forget to regroup the ones, tens, hundreds, thousands, whenever the digit in your subtrahend is larger than its corresponding digit in the minuend.
- Look back.
You need to check if your answer is correct. Add the difference and the subtrahend to be sure that your answer is correct. When the sum is congruent with your minuend, therefore your difference is right.
What I Can Do
Find what number is being asked.
- What is the difference between 8 753 and 962?
- What number is 320 less than 1 975?
- Subtract 514 from 2 469?
- What is 6 788 less than 899?
- Take away 485 from 3 274.
Assessment
Fill in the box with the correct difference. Check your answer by adding your difference and the subtrahend. Do this on your paper.
| 1.) 8 325 | 2.) 6 546 | 3.) 7 432 |
|---|---|---|
| – 3 124 | – 3 657 | – 323 |
| _____ | _____ | _____ |
| 4.) 843 | 5.) 10 421 |
|---|---|
| – 564 | – 3 210 |
| _____ | _____ |
Additional Activities
Table of fruits harvested in a farm.
| Fruits | Variety | Number of Fruits | Total |
|---|---|---|---|
| Mango | Apple Mango | 568 | 1 011 |
| Mango | Carabao Mango | ||
| Banana | Lakatan | 443 | |
| Banana | Latundan |
[transcriber’s note: the cells for Number of Fruits and Total are merged in the original; each value is placed in the first row of its group]
Answer the questions below.
- How many Apple Mangos are there if there are 253 Carabao Mangos?
- How many Latundan bananas are there if there are 275 Lakatan bananas?
- How many fruits are left when 253 Carabao Mangos were sold?
- How many fruits are left when 275 Lakatan were sold?
Answer Key
Additional Activity
1.) 315 2.) 168 3.) 758 4.) 736
Assessment
- 5201
- 2889
- 7109
- 279
- 7211
What I Can Do
1.) 7791 2.) 1655 3.) 1955 4.) 5889 5.) 2789
What’s More
1.) 5383 2.) 3321 3.) 5889 4.) 5879 5.) 89
What’s In
- 687
- 435
- 1 114
- 1 200
- 1 800
What’s New
Activity 1
- 2221 = 2000 + 200 + 20 + 1
- 3213 = 3000 + 200 + 10 + 3
- 412 = 400 + 10 + 2
- 6002 = 6000 + 0 + 0 + 2
Activity 2
1 913
5 346
− 2 718
2 6286 334
− 1 352
4 982
[transcriber’s note: the page shows no subtrahend beside item 1, so the item is transcribed as printed]
What I Know
- B
- D
- A
- B
- B
References:
Department of Education. 2016. “About the K to 12 Mathematics Curriculum Guide (Grade 1 to 10)”. Accessed February, 2020. http://lrmds.deped.gov.ph/.
Department of Education. 2010. Lesson Guide in Mathematics Grade 3. 134-135. Pasig City: Bureau of Elementary Education in coordination with Ateneo De Manila University.
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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