Comprehensive Math 4 Guide: Adding and Subtracting Large Numbers with Regrouping

MATH 4
TERM 1 WEEK 8
D
A
Y
1
Adding Numbers

Have a drill on addition using flashcards.

Watch and learn addition.
https://www.youtube.com/watch?
v=1Al2Fc3wOIQ

When adding numbers, regrouping is necessary
when the sum of the digits in a place-value
column is 10 or more. The extra value is carried
over to the next higher place value.
Example (Without Regrouping):
234,125
+ 123,341
-----------
357,466
Presentation

Since the sum of each column is less than 10,
regrouping is not needed.
Example (With Regrouping):
456,789
+ 273,456
-----------
730,245

In some columns, the digits add up to 10 or
more, so regrouping is necessary. Learners
should always start adding from the ones
place and check whether a digit needs to
be carried to the next column.

To add large numbers accurately:
Align the numbers according to their place
values.
Begin adding from the ones place.
Regroup whenever the sum of a column is 10
or more.
Continue adding each column until reaching
the highest place value.
Check the answer using estimation.

Example Without Regrouping:
321,145
+ 214,352
-----------
535,497
Example With Regrouping:
589,674
+ 264,589
-----------
854,263

Accuracy is important when working with large
numbers because a small error can greatly affect
the final answer.

Directions: Find the sum.
1. 234,125 + 123,341 = ________
2. 321,456 + 214,332 = ________
3. 405,213 + 192,654 = ________
4. 510,320 + 243,165 = ________
5. 432,111 + 156,777 = ________
Activity 1

6. 301,425 + 284,154 = ________
7. 611,243 + 122,456 = ________
8. 412,125 + 173,654 = ________
9. 523,241 + 264,318 = ________
10.340,526 + 251,143 = ________

Activity 2
Directions: Add the following numbers.
1. 478,965 + 234,789 = ________
2. 567,895 + 234,178 = ________
3. 389,467 + 218,596 = ________
4. 456,789 + 273,456 = ________
5. 598,675 + 124,387 = ________

6. 367,895 + 245,178 = ________
7. 489,567 + 321,486 = ________
8. 675,348 + 289,472 = ________
9. 529,876 + 381,259 = ________
10. 478,659 + 245,378 = ________

Directions: Find the missing addend.
1. 365,450 + _____ = 825,900
2. 245,670 + _____ = 700,000
3. 456,200 + _____ = 800,000
4. _____ + 154,375 = 500,000
5. 275,500 + _____ = 900,000
Activity 3

6. _____ + 234,150 = 750,000
7. 412,300 + _____ = 900,000
8. _____ + 365,250 = 800,000
9. 124,875 + _____ = 600,000
10. _____ + 487,560 = 900,000

Directions: Find and correct the error.
478,965
+234,789
----------
603,654
567,895
+234,178
-----------
791,963
Activity 4
389,467
+218,596
-------------
507,953
456,789
+273,456
------------
720,145
598,675
+124,387
------------
612,952

Directions: Solve.
1. 456,789 + 321,654 = ________
2. 287,456 + 398,745 = ________
3. 542,389 + 247,596 = ________
4. 634,875 + 218,364 = ________
5. 495,387 + 386,259 = ________
6. 576,489 + 243,675 = ________
7. 369,875 + 458,256 = ________
8. 286,754 + 513,467 = ________
9. 487,296 + 324,587 = ________
10.398,764 + 501,125 = ________
Activity 5

Directions: Solve each problem.
1. A library has 345,678 books. It received 234,125
more books. How many books does it have
now?
2. A school collected 245,780 bottle caps in the
first month and 156,245 in the second month. How
many bottle caps were collected altogether?
Activity 6

3. A city recorded 412,567 tourists in June and
287,233 tourists in July. What is the total number
of tourists?
4. Ana saved 125,450 and later added
₱
234,275. How much money does she have
₱
now?
5. A factory produced 356,780 toys in January
and 243,175 toys in February. What is the total
production?

6. A charity organization received 278,450
donations in cash and 125,875 donations in
goods. What is the total value?
7. A farmer harvested 345,600 mangoes from one
farm and 154,275 from another. What was the
total harvest?
8. Two schools have enrollments of 412,500 and
287,350 learners. What is the combined
enrollment?

9. A bookstore sold 224,875 books in the first
quarter and 365,125 in the second quarter.
How many books were sold in all?
10.A company earned 456,890 in the first month
₱
and 321,675 in the second month. What was
₱
the total income?

Add the following numbers. Show your solution
when necessary.
A. Without Regrouping
1) 234,123 + 345,234 = ______
2) 123,456 + 234,123 = ______
3) 456,321 + 123,456 = ______
4) 210,345 + 120,234 = ______
5) 543,210 + 123,456 = ______
Assessment

With Regrouping
1) 456,789 + 234,567 = ______
2) 378,945 + 246,786 = ______
3) 589,467 + 234,895 = ______
4) 678,954 + 123,789 = ______
5) 495,678 + 387,945 = ______

Self-Assessment
• 9–10 correct: Excellent! You can accurately add
numbers with sums up to 1,000,000 with and without
regrouping.
• 7–8 correct: Very Good! You understand the
concept well. Continue practicing regrouping.
• 5–6 correct: Good effort! Review place value and
carrying/regrouping steps.
• 0–4 correct: Keep practicing. Ask for help and
review worked examples with your teacher or
classmates.

MATH 4
Subtracting Numbers
TERM 1 WEEK 8
D
A
Y
2

Have a drill on subtraction using flashcards.

Watch and learn subtraction.
v=8_X680JiWDc

Presentation
Subtraction is the process of finding the
difference between two numbers. When
subtracting numbers less than 1,000,000, we
must align the digits according to their place
values and subtract starting from the ones
place.

A. Subtraction Without Regrouping
Subtraction without regrouping happens
when the digit in the minuend (top number) is
greater than or equal to the digit directly
below it in each place-value column.
Example:
568,742
- 234,521
334,221

Steps:
1. Align the numbers according to place
value.
2. Start subtracting from the ones place.
3. Subtract each column from right to left.
4. Write the difference in the correct place
value.
Since all top digits are greater than the
bottom digits, regrouping is not needed.

B. Subtraction With Regrouping
Regrouping is necessary when the digit in the
minuend is smaller than the digit below it. We
borrow 1 from the digit to its left and add 10
to the current digit.
Example:
405,372
- 178,185
227,187

Steps:
1. Align the numbers properly.
2. Begin subtracting from the ones place.
3. If the top digit is smaller than the bottom
digit, regroup by borrowing 1 from the next
higher place value.
4. Continue subtracting column by column.
5. Check the answer using estimation or
addition.

Regrouping helps make subtraction possible
when the top digit is less than the bottom
digit.

2. Subtract Numbers Less Than 1,000,000 Without
and With Regrouping Accurately
To accurately subtract large numbers:
• Align digits according to place value.
• Start from the ones place and move left.
• Regroup when necessary.
• Write each difference carefully.
• Check the answer using addition.

Example Without Regrouping
897,654
- 345,123
552,531
Example With Regrouping
700,250
- 285,475
414,775

Accuracy is important because errors in one place
value can affect the entire answer.
Real-Life Application
Subtraction is useful in everyday life. We use it to:
• Determine remaining savings after expenses.
• Calculate change when shopping.
• Find the difference between populations,
distances, or scores.
• Keep track of inventory and supplies.

Example:
A school received 850,000 notebooks at the
beginning of the year. After distributing 325,450
notebooks to learners, how many notebooks
remained?
850,000
- 325,450
524,550
Answer: There are 524,550 notebooks remaining.

Directions: Subtract the following numbers.
1. 568,742 − 234,521 = ________
2. 897,654 − 345,123 = ________
3. 765,432 − 214,321 = ________
4. 654,987 − 432,765 = ________
5. 783,541 − 251,320 = ________
Activity 1

6. 932,864 − 421,352 = ________
7. 875,643 − 254,321 = ________
8. 746,532 − 325,421 = ________
9. 684,275 − 263,154 = ________
10. 895,764 − 374,253 = ________

Directions: Find the difference.
1) 405,372 − 178,185 = ________
2) 700,250 − 285,475 = ________
3) 856,301 − 478,924 = ________
4) 935,450 − 286,789 = ________
5) 804,125 − 395,687 = ________
6) 750,000 − 286,475 = ________
7) 612,340 − 298,765 = ________
8) 900,100 − 485,275 = ________
9) 840,300 − 597,845 = ________
10)768,251 − 389,476 = ________
Activity 2

Directions: Find the missing subtrahend or
minuend.
1. 825,900 − _____ = 365,450
2. _____ − 245,670 = 454,330
3. 800,000 − _____ = 456,200
4. _____ − 154,375 = 345,625
5. 900,000 − _____ = 275,500
Activity 3

6. _____ − 234,150 = 515,850
7. 900,000 − _____ = 412,300
8. _____ − 365,250 = 434,750
9. 600,000 − _____ = 124,875
10._____ − 487,560 = 412,440

Directions: Find and correct the error.
700,250
- 285,475
525,875
856,301
- 478,924
488,377
900,100
- 485,275
525,925
804,125
- 395,687
519,438
Activity 4

Activity 5
Directions: Solve the following.
1. 987,654 − 456,789 = ________
2. 845,678 − 297,456 = ________
3. 900,000 − 345,678 = ________
4. 756,321 − 489,765 = ________
5. 650,890 − 275,456 = ________

6. 999,999 − 555,555 = ________
7. 825,430 − 348,765 = ________
8. 780,025 − 456,789 = ________
9. 902,468 − 387,249 = ________
10.875,000 − 428,375 = ________

1. A school had 850,000 notebooks. It
distributed 325,450. How many notebooks
remained?
2. A library had 675,890 books. It lent out
245,375 books. How many books were left?
Activity 6

3. There were 950,000 learners in a division. If
425,680 graduated, how many remained?
4. A school received 800,000 sheets of paper
and used 345,875. How many sheets
remained?
5. The school canteen earned 650,000 and
₱
spent 275,450. What was the remaining
₱
amount?

6. A school ordered 725,500 pencils and
distributed 312,275. How many were left?
7. A library had 900,000 books and removed
245,675 damaged books. How many books
remained?
8. A school planted 500,000 trees and 175,250
died. How many survived?

9. A division had 845,250 learners. After
transfers, 125,450 left. How many
remained?
10.From 975,000 textbooks, 364,875 were
distributed. How many textbooks
remained?

Subtract the following numbers. Show your
solution when necessary.
A. Without Regrouping
1. 865,432 − 234,121 = ______
2. 789,654 − 123,432 = ______
3. 654,321 − 321,111 = ______
4. 945,876 − 234,565 = ______
5. 532,110 − 221,010 = ______
Assessment

B. With Regrouping
1. 700,345 − 258,179 = ______
2. 845,230 − 467,891 = ______
3. 600,000 − 278,456 = ______
4. 918,507 − 384,928 = ______
5. 503,210 − 186,745 = ______

Self-Check
• 9–10 correct: Outstanding! You can subtract
numbers less than 1,000,000 accurately with and
without regrouping.
• 7–8 correct: Very Good! Continue practicing
regrouping in subtraction.
• 5–6 correct: Good effort! Review place value and
borrowing/regrouping steps.
• 0–4 correct: Keep practicing. Ask for support and
work through examples with your teacher or
classmates.

MATH 4
Multiplying Numbers
TERM 1 WEEK 8
D
A
Y
3

Have a drill on multiplication using flashcards.

Watch and learn multiplication without
regrouping.
v=OPYfY7NG5TU

1. Recognize the Steps in Multiplying 3- to 4-
Digit Numbers by a 1-Digit Number
Without Regrouping
Multiplication without regrouping occurs
when the product of each digit and the 1-
digit multiplier is less than 10, so there is no
need to carry over to the next place value.
Presentation

Steps in Multiplication Without Regrouping
1. Arrange the numbers vertically, aligning
place values.
2. Start multiplying from the ones place.
3. Multiply each digit of the larger number
by the 1-digit multiplier.

4. Write each product directly under the
correct place value.
5. Continue until all digits have been
multiplied.
6. Read the final product.

Example 1: Multiplying a 3-Digit Number by
a 1-Digit Number
213
× 3
639
No regrouping is needed because each
product is less than 10.
Solution:
• 3 × 3 = 9
• 3 × 1 = 3
• 3 × 2 = 6
Product = 639

Example 2: Multiplying a 4-Digit Number by a 1-
Digit Number
2,123
× 4
8,492
Solution:
• 4 × 3 = 12? (This would require regrouping, so
let's use another example.)

Correct example:
2,111
× 4
8,444
• 4 × 1 = 4
• 4 × 1 = 4
• 4 × 1 = 4
• 4 × 2 = 8
Product = 8,444
No regrouping is needed.

2. Multiply 3- to 4-Digit Numbers by a 1-Digit
Number Without Regrouping Accurately
To multiply accurately:
• Align numbers correctly.
• Multiply from right to left.
• Observe place values.
• Check that no regrouping is needed.
• Review your work for accuracy.

Practice Examples
Example A
321
× 2
642
Example B
1,222
× 3
3,666
Example C
2,111
× 2
4,222

Situation:
A school has 2,111 learners. Each learner receives 3
notebooks.
2,111
× 3
6,333
Answer: The school needs 6,333 notebooks.

Multiply the following:
1. 111 × 2 = ______ 2. 222 × 3 = ______
3. 313 × 2 = ______ 4. 414 × 2 = ______
5. 121 × 4 = ______ 6. 232 × 3 = ______
7. 123 × 2 = ______ 8. 341 × 2 = ______
9. 212 × 4 = ______ 10.421 × 2 = ______
Activity 1

Activity 2
Fill in the Missing Product
1. 111 × 3 = ______ 2. 202 × 4 = ______
3. 322 × 2 = ______ 4. 412 × 2 = ______
5. 133 × 3 = ______ 6. 221 × 4 = ______
7. 342 × 2 = ______ 8. 124 × 2 = ______
9. 331 × 3 = ______ 10. 212 × 3 = ______

Choose the Correct Answer
1. 111 × 4 = _____
A. 444
B. 414
C. 04
2. 212 × 2 = _____
A. 426
B. 424
C. 422
Activity 3

3. 123 × 2 = _____
A. 246
B. 236
C. 256
4. 202 × 3 = _____
A. 606
B. 602
C. 620

5. 321 × 2 = _____
A. 642
B. 622
C. 652
6. 101 × 4 = _____
D. 404
E. 414
F. 444

7. 232 × 3 = _____
A. 696
B. 686
C. 676
8. 122 × 2 = _____
D. 244
E. 224
F. 264

9. 141 × 2 = _____
A. 282
B. 262
C. 272
10. 312 × 2 = _____
D. 624
E. 614
F. 634

Activity 4
A. Write T if the statement is true and F if false.
1. 111 × 2 = 222 _____ 2. 123 × 2 = 246 _____
3. 232 × 2 = 444 _____ 4. 202 × 3 = 606 _____
5. 321 × 2 = 642 _____ 6. 101 × 3 = 303 _____
7. 212 × 2 = 424 _____ 8. 122 × 4 = 488 _____
9. 141 × 2 = 282 _____ 10.331 × 2 = 662 _____

B. Match Column A with Column B.
Column A
1. 111 × 3
2. 202 × 2
3. 123 × 2
4. 141 × 2
5. 221 × 3
6. 101 × 4
7. 232 × 3
8. 122 × 2
9. 321 × 2
10. 212 × 2
Column B
A. 282
B. 244
C. 404
D. 333
E. 696
F. 642
G. 404
H. 246
I. 663
J. 424

A. Find the product.
1.121 × 2 = _____ 2. 131 × 3 = _____
3.202 × 2 = _____ 4. 323 × 2 = _____
5.111 × 4 = _____ 6. 232 × 2 = _____
7.341 × 2 = _____ 8. 221 × 3 = _____
9.312 × 2 = _____ 10. 123 × 4 = _____
Activity 5

Complete the table.
Number Multiplier Product
111 2 ______
121 4 ______
123 2 ______
202 3 ______
212 2 ______
221 3 ______
232 3 ______
312 2 ______
321 2 ______
122 4 ______

1. A library has 111 books in each shelf. There
are 2 shelves. How many books are there?
2. A farmer planted 121 corn plants in each
row. There are 4 rows. How many corn
plants are there?
Activity 6

3. A teacher prepared 123 worksheets for each
class. She has 2 classes. How many
worksheets?
4. A baker made 212 cupcakes daily for 2 days.
How many cupcakes?

5. A store sold 202 notebooks each day for 3
days. How many notebooks?
6. A school has 141 pupils in each grade level.
There are 2 grade levels. How many pupils?

7. A gardener planted 221 flowers in each
section. There are 3 sections. How many
flowers?
8. A museum displayed 101 paintings in each hall.
There are 4 halls. How many paintings?

9. A toy shop has 312 toys in each box. There
are 2 boxes. How many toys?
10.A bakery packs 122 cookies per tray. There
are 2 trays. How many cookies?

Multiply each number correctly. Show your
solution if needed.
1. 111 × 3 = ______
2. 122 × 2 = ______
3. 212 × 4 = ______
4. 123 × 2 = ______
5. 221 × 3 = ______
Assessment

6. 341 × 2 = ______
7. 232 × 3 = ______
8. 321 × 2 = ______
9. 101 × 4 = ______
10. 421 × 2 = ______

Learner Feedback Guide
Score Feedback
9–10 Excellent! You can accurately multiply 3-digit numbers by
a 1-digit number without regrouping.
7–8 Great job! Continue practicing to improve speed and
accuracy.
5–6 Good effort! Review place value and multiplication facts.
0–4 Keep learning! Work with your teacher, peer, or family
member for additional practice.

MATH 4
Multiplying Numbers
TERM 1 WEEK 8
D
A
Y
4

Multiply as fast as you can!
101 × 2 = ______ 111 × 4 = ______
122 × 2 = ______ 131 × 3 = ______
202 × 4 = ______ 212 × 3 = ______
221 × 2 = ______ 232 × 2 = ______
321 × 2 = ______ 123 × 2 = ______

Watch and learn multiplication with
regrouping.
v=OZzD2mCxAPs

Multiplication with regrouping is necessary
when the product of a digit and the
multiplier is 10 or greater. The tens digit is
carried over (regrouped) to the next place
value.
Presentation

Steps in Multiplication with Regrouping
1. Arrange the numbers vertically according
to place value.
2. Start multiplying from the ones place.
3. Multiply the digit by the 1-digit multiplier.

4. If the product is 10 or more, write the ones
digit and regroup the tens digit to the next
column.
5. Continue multiplying each digit, adding
any regrouped number.

6. Repeat the process until all digits have
been multiplied.
7. Write the final product and check your
answer.

Example 1: Multiplying a 3-Digit Number by a 1-Digit
Number
347
× 3
Solution:
• 3 × 7 = 21 → Write 1, regroup 2
• 3 × 4 = 12 + 2 = 14 → Write 4, regroup 1
• 3 × 3 = 9 + 1 = 10
347
× 3
1,041
Product = 1,041

Example 2: Multiplying a 4-Digit Number by a 1-Digit
Number
2,486
× 4
Solution:
• 4 × 6 = 24 → Write 4, regroup 2
• 4 × 8 = 32 + 2 = 34 → Write 4, regroup 3
• 4 × 4 = 16 + 3 = 19 → Write 9, regroup 1
• 4 × 2 = 8 + 1 = 9
2,486
× 4
9,944
Product = 9,944

2. Multiply 3- to 4-Digit Numbers by a 1-Digit
Number with Regrouping Accurately
To multiply accurately:
• Align digits properly.
• Multiply from right to left.
• Regroup whenever the product is 10 or more.
• Add regrouped digits correctly.
• Check your work by estimating or reviewing
each step.

Practice Examples
Example A
568
× 4
2,272
Example B
1,735
× 5
8,675
Example C
3,246
× 2
6,492

A bookstore sold 2,345 notebooks. Each
notebook costs 4.
₱
2,345
× 4
9,380
Answer: The total sales amount to 9,380.
₱

Solve each before moving to the next.
1. 111 × 2 = ______ 2. 121 × 3 = ______
3. 212 × 2 = ______ 4. 232 × 3 = ______
5. 202 × 4 = ______ 6. 321 × 2 = ______
7. 122 × 2 = ______ 8. 141 × 3 = ______
9. 221 × 2 = ______ 10. 123 × 2 = ______
Activity 1

B. Multiply as quickly and accurately as you
can.
1. 698 × 2 = ______ 2. 784 × 3 = ______
3. 596 × 4 = ______ 4. 875 × 2 = ______
5. 1,359 × 3 = ______ 6. 2,478 × 2 = ______
7. 1,698 × 4 = ______ 8. 3,245 × 2 = ______
9. 1,875 × 3 = ______ 10. 2,469 × 4 = ______

A. Multiply.
1. 248 × 3 = ______ 2. 367 × 2 = ______
3. 459 × 4 = ______ 4. 582 × 3 = ______
5. 674 × 2 = ______ 6. 1,248 × 3 = ______
7. 2,356 × 2 = ______ 8. 1,479 × 4 = ______
9. 3,284 × 2 = ______ 10. 2,175 × 3 = ______
Activity 2

B. Correct the wrong answer.
1. 348 × 2 = 686 2. 275 × 4 = 1,000
3. 489 × 3 = 1,357 4. 1,238 × 2 = 2,366
5. 1,456 × 3 = 4,268 6. 678 × 4 = 2,612
7. 2,345 × 2 = 4,590 8. 1,789 × 3 = 5,267
9. 875 × 4 = 3,200 10. 1,999 × 2 = 3,988

Comprehensive Math 4 Guide: Adding and Subtracting Large Numbers with Regrouping

Comprehensive Math 4 Guide: Adding and Subtracting Large Numbers with Regrouping

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Comprehensive Math 4 Guide: Adding and Subtracting Large Numbers with Regrouping