DEPARTMENT OF EDUCATION

REGION III
Schools Division of Cabanatuan City
Maharlika Highway, Cabanatuan City

Addition and Subtraction of

Decimals and Mixed Decimals
through Ten Thousandths without
and with Regrouping

MATHEMATICS

SELF-LEARNING MODULE

Writer,Illustrator,Layouter:

6
Oliver T. Toledo
(Master Teacher I, Mabini Homesite Integrated School)

Project EL AR:
Enhance Learning
thru Adequate Resources
 GUIDE FOR THE LEARNER, PARENT, GUARDIAN
AND LEARNING FACILITATOR

To You, Learner:

Welcome to Mathematics 6 Self-Learning Module (SLM) on adding and

subtractring decimals and mixed decimals through ten thousandths without
and with regrouping. This module was made to give you with fun and mean-
ingful time for guided and independent learning at your convenience. You
will be able to process the contents of this Module while being an active
learner.

To You, Parent/s, Guardian/s and Learning Facilitator/s:

This Module was collaboratively developed and reviewed by the

teachers, school heads and supervisors of DepEd Division of Cabanatuan
City to assist you in helping the learners meet the standards set by the K to 12
Curriculum while overcoming their different constraints in schooling.

As a facilitator, you are expected to orient the learners on how to use

this module. You also need to keep track of the learners' progress while al-
lowing them to manage their own learning. Furthermore, you are expected
to encourage and assist the learners as they do the tasks included in the
module.

This Module is about solving routine or non-routine problems involving

division without or with any of the other operations of fractions and mixed
fractions using appropriate problem solving strategies and tools.

It contains various activities which are designed to help the pupils to

further improve their problem solving skills. This skill would soon be applied in
their everyday life.

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 OBJECTIVES:

1. Add and Subtract decimals and Mixed decimals through ten

thousandths without and with regrouping.

2. Being Thrifty.

COMPETENCY

Adds and Subtracts decimals and mixed decimals through ten thousandths without
and with regrouping.

M6NS-Id 106.2

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 WHAT DO YOU ALREADY KNOW?

Answer the following questions.

Write your answer on your answer sheet or in a piece of paper.

a. What is 0.5 + 0.3 + 3.5 + 4.2 ?

b. Use vertical addition to add: 12.4 + 5.0

+23.3 + 27.5

c. What is the sum of 1.4 and 13.7?

d. What is 12.25 + 9.08?

e. What is the difference between 12.7 -

3.4?

Explain and defend your answer.

A. Are you sure to your answer?

B. Why?
C. How did you get the answer?
D. What did you do to find the answer?
E. Can you explain your solution?

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 WHAT YOU NEED TO KNOW?

Presentation of the Lesson/Topic

Regina Salve saved her money to bought 2 pieces of white cloth which
measure 0.4525 meters and a 0.3415 meters. How many meters of cloth were left
if she used 0.4316 meters for her project?
Let us help Regina.
A. What is being asked in the problem?
B. What are the given data?
C. What is the operation to be used?
D. How will you solve the problem?
E. what is you final answer?

REMEMBER :

Saving money and power is a good act . Being thrifty .

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 Regina Salve saved her money to bought 2 pieces of white cloth which meas-
ure 0.4525 meters and a 0.3415 meters. How many meters of cloth were left if she
used 0.4316 meters for her project?

To help Regina, first, you must understand the problem and answer the following
questions:
 What is asked in the problem?
How many meters of cloth used for her project?
 What are given in the problem?
0.4525 meters of cloth, 0.3415 meters of cloth and 0.4316 meters

Next is you have to plan.

 What operation shall we use to solve? Select your own strategy.
Addition and Subtraction are the operations to be used. We need to add the
measure of two cloth to get its total meters and subtract meters of cloth used for the
project.
Here is the simple solution. Let us perform the activities needed to answer the problem:
* To add or subtract decimal numbers is similar to the process of adding and sub-
tracting whole numbers.

1. Arrange the digits in columns and align the decimal points.

2. Insert zeros in empty decimal place value ( if needed) so that all of numbers
have the same number of decimal places.

3. Add or Subtract decimal numbers as whole numbers.

4. Regroup numbers if necessary.

5. Place decimal point between the digits vertically aligned to all the addends

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 To add and subtract decimals and mixed decimals through ten thousandths
without and with regrouping.

To add or subtract decimal numbers:

1. Arrange the digits in columns and align the decimal points

2. Insert zeros in empty decimal place value ( if necessary) so that all of the num-
bers have the same number of decimal places.

3. Then, Add or Subtract the decimal umbers as whole numbers

4. Regroup numbers if necessary.

5. Do not forget to place the decimal point in the sum.

Study this:

What number names the shaded parts of A and B?

To get the answer, we need to add 0.3 and 0.47

0.3 0.30
+ 0.47 + 0.47
0.77

What is the difference between the shaded parts of B and A?

To get the answer, we need to subtract 0.47 and 0.3

0.47 0.47
_ 0.3 _ 0.30
0.17

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 Solving Problems with decimals is like solving applied problems. We
need to understand first the given problem and plan for which operation
(s) to use. You may draw an illustration to help you visualize your plan.
Then solve and check.

Let us try solving another problem.

Alliyah, Lyka and Abigail went to the school clinic to find out their weights.
Alliyah’s weight is 32.58 kilograms. Lyka’s weight is 33.56 kilograms, while Abigail weigh
35.84 kilograms. What is the total weight of the three pupils?
Understand

 What is asked in the problem?

The total weight of the three pupils.
 What are given in the problem?
Alliyah’s weight is 32.58 kilograms
Lyka’s weight is 33.56 kilorams
Abigail weighs 35.84 kilograms
Plan
 What operation shall we use to solve? Select your own strategy.
Add the weights of the three students. That is, 32.58 + 33.56 + 35.84
Solve . Show your computation.
Add: 32.58 + 33.56 + 35.84
1. Line up the decimal points. 2. Add as with whole numbers.
11 1

32.52 32.58
+ 33.56 + 33.56
35.84 35.84
101.98

Answer: The total weight of the three students is 101.98 kg.

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 Check your answer. Mentally compute the total weight using estimation. Is
the answer reasonable? This is the way to check your if the answer is correct.

Another Example:

Marissa bought a dress worth Php1966.99. If she gave Php2000.00 to

the cashier, how much is her change?
Solution :

19 9 91
Php 2000.00
__ Php 1966.99
Php 33.01

Answer: Php 33.01 change she will receive from Php2000.00

Remember :
To add and subtract decimals and mixed decimals through ten thousandths without
and with regrouping.

To add or subtract decimal numbers:

1. Arrange the digits in columns and align the decimal points

2. Insert zeros in empty decimal place value ( if necessary) so that all of the num-
bers have the same number of decimal places.

3. Then, Add or Subtract the decimal umbers as whole numbers

4. Regroup numbers if necessary.

5. Do not forget to place the decimal point in the sum.

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 WHAT HAVE YOU LEARNED?

Read and analyze the problem. Answer the questions based on

the problem below.

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 ACTIVITY NUMBER 1

Solve the indicated operations.

1. 2.53 2. 9.78 3. 7.254

+ 4.26 + 7.36 + 8.733

4. 73.401 5. 63.24 6. 45.6

- 3.7 - 7.527 + 3.7

7. 15.826 8. 4.6783 9. 7.89

+ 72.344 - 2.7524 + 2.5678

10. 8.733
- 4.6882

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 ACTIVITY NUMBER 2

Read and solve the problem carefully. Write the correct

answer on the space provided before each number.

___________________1. The sum of 23.456, 90.354, and 345.10.

___________________2. 234.45 added to the difference of 89 and 23.765.

___________________3. Take away 45.320 from 890.45.

___________________4. Increase 27.4578 by 5.783.

___________________5. Add 15.729 to the difference of 26.84 and 4.5.

___________________6. Subtract 68.501 from the sum of 21.54 and 80.27.

___________________7. Take away 28.567 from the sum of 19.5403 and 27.6921.

___________________8.The sum of 56.78 and 19.452 and 14.23.

___________________9.Deduct 15.729 from the sum of 26.84 and 4.5.

___________________10. Added 24.543 by 6.7543.

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 ACTIVITY NUMBER 3

Read and Solve each problem. Show all the steps.

1. Raffy and Rafa have a combined weight of 118.42 kilograms. If Raffy is heavier
by 8.0625 kilograms, how much do each of them weigh?

What is asked?
What are given?
What operation to be used?
Solution.
Final Answer.

2. The water bill costs Php875.50 while the phone bill costs Php687.25. How
much will be needed to pay for the bills?

What is asked?
What are given?
What operation to be used?
Solution.
Final Answer.

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 14
What Do You Already Know? What Have You Learned?
A. 8.5
A. Php 452.75
B. 68.2
B. Php 47.25
C. 15.1
D. 21.33
E. 9.3
Activity Number 1 Activity Number 2
1. 6.79 1. 458.91
2. 17.14 2. 347.215
3. 15.987 3. 845.13
4. 69.701 4. 33.2408
5. 55.713 5. 38.069
6. 49.3 6. 33.309
7. 88.170 7. 18.6654
8. 1.9259 8. 90.462
9. 5.3222 9. 15.611
10. 4.0448 10. 31.29.73
Activity Number 3
A. Raffy is 63.24.13 kilograms while Rafa is 55.1788 kilograms
B. Php 1562.75 needed to pay for the bills.
ANSWER KEYS
 REFERENCES

Books

Marjoseph H. Perez, et.al, 21st Century MATHletes (Quezon City, Philippines: Vibal Group,
Inc., 2016), pages 44-55
Olivia M. Ganaban, Understanding Mathematics 5, Vicarish Publication and Trading Inc.

Pages 155 –159

Online Sources

Dep ed resources,
Grade 6 Daily Lesson Log DLL—1st Quarter SY 2019-2020, August 3, 2019 https://
www.depedresources.com/grade-6-daily-lesson-log-dll-1st-quarter-sy-2019-2020/

Guro Ako Admin,Grade 6 K-12 Quarter 1 TG (Teachers Guide Compilation), July 3, 2017

https://guroako.com/2017/07/03/grade-6-k-12-tg-teachers-guidequarter-1/

Department of Education, K to 12 Curriculum Guide, https://www.deped.gov.ph/wp-

content/uploads/2019/01/Math-CG_with-tagged-math-equipment.pdf

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 Adds and Subtracts Decimals and
Mixed Decimals through Ten Thousandths
without and with Regrouping

This module on Adding and Subtracting Decimals and Mixed Decimals through
ten thousandths without and with regrouping is written to help you further improved
your problem solving skills in decimals.
It contains different activities which are anchored on real-life problems that will
engage you in the mathematical ideas and concepts to be explained in this module.
Through this module, we hope to help you understand mathematical concepts
in relation with your everyday life.

DEPARTMENT OF EDUCATION Region 3 Division of Cabanatuan City

Curriculum Implementation Division (CID)
Learning Resource Management and Development System (LRMDS)
This self-learning module (SLM) is developed by the SDO Cabanatuan City CID-LRMDS Team under
Project EL AR: Enhanced Learning thru Adequate Resources.
Cover and page elements illustrations by Jefferson U. De Jesus ● Project EL AR logo by Gemmarie G. Rivas