6 mathematics modules

Mathematics Modules

Quarter 1 – Weeks 1 – 4

6 6

Mathematics

Quarter 1 - Module 1:

Addition and Subtraction of

Simple Fractions and Mixed

Numbers

6

2

Mathematics - Grade 6 Alternative Delivery Mode Quarter 1 - Module 1: Addition and Subtraction of Simple Fractions and Mixed Numbers Solving Routine and Non Routine Problems Involving Addition And Subtraction of Simple Fractions and Mixed Numbers Second Edition, 2021 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 OIC-Schools Division Superintendent: Carleen S. Sedilla CESE OIC-Assistant Schools Division Superintendent and OIC-Chief, CID: Jay F. Macasieb DEM, CESE

Printed in the Philippines by the Schools Division Office of Makati City through the support of the City Government of Makati (Local School Board) Department of Education - Schools Division Office of Makati City

Office Address: Gov. Noble St., Brgy. Guadalupe Nuevo

City of Makati, Metropolitan Manila, Philippines 1212

Telefax: (632) 882 5861 / 882 5862

E-mail Address: [email protected]

Development Team of the Module

Writer: Catalina P. Ramos Editor: Patricia Ulynne F. Garvida Reviewer: Michael R. Lee Layout: Ma. Fatima D. Delfin and Michiko Remyflor V. Trangia Management Team: Neil Vincent C. Sandoval Education Program Supervisor, LRMS Michael R. Lee

Education Program Supervisor, Mathematics

3

This module was designed and written with you in mind. It is here to help you master the

addition and subtraction of simple fractions and mixed numbers. The scope of this module permits it to be used in many different learning situations. The language used recognizes the

diverse vocabulary level of students. 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

textbook you are now using. The module has two lessons, namely:

Lesson 1 - Addition and Subtraction of Simple Fractions and Mixed Numbers

Lesson 2 - Solving Routine and Non-Routine Problems Involving Addition and Subtraction of Fractions Using Appropriate Problem Solving Strategies

After going through this module, you are expected to:

1. add and subtract simple fractions and mixed numbers without or with regrouping; and

2. solve routine and non-routine problems involving addition and subtraction of

fractions using appropriate problem solving strategies.

What I Know

Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper.

1. In adding or subtracting fractions, fractions must be ____________.

A. similar B. dissimilar C. proper D. improper

2. What is the Least Common Denominator of 3

4 ,

5

6 ,

7

8 ?

A. 8 B. 12 C. 16 D. 24

3. Which set of similar fractions is equivalent to 4

5 ,

1

2 ,

7

10

A. 8

10 ,

5

10 ,

7

10 C.

4

5 ,

2

5 ,

14

5

B. 10

8 ,

10

5 ,

10

7 D.

5

4 ,

5

2 ,

5

14

4. In adding or subtracting dissimilar fractions, which step are you going to do first?

A. Change dissimilar fractions to similar fractions

B. Change dissimilar fractions to mixed numbers

C. Change dissimilar fractions to proper fractions

D. Change dissimilar fractions to improper fractions

5. What is the sum of 3

8 and

7

8 ?

A. 15

8 B. 1

1

2 C. 1

1

4 D. 1

1

2

6. What is the difference between 10

12 and

2

3 ?

A. 8

9 B.

8

12 C.

2

9 D.

1

6

7. What is N - 45

6 = 2

1

6 ?

A. 6 B. 7 C. 24

6 D. 2

6

6

What I Need to Know

4

8. If you subtract N from 82

5 , the difference is 3

4

5. What is N?

A. 53

5 B. 5

2

5 C. 4

3

5 D. 4

2

5

9. What is 7

9 increased by

2

3 ?

A. 9

12 B.

5

6 C. 1

4

9 D. 1

9

12

10. Find the sum of 63

8 and 5

1

3 .

A. 114

11 B. 11

4

8 C. 11

4

24 D. 11

17

24

Lesson

1 Addition and Subtraction of Simple

Fractions and Mixed Numbers

Fractions represent equal parts of a whole. They are important because they tell you

what portion of a whole you need, have, or want. They are used in our everyday life, like in cooking, telling time, and other daily activities. In this lesson, you will learn how to add and to

subtract simple fractions and mixed numbers with and without regrouping. It is important to

know the steps in addition and subtraction of fractions, most especially, if they have different

denominators.

What’s In

Let us recall some basic facts about fractions. Look at the following sets of fractions.

You have learned that dissimilar fractions can be

changed to similar fractions.

Take a look again in this set of dissimilar fractions.

Let’s change them to similar fractions. Do you remember the steps?

First, find the Least Common Denominator or LCD of the fractions.

The LCD is the least common multiple of the given numbers. So, we can find the LCD of 4, 12, and 3 by listing their multiples.

Multiples of 4: 4, 8, 12, 16, 20, 24 …..

Multiples of 12: 12, 24, 48, 60 …….

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24 …..

Common Multiples are 12 & 24

Notice that the least common multiple is 12, therefore, the LCD of 4, 12,

and 3 is 12.

Then change dissimilar fractions to similar fractions. (Use the idea of equivalent

fractions.)

3

4 ,

5

12 ,

2

3

7

12 ,

5

12 ,

4

12

, ,

3

4 ,

5

12 ,

2

3

, ,

Remember, that fractions with the same

denominators are similar fractions while

fractions with different denominators are

dissimilar fractions.

5

x 3 x 1 x 4

3

4 =

9

12

5

12 =

5

12

2

3 =

4

12

x 3 x 1 x 4

So, the similar fractions of is

Let’s have more examples:

Change the following dissimilar fractions to similar fractions

1. 5

6 ,

7

9 ,

1

3 The LCD is 18. So

5

6 ,

7

9 ,

1

3 can be expressed as

15

18 ,

14

18 ,

6

18 ,

respectively.

2. 8

10 ,

2

5 ,

3

4 The LCD is 20. So

8

10 ,

2

5 ,

3

4 can be expressed as

16

20 ,

8

20 ,

15

20 ,

respectively.

What’s New

How to Add and Subtract Simple Fractions and Mixed Numbers?

Take a look at this problem. Read and analyze it.

Let’s use bar model to represent the problem.

= 33

4 meters of cloth needed to make a seat cover

Kim has already 3 pieces of cloth:

1

4 m,

3

4 m ,

2

4 m

If Kim will put the 3 pieces altogether, he will have

+ +

1

4

3

4

2

4

= 6

4 =1

2

4 𝑜𝑟 1

1

2 m

This means that the pieces of cloth that Kim has is not enough for the seat

cover. How much more does he need?

So, Kim needs to subtract the total length of cloth he has from the length of the cloth

actually needed for the seat cover.

33

4

– 12

4

_

2 1

4

3

4 ,

5

12 ,

2

3

9

12 ,

5

12 ,

4

12

, ,

Kim needs 33

4 meters of cloth to make a seat cover for his car. He has 3 pieces of cloth

which measures 1

4 ,

3

4 , and

2

4 meters, respectively. Do you think these are enough?

6

Kim needs 21

4 m more of cloth.

What do you notice to the fractions that we added or subtracted?

a. 1

4 +

3

4 +

2

4 =

6

4 = 1

2

4 or 1

1

2

b. 33

4 – 1

2

4 = 2

1

4

They are similar fractions. In adding and subtracting similar fractions, add or subtract the numerators, then copy the common denominator. Always express the sum or difference in

its simplest form. Let’s have another problem.

Let’s us use the bar model again to solve the problem.

a. 13

4 m

21

2m

If you look at the bar model, 4

4 (Which is equal to 1) is also equal to

2

2 (Which is also equal to 1). So,

=

In this case,

Therefore,

13

4

+ 22

4

35

4 or 4

1

4

If you have noticed, we changed the dissimilar fraction to similar fraction first, before

we added them together.

13

4 + 2

1

2 1

3

4 + 2

2

4 = 3

5

4 or 4

1

4 m of cloth altogether

b. To solve question number 2, we have to subtract the 13

4 from 2

1

2. Same thing in

subtraction, we will change dissimilar fractions first to similar fractions before we subtract

them.

22

4

– 13

4

Mrs. Ramos bought 13

4 m of material to make a pair of pants and 2

1

2 m of the same

material to make a blouse.

a. How much material did she buy altogether?

b. How much more material did she use for making a blouse than a pair of

pants?

𝟐𝟏

𝟐 is equal to

𝟐𝟐

𝟒

7

21

2 – 1

3

4 2

2

4 – 1

3

4 =

3

4

The amount of material used in making a blouse is 3

4 m more than the amount of

material used in making a pair of pants.

What is It

In addition and subtraction of simple

fractions and mixed numbers, we have to

remember the following:

Similar Fractions

1. If they are simple fractions, add or subtract the numerator then

copy the common denominator. Express the answer in simplest

form Examples:

1. 3

8 +

1

8 =

4

8

÷4

÷4 or

1

2 2.

9

12 –

7

12 =

2

12 ÷2

÷2 or

1

6

2. If they are mixed numbers, add or subtract the whole

numbers and fractional parts separately. Express the

answer in simplest form. Examples:

1. 4 7

9 + 7

5

9 = 11 +

12

9 = 11 + 1

3

9 = 12

3

9

÷3

÷3 or 12

1

3

2. 9 2

7 – 4

5

7 We cannot subtract 5 from 2.

So, we regroup.

92

7 8

7

7 +

2

7 = 8

9

7

Therefore,

89

7 – 4

5

7 = 4

4

7

3. Subtract 35

8 from 6.

6 – 35

8 Rename 6 as a mixed number 5

8

8

58

8 – 3

5

8 = 2

3

8

Dissimilar Fractions

In adding or subtracting dissimilar fractions , follow the steps:

1. Change dissimilar fractions to similar fractions.

4

5 +

1

2 (Find the LCD)

8

10 +

5

10

5

6 –

7

12 (Find the LCD)

10

12 –

7

12

2. Add or subtract the similar fractions . Express the answer in simplest form.

8

10 +

5

10 =

13

10 or 1

3

10

10

12 –

7

12 =

3

12 ÷3

÷3 =

1

4

3. If they are mixed numbers , add or subtract the whole numbers

and fractional parts separately. Regroup the numbers if it is needed.

63

8 + 2

3

4 6

3

8 + 2

6

8 = 8

9

8 = 8 + 1

1

8 = 9

1

8

122

3 – 9

1

5 12

10

15 – 9

3

15 = 3

7

15

8

Let us have more examples:

Example 1: What is the sum of 9

15 +

12

15 ?

9

15 +

12

15 =

21

15 =

21

15

÷3

÷3 =

7

5 or 1

2

5

Example 2: If you subtract 510

18 from 15

8

18 , what is the difference?

158

18 14

18

18 +

8

18 = 14

26

18

1426

18 – 5

10

18 = 9

16

18

÷2

÷2 = 9

8

9

Example 3: What should be added to 4

5 to get 1

1

10 ?

In this case we have to subtract 11

10 –

4

5

11

10 1

1

10

11

10

– 4

5

8

10

8

10

3

10

Example 4: Daewong took 11

4 hours to walk from House A to House B. He took 1

16 hours

from House B to House C. How long did it take to walk from House A to House C?

Solution: 11

4 + 1

16 1

3

12 + 1

212

= 25

12

∴Daewong took 25

12 hours to walk from House A to House C

What’s More

Activity 1. Add or subtract the following. Fill in the box with the correct answer.

1. 10

18 +

5

18 = 6.

5

9 +

2

3 =

9 +

9 =

2. 10

15 – =

2

15 7.

5

6 –

7

9 =

15 –

14 =

3. – 82

12 = 6

5

12 8. 6

6

8 + 7

2

3 = 6 + 7

=

4. 7 – = 24

7 9. 10 – 4

9

14 = – =

5. 159

20 + 13

8

20 = 10. 9

6

7 – 3

2

3 = – =

Activity 2. Solve the following.

1. If N – 4

7 =

1

2 , what is N?

2. 153

10 increased by 3

5

6 .

3. What is the difference between 102

9 and 5

2

3 ?


4 +

3

6 +

4

8 +

6

12 .

5. Subtract 98

15 from 20.

9

Activity 3. Help Jungkook and J-Hope find their bookmarks. Solve the

following then complete the sentences with letters.

1. Jungkook has bookmarks with answers larger than 4.

They are and .

2. One of the bookmarks of J-Hope is lost. This bookmark has an answer less than 2. It is

What I Have Learned

What I Can Do

Solve each problem. Shade the circle that corresponds to the correct answer.

1. Jeff had a stick of 8 1

5 meters long. He cut a piece of 5

2

5 meters long. How much was left?

13 3

5 13

1

5 3

1

5 2

4

5

2. Franz poured 2 5

9 L of vinegar and 8

1

2 L of water into an empty jar. What is the volume of the

mixture in the jar now?

11 1

18 11

6

11 10

1

18 10

6

11

3. Trina needs 31

4 cups of milk to prepare a salad. She already has 2 containers with

1

4 cup and

2

3

cup of milk. How many more cups of sugar does she need?

214 2

13 1

14 1

13

4. Lance rides his bicycle 1

2 km to school,

3

4 km to a ball field, and

7

10 km home. How

far did he ride in all?

11

16 m

11

20 m 1

1120

m 11920

m

21

2 + 3

3

4 + 1

5

8

T 1

15 +

2

3 +

4

10

E

88

10 – 3

3

4

A 15

5

6 – 12

2

3

M

In adding or subtracting similar fractions, add or

subtract the numerators then copy the denominator. To add or subtract dissimilar fractions, change them

first to similar fractions. Then add or subtract the

similar fractions.

If they are mixed numbers, add or subtract the whole

numbers and fractional parts separately. Always express the answer in simplest form.

10

5. Aerin prepared 42

5 liters of buko juice and 7

2

3 liters of calamansi juice to sell one Saturday. How

much more calamansi juice did she prepare than buko juice?

34

15 3

1

2 11

4

15 11

2

15

Assessment


1. What is the Least Common Denominator of 3

4 ,

10

12 ,

5

9 ?

A. 12 B. 18 C. 24 D. 36

2. Which of the following is the similar fractions of 9

10 ,

3

5 ,

1

4 ?

A. 9

10 ,

15

10 ,

4

10 B.

18

20 ,

12

20 ,

5

20 C.

9

15 ,

3

15 ,

4

15 D.

9

19 ,

3

19 ,

4

19

3. Which set of fractions has the LCD of 24?

A. 7

9 ,

8

12 B.

5

6 ,

4

7 C.

7

8 ,

2

3 D.

3

4 ,

5

9


14 + 6

3

14 + 2

1

14.

A. 87

14 B. 9

4

14 C. 8 D. 9

5. Subtract 147

15 from 20.

A. 58

15 B. 5

13

15 C. 6

8

15 D. 6

13

15

Additional Activities

Add or subtract by following the arrows to find the missing fractions.

– 1

4

– 1 1

4

+ 2 1

2

– 1 1

2

– 1 1

3

+ 3 5

6

+ 2 3

4 + 1

5

12

– 4 2

3

Mathematics


Multiplication of Fractions

and Problem Solving

6

2

Mathematics - Grade 6 Alternative Delivery Mode Quarter 1 - Module 2: Multiplication of Fractions and Problem Solving Second Edition, 2021 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 OIC-Schools Division Superintendent: Carleen S. Sedilla CESE OIC-Assistant Schools Division Superintendent and OIC-Chief, CID: Jay F. Macasieb DEM, CESE

Printed in the Philippines by the Schools Division Office of Makati City through the support of the City Government of Makati (Local School Board) Department of Education - Schools Division Office of Makati City

Office Address: Gov. Noble St., Brgy. Guadalupe Nuevo


Telefax: (632) 882 5861 / 882 5862



Writer: Narcisa F. Alacapa Editor: Patricia Ulynne F. Garvida

Reviewer: Michael R. Lee Layout: Ma. Fatima D. Delfin and Michiko Remyflor V. Trangia Management Team: Neil Vincent C. Sandoval Education Program Supervisor, LRMS Michael R. Lee Education Program Supervisor, Mathematics

3

What I Need to Know

This module was designed and written with you in mind. It is here to help you master Multiplication of Fractions and Solving Word Problems Involving Fractions. The writer

simplifies and enumerates the different models of multiplying fractions. The lessons are

presented through illustrations and real life problems that will help students relate Mathematics

to their daily experiences. This module consists of the following most essential learning

competencies:

Multiplies simple fractions and mixed fractions. Solves routine and non-routine problems involving multiplication with or without

addition or subtraction of fractions and mixed fractions using appropriate problem

solving strategies and tools.


1. master multiplication of fraction in different types; 2. identify methods appropriate for solving problems; and

3. gain more confidence in solving mathematical problems involving fractions.

What I Know


1. The model shows the product of 1

5 and 8. Multiply

1

5 x 8.

A. 1 1

5 B. 1

2

5 C. 1

3

5 D. 1

4

5

2. Complete the multiplication sentence.

A. 1 B. 2 C. 3 D. 4

3. What is 1

5 x

1

2 ?

A. 1

7 B.

2

10 C.

2

7 D.

1

10

4. Find 1

4 of

1

4

A. 2

8 B.

1

8 C.

1

16 D.

1

8

5. Multiply, write your answer as a fraction as a mixed number or a whole number.

6 x 1

3 =

A. 2 B. 1

2 C. 3 D.

1

3

4

Lesson

1 Multiplication of Fractions

and Problem Solving

When teaching multiplication with fractions, it is best to give the different underlying

meanings of the operation. Some reference books enumerate the following models of

multiplication, with each expressing a different meaning:

Case 1: Whole Number × Fraction

Case 2: Fraction × Whole Number

Case 3: Fraction × Fraction

Case 4: Mixed Number × Mixed Number

Case 1 implies repeated addition, while Case 2 involves finding the fractional part of a set of

objects. Case 3 is represented by the expression: Fraction × Fraction. It involves finding the

fractional part of a region, making use of the area model wherein the fractions serve as the length

and width of a rectangular area, but the area model applies also to problems dealing with volume.

Case 4 is represented by “Mixed Number × Mixed Number” and may be viewed as an extension

of Case 3 wherein the factors are more than 1 unit or mixed number. Since case 4 is multiplying mixed number, and to better understand our lesson, let us have a review of converting mixed

number to improper fraction and vice versa.

Converting Mixed Number to Improper Fractions

Example: Convert 3 𝟐

𝟓 to an improper fraction.

Multiply the whole number part by the denominator:

3 × 5 = 15 Add that to the numerator: 15 + 2 = 17

Then write that result above the denominator: 17

5

Converting Improper Fractions to Mixed Fractions

Example: Convert 11

4 to a mixed fraction. Divide: 11 ÷ 4 = 2 with a remainder of 3. Write down

the 2 and then write down the remainder (3) above the denominator (4).

Answer: 2 3

4

What’s In

To convert a mixed fraction to an improper

fraction, follow these steps:

Multiply the whole number part by the

fraction's denominator

Add that to the numerator

Then write the result on top of the denominator

To convert an improper fraction to a mixed fraction, follow these steps:

Divide the numerator by the denominator

Write down the whole number answer

Then write down any remainder above the denominator

5

Let us try!

What’s New

How do you multiply fractions using models?

What is It

There are eight ways on how to multiply fractions.

Type 1. Whole Number x Fraction

A. Change the following improper

fraction to mixed number.

1. 10

4 =

2. 9

4 =

3. 12

5 =

4. 11

4 =

5. 20

8 =

B. Change the following mixed

number to improper fraction.

1. 3 1

2 =

2. 2 1

5=

3. 1 1

2=

4. 3 2

3=

5. 5 1

2=

Ex. 10 x 𝟏

𝟐

Step 1. Write the whole number as an improper fraction. 𝟏𝟎

𝟏 x

𝟏

𝟐

Step 2. Multiply the numerators then multiply the denominators. 𝟏𝟎

𝟏 x

𝟏

𝟐 =

𝟏𝟎

𝟐

Step 3. Simplify the product. 𝟏𝟎

𝟏 x

𝟏

𝟐 =

𝟏𝟎

𝟐= 5

TRY IT

8 x 𝟏

𝟐

15 x 𝟏

𝟑

You can use paper folding

or the box method. You

will need two different color writing instruments.

Step 1: Draw a

rectangle.

Step 2: Divide the

rectangle vertically into

rows by looking at the

denominator of the first

fraction. Then shade in the number of rows

based on the

numerator.

Step 3: Divide the

rectangle horizontally

into rows by looking at

the denominator of the

second fraction. Then shade in the number of

rows based on the

numerator with a

different color.

Step 4: Determine

your answer by

counting the total

number of rectangles for the denominator

and the total number

of squares that are

shaded by both colors

for the numerator.

Then simplify, if necessary.

How about multiplying

fractions without models?

6

Type 2. Fraction x Whole Number

Type 3. Fraction x Fraction

Type 4. Whole Number x Mixed Number

Type 5. Mixed Number x Whole Number

Ex. 𝟐

𝟑 x

𝟏

𝟒

Step 1. Just multiply numerator by numerator and denominator by denominator.

𝟐

𝟑 x

𝟏

𝟒 =

𝟐

𝟏𝟐

Step 2. Simplify the product. 𝟐

𝟑 x

𝟏

𝟒 =

𝟐

𝟏𝟐 =

𝟏

𝟔

𝟐

𝟑 x

𝟏

𝟒

𝟐

𝟑 x

𝟏

𝟒

TRY IT!

𝟐

𝟑 x

𝟏

𝟔

𝟒

𝟓 x

𝟏

𝟖

Ex. 12 x 1 𝟏

𝟐

Step 1. Write the whole number as an improper fraction and changed mixed number to

improper fraction. 𝟏𝟐

𝟏 x

𝟑

𝟐

Step 2. Multiply the numerators then multiply the denominators. 𝟏𝟐

𝟏 x

𝟑

𝟐 =

𝟑𝟔

𝟐

Step 3. Simplify the product. 𝟏𝟐

𝟏 x

𝟑

𝟐 =

𝟑𝟔

𝟐 = 18

TRY IT!

𝟏𝟓 x 1 𝟏

𝟓

𝟒 x 1 𝟏

𝟖

Using Cancellation Method. Type 4 ( WN x MN )

Ex. 1 𝟏

𝟑 x 12

Step 1. Write the whole number as an improper fraction and change the mixed number into

improper fraction. 1 𝟏

𝟑 x 12 =

𝟒

𝟑 x

𝟏𝟐

𝟏

Step 2. Multiply the numerators, then multiply the denominators. 𝟒

𝟑 x

𝟏𝟐

𝟏 =

𝟒𝟖

𝟑

Step 3. Simplify the product. 𝟒

𝟑 x

𝟏𝟐

𝟏 =

𝟒𝟖

𝟑 = 16

TRY IT!

2 𝟏

𝟑 x 6

1 𝟏

𝟑 x 4

Using Cancellation Method. Type 3 ( F x F )

Ex. 𝟐

𝟑 x 9

Step 1. Write the whole number as an improper fraction. 𝟐

𝟑 x

𝟗

𝟏

Step 2. Multiply the numerators then multiply the denominators.

𝟐

𝟑 x

𝟗

𝟏 =

𝟏𝟖

𝟑


𝟑 x

𝟗

𝟏 =

𝟏𝟖

𝟑 = 6

TRY IT!

𝟐

𝟓 x 10

𝟏

𝟒 x 12

7

Type 6. Fraction x Mixed Number

Type 7. Mixed Number X Fraction

Type 8. Mixed Number x Mixed Number

What’s More

What do you do if you have a word problem which involves multiplication of fractions?

Well, let us start a problem solution by applying the four steps in word problem. First, you have to Understand the Problem by knowing what is asked and identifying the given facts

or information needed to solve the problem. Second, Plan What to Do which means thinking of

the processes or operations to be used to solve the problem. Third, Do the Plan which means

you have to carry out and execute your plan. Solve and write the answer with the correct label

or unit of measure. Lastly, Look Back if the answer makes sense or not. Let us try this!

Ex. 𝟐

𝟓 x 1

𝟏

𝟐

Step 1. Change the mixed number to improper fraction. 𝟐

𝟓 x

𝟑

𝟐

Step 2. Multiply the numerators, then multiply the denominators. 𝟐

𝟓 x

𝟑

𝟐 =

𝟔

𝟏𝟎


𝟓 x

𝟑

𝟐 =

𝟔

𝟏𝟎 =

𝟑

𝟓

TRY IT!

𝟏. 𝟐

𝟔 𝐱 𝟏

𝟏

𝟏𝟎

𝟐.. 𝟏

𝟓 𝐱 𝟐

𝟐

𝟑

Ex 2 𝟏

𝟒 x

𝟐

𝟑

Step 1. Change the mixed number to improper fraction. 2 𝟏

𝟒 x

𝟐

𝟑 =

𝟗

𝟒 x

𝟐

𝟑

Step 2. Multiply the numerators, then multiply the denominators. 2 𝟏

𝟒 x

𝟐

𝟑 =

𝟗

𝟒 x

𝟐

𝟑 =

𝟏𝟖

𝟏𝟐

Step 3. Simplify the product. 2 𝟏

𝟒 x

𝟐

𝟑 =

𝟗

𝟒 x

𝟐

𝟑 =

𝟏𝟖

𝟏𝟐=

𝟑

𝟐 =1

𝟏

𝟐

Using Cancellation Method. Type 7 (MN x F )

TRY IT!

1. 1 𝟏

𝟐 x

𝟐

𝟓

2. 1 𝟏

𝟑 x

𝟏

𝟓

Ex. 1 𝟐

𝟑 x 𝟐

𝟏

𝟒

Step 1. Change the mixed number to improper fraction. 1 𝟐

𝟑 x 𝟐

𝟏

𝟒 =

𝟓

𝟑 x

𝟗

𝟒

Step 2. Multiply the numerators, then multiply the denominators. 1 𝟐

𝟑 x 𝟐

𝟏

𝟒 =

𝟓

𝟑 x

𝟗

𝟒 =

𝟒𝟓

𝟏𝟐

Step 3. Simplify the product. . 1 𝟐

𝟑 x 𝟐

𝟏

𝟒 =

𝟓

𝟑 x

𝟗

𝟒 =

𝟒𝟓

𝟏𝟐=

𝟏𝟓

𝟒 = 3

𝟑

𝟒

Using Cancellation Method. Type 8 (MN x MN)

TRY IT!

1. 2 𝟐

𝟑 x 𝟏

𝟏

𝟒

2. 1 𝟏

𝟓 x 𝟏

𝟏

𝟑

8

UNDERSTAND What do you need to know?

The number of eggs that mother use in preparing leche flan.

PLAN What steps do you need to solve the problem?

Multiply ¾ by 24 (1 dozen eggs is 12 so 2 dozen is equal to 24 eggs)

LOOK BACK What does the result tell you?

The result tells that there are 18 eggs used in making leche flan.

DO THE PLAN

How do you solve the problem?

We can multiply fractions in two ways: by using models or without using models.

There are eight ways of multiplying fractions.

Type 1. Whole Number x Fraction

Type 2. Fraction x Whole Number

Type 3. Fraction x Fraction Type 4. Whole Number x Mixed Number

Type 5. Mixed Number x Whole Number

Type 6. Fraction x Mixed Number

Type 7. Mixed Number x Fraction

Type 8. Mixed Number x Mixed Number To multiply simple fractions, multiply the numerators then multiply the denominators. Use

cancellation, if possible, between the numerator and denominator.

In solving problems, we can apply these four steps: First, you have to Understand the

Problem by knowing what is asked and identifying the given facts or information needed to

solve the problem. Second, Plan What to Do which means thinking of the processes or

operations to be used to solve the problems. Third, Do the Plan which means you have to carry out and execute your plan. Solve and write the answer with the correct label or unit

of measure. Lastly, Look Back if the answer makes sense or not.

What I Can Do

Solve the following problem.

What I Have Learned

Nanay Rosalina has 90 meters of cloth. She used 3

4 of the cloth to make a facial mask

for her community. How many meters of cloth did she use? Show your solution here:

During the quarantine period, my mother

prepared food for our family. She used ¾ of

2 dozen eggs in preparing leche flan. How

many eggs did she use in making leche flan?

9

Assessment

Multiple Choice. Choose the letter of the best answer. Write the chosen letter on a separate sheet

of paper.

1. Multiply 2 x 𝟑

𝟓

A. 1 1

5 B. 2

1

5 C. 3

1

5 D. 4

1

5

2. Solve 𝟏

𝟐 x

𝟒

𝟓

A. 1

5 B.

2

5 C.

3

5 D.

4

5

3. Solve 11

3 x

3

8

A. 1

4 B.

1

3 C.

1

2 D.

2

5

4. Find the product . 1𝟏

𝟓 x 1

𝟑

𝟓

A. 1 1

5 B. 1

1

23 C.1

23

25 D.2

2

5

5. What is 2𝟏

𝟐 x 2

𝟏

𝟐?

A. 5 1

4 B. 6 C.6

1

4 D.6

2

5

Angel had 300 1

2 sacks of rice in her storeroom. She donated

3

4 sacks of rice to the

COVID-19 victims in her barangay. How many sacks of rice did she donate?

Show your solution here:

Raymond is a delivery boy. During the quarantine period, he bought 320 pieces of bread

every day. He saved 1

8 of it for his family and gave the remaining pieces to the homeless.

How many pieces of bread did he give?


A bakery uses 3 2

5 sacks of flour every day, how many sacks does the bakery use in a

week?


A kilo of rice costs ₱45.00. How much will 2 3

4 kilos of rice cost?


10


FUN AND LEARN! Fill in the missing words.

Activity 2

Is the product of each less than 1, equal to 1, or greater than 1?

Place each product into the correct box

1

5 x 1 8 x

1

5 1x

1

6

1

12 x 5 1 x

1

3

Less than 1 Equal to 1 More than 1

Mathematics


Division of Simple Fractions

and Mixed Fractions

6

2

Mathematics - Grade 6 Alternative Delivery Mode Quarter 1 - Module 3: Division of Simple Fractions and Mixed Fractions Second Edition, 2021 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 OIC-Schools Division Superintendent: Carleen S. Sedilla CESE OIC-Assistant Schools Division Superintendent and OIC-Chief, CID: Jay F. Macasieb DEM, CESE

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Writer: Fredelyn G. Calanag Editor: Patricia Ulynne F. Garvida

Reviewer: Michael R. Lee Layout: Ma. Fatima D. Delfin and Michiko Remyflor V. Trangia Management Team: Neil Vincent C. Sandoval Education Program Supervisor, LRMS Michael R. Lee Education Program Supervisor, Mathematics

3

What I Need to Know

This module was carefully written to help you acquire the necessary skills needed

in dividing simple fractions and mixed fractions the easy way. Likewise, it would be

easy for you to solve problems by using different problem-solving strategies. The

language used recognizes the diverse vocabulary level of students. 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 textbook you are now using.

The module has one lesson: Dividing Simple Fractions and Mixed Fractions


1. divide fraction by another fraction;

2. divide a whole number by a fraction or vice versa;

3. divide a whole number by a mixed fraction or vice versa;

4. divide a mixed fraction by a mixed fraction; and

5. solve routine and non-routine problems.

Choose the letter of the best answer. Write the chosen letter on a separate sheet of

paper.

1. How many 𝟏

𝟑𝒔 are there in

𝟏

𝟗 ?

A. 1

2 B.

1

3 C. 2 D. 3

2. In 𝟐

𝟏𝟎÷

𝟏

𝟏𝟎= 𝑵, what is the value of N?

A. 1 B. 2 C. 1

5 D.

1

10

3. What is 𝟓

𝟗 ÷

𝟐

𝟑 ?

A. 5

6 B.

6

5 C.

7

12 D.

10

27

4. What value of N makes the equation true? 𝟖

𝟏𝟎 ÷

𝟐

𝟒= 𝑵

A. 16

24 B.

10

14 C. 1

3

10 D. 1

3

5

5. If you divide 8 by 𝟏

𝟔 , what is the quotient?

A. 11

3 B. 1

2

6 C. 42 D. 48

6. What is 45 divided by 𝟗

𝟏𝟎 ?

A. 2

81 B.

50

9 C. 50 D. 450

What I Know

4

7. In 𝟕 ÷ 𝟏𝟓

𝟗= 𝑵, what is the value of N?

A. 65

9 B. 5

1

2 C. 4

1

2 D. 3

1

2

8. What is 𝟕

𝟏𝟎 ÷ 𝟗 ?

A. 3

90 B.

7

90 C. 7

3

10 D. 7

7

10

9. What is the quotient of 𝟓𝟏

𝟐 𝒂𝒏𝒅

𝟏𝟏

𝟏𝟓 ?

A. 41

30 B. 5

11

30 C. 7

1

3 D. 7

1

2

10. What is 𝟓

𝟗 𝑑𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦

𝟐

𝟑 ?

A. 3

6 B.

5

6 C. 6

5

6 D. 6

3

6

11. If you divide 𝟏

𝟒 𝒃𝒚

𝟓

𝟏𝟓 , what is the quotient?

A. 1

4 B.

3

4 C. 2

3

4 D. 3

3

4

12. What is the quotient of 𝟑

𝟓 𝑎𝑛𝑑 𝟏

𝟓

𝟔 ?

A. 11

10 B.

18

30 C.

18

55 D.

33

30

13. What is 𝟒𝟏

𝟐 ÷ 𝟏

𝟓

𝟔 ?

A. 25

11 B. 3

4

6 C. 3

5

11 D. 5

6

8

14. In 𝟓𝟔

𝟖 ÷ 𝟐

𝟏

𝟒= 𝑵, what is the value of N?

A. 25

9 B. 3

5

4 C. 5

2

9 D. 7

7

12

15. What is 𝟗𝟏

𝟐 𝑑𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 𝟑

𝟑

𝟒 ?

A. 124

6 B. 6

2

4 C. 3

8

15 D. 2

8

15

16. A bag of flour weighing 𝟔

𝟏𝟐 kilos was repacked at

𝟏

𝟒 kilo each. How many packs

were made?

A. 7

16 B.

6

24 C. 4 D. 2

17. Aling Minda has a roll of aluminum foil that is 𝟒

𝟓 𝒎𝒆𝒕𝒆𝒓 long. She cuts it into

𝟏

𝟏𝟎

meter long per piece for wrapping inihaw na bangus. How many bangus can she wrap with it?

A. 10 B. 8 C. 2

5 D.

5

15

18. A rope is 6 meters long. A knot is tied every 𝟑

𝟏𝟎 meter long. How many knots

are there? A. 60 B. 40 C. 20 D. 10

19. A bamboo is 𝟐𝟒𝟐

𝟓𝒎𝒆𝒕𝒆𝒓𝒔 long. If it is cut into 12 pieces, how long will each

piece be?

A. 11

15𝑚𝑒𝑡𝑒𝑟𝑠 B. 1

1

30𝑚𝑒𝑡𝑒𝑟𝑠 𝐶. 2

1

15𝑚𝑒𝑡𝑒𝑟𝑠 𝐷. 2

1

30𝑚𝑒𝑡𝑒𝑟𝑠

20. If 𝟕𝟕

𝟖 𝒎𝒆𝒕𝒆𝒓 of cloth is divided into

𝟐

𝟑 . What is the answer?

A. 260

64 𝐵. 2

61

64 𝐶. 5

6

16 𝐷. 11

13

16

5

Re

Two fractions

are reciprocals

of each other if

their product

equals 1.

Lesson

1

Dividing Simple Fractions

and Mixed Fractions

In this lesson, you will learn how to divide a fraction by another fraction; a whole

number by a fraction or vice versa; and mixed fractions. You will discover that dividing

a fraction is the same as multiplying by its reciprocal.

Let’s recall the following concepts for better understanding of the lesson.

A fraction (such as 2

7 ) has two numbers:

numerator 2

denominator 7

In a division sentence (such as 3

4 ÷

1

2),

3

4 is the dividend and

1

2 is the

divisor.

dividend 𝟑

𝟒 ÷

𝟏

𝟐 divisor

What’s In

As mentioned earlier, dividing fractions is just like multiplying the fraction by the

reciprocal (inverse) of the other.

How do you find the reciprocal of a fraction?

Example 1. Find the reciprocal of 𝟓

𝟗.

Let’s turn the fraction 𝟓

𝟗 upside down or flip it over to get its reciprocal.

This gives us

fraction 𝟓

𝟗

𝟗

𝟓 reciprocal

Example 2. Find the reciprocal of 8.

First, rewrite 8 as a fraction with 1 as its denominator. ( 8

1 )

By having a denominator, we can now find the reciprocal. This gives us

whole number 𝟖 𝟏

𝟖 reciprocal

6

multiplication symbol

Example 3. Find the reciprocal of 𝟐𝟑

𝟓.

First, change 𝟐𝟑

𝟓 into an improper fraction and then, turn it upside down or flip

it over.

mixed number 𝟐𝟑𝟓

𝟏𝟑

𝟓 improper fraction

𝟓

𝟏𝟑 reciprocal

Therefore: The reciprocal of 𝟐𝟑

𝟓 is

𝟓

𝟏𝟑 .

What’s New

How do you divide simple fractions?

Let’s solve the problem below using shaded regions.

Problem: How many 1

3 sections are there in

3

5 ?

Find: 3

5 ÷

1

3

Solution: First, draw a rectangle with 5 equal vertical sections and shade 3 parts to

represent 3

5.

Then, draw another rectangle with 3 equal horizontal sections and shade 1 part to

represent 1

3. (Note: The two rectangles should be of equal size.)

Answer: 3

5 ÷

1

3= 1

4

5

Let’s solve the problem below using actual computation (algorithm).

Problem: How many 𝟏

𝟑 sections are there in

𝟑

𝟓 ?

Find: 3

5 ÷

1

3

Solution: dividend 3

5 ÷

1

3 divisor

Step 1. Copy the dividend and find the reciprocal of the divisor.

3

5 ÷

3

1 reciprocal

Step 2. Change the operation to multiplication.

3

5 ×

3

1

Step 3. Multiply the numerators. Multiply the denominators.

3

5 ×

3

1=

3𝑥3

5𝑥1=

9

5

7

multiplication symbol

What is It

How do you divide mixed numbers or mixed fractions?

Problem: A train runs 21

2 𝑘𝑖𝑙𝑜𝑚𝑒𝑡𝑒𝑟𝑠 in an hour. If the train tracks measure

311

2𝑘𝑖𝑙𝑜𝑚𝑒𝑡𝑒𝑟𝑠, how long will it take the train to reach its destination?

Find: 311

2 ÷ 2

1

2

Solution: dividend 𝟑𝟏𝟏

𝟐 ÷ 𝟐

𝟏

𝟐 divisor

Step 1. Change the mixed numbers (dividend & divisor) into improper fractions.

63

2 ÷

5

2

Step 2. Write the reciprocal of the divisor.

63

2 ÷

2

5 reciprocal

Step 3. Change the operation to multiplication.

63

2 ×

2

5

Step 4. Multiply the numerators. Multiply the denominators.

63

2 ×

2

5=

63𝑥2

2𝑥5=

126

10 or you can use cancellation

63

2 ×

2

5=

63𝑥1

1𝑥5=

63

5

Step 5. Simplify your answer if necessary.

63

5= 12

3

5 write as a mixed number

Answer: It will take the train 123

5 ℎ𝑜𝑢𝑟𝑠 to reach its destination.

Always express your answer in simplest form.

1

1

8

Activity: Find the quotient.

What I Have Learned

1. To divide a fraction by another fraction, multiply the dividend by the reciprocal of the divisor.

2. To divide a whole number by a fraction or vice versa, rename the whole number as a fraction with a denominator of 1. Then, multiply the dividend by the reciprocal of the divisor.

3. To divide a mixed number by a fraction or vice versa, change the mixed number into an improper fraction. Then, multiply the dividend by the reciprocal of the divisor.

4. To divide mixed numbers, rename the mixed numbers into improper fractions. Then, multiply the dividend by the reciprocal of the divisor.

5. To solve routine and non-routine problems involving division of simple fractions and mixed numbers, use the appropriate problem-solving strategy and check whether the answer is reasonable or not.

6. Always express the answer in simplest or lowest term.

How will you solve the problem below?

Problem: Suppose you have 𝟐𝟏

𝟐 𝑠𝑜𝑙𝑜 𝑝𝑖𝑧𝑧𝑎𝑠 that you want to divide equally among

your 10 friends. How much piece will each of your friends get?

What’s More

Set A Set B Set C Set D

1. 𝟏

𝟖 ÷

𝟏

𝟐 1. 5 ÷

2

3 1. 3

1

3 ÷ 2

3

5 1. 3

1

4 ÷

1

2

2. 𝟑

𝟒 ÷

𝟐

𝟓 2. 9 ÷

3

4 2. 1

5

6 ÷ 2

1

8 2. 18 ÷ 1

1

8

3. 𝟐

𝟒 ÷

𝟏

𝟔 3. 13 ÷

13

25 3. 6

1

2 ÷ 2

1

4 3. 2

1

4 ÷ 3

4. 𝟓

𝟖 ÷

𝟐

𝟓 4.

8

12 ÷ 16 4. 5

3

8 ÷ 4

1

3 4. 6

4

7 ÷ 2

3

5

5. 𝟓

𝟕 ÷

𝟏𝟎

𝟏𝟓 5.

5

18 ÷ 25 5. 21

2

3 ÷ 12

1

2 5. 24

2

3 ÷ 2

1

18

What I Can Do

9

Assessment

Multiple Choice. Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper.

1. If you divide 𝟓

𝟕 by

𝟏𝟎

𝟏𝟓 , what is the quotient?

A. 11

4 B. 1

1

2 C.

5

8 D.

15

22

2. What is 𝟒

𝟏𝟐 divided by

𝟐

𝟑 ?

A. 1

4 B.

1

3 C.

1

2 D. 2

3. In 𝟑𝟎 ÷𝟓

𝟔= 𝑵, what is the value of N?

A. 5 B. 25 C. 30 D. 36

4. What is 𝟓

𝟕 ÷ 𝟑

𝟏

𝟐 ?

A. 10

49 B.

26

49 C. 6

1

2 D. 9

1

2

5. What is the quotient of 𝟒𝟑

𝟖 𝒂𝒏𝒅 𝟑

𝟏

𝟑 ?

A. 43

8 B. 2

5

16 C. 1

5

16 D.

5

16

6. If you divide 10 by 𝟑

𝟓 , what is the quotient?

A. 202

3 B. 16

2

3 C. 15

2

3 D. 10

2

3

7. What value of N makes the equation true? 𝟓

𝟏𝟖 ÷

𝟐

𝟓= 𝑵

A. 7

23 B.

10

20 C.

20

36 D.

25

36

8. What is 𝟏

𝟔 𝑑𝑖𝑣𝑖𝑑𝑒𝑑 𝑏𝑦 𝟒

𝟏

𝟗 ?

A. 3

74 B. 2

24

74 C. 2

35

74 D. 3

3

74

9. What is the quotient of 𝟑

𝟒 𝒂𝒏𝒅 𝟏𝟐 ?

A. 1

16 B.

1

12 C.

1

6 D.

1

4

10. In 𝟏𝟏𝟏

𝟒÷ 𝟏

𝟏

𝟑= 𝑵, what is the value of N?

A. 333

4 B. 11

1

4 C. 8

7

16 D. 5

5

8

11. What is 𝟓

𝟏𝟐 ÷ 𝟏𝟒 ?

A. 55

6 B. 5

4

6 C.

1

36 D.

5

168

12. What is the quotient of 𝟓𝟏

𝟐 𝒂𝒏𝒅 𝟐

𝟐

𝟓 ?

A. 131

5 B. 2

7

24 C. 2

1

8 D. 2

1

2

10

13. Kate has 𝟏𝟒𝟏

𝟐 𝑚𝑒𝑡𝑒𝑟𝑠 of curtain materials. She cut it into 4 panels. How long

is each panel?

A. 35

8 𝑚𝑒𝑡𝑒𝑟𝑠 B. 4

1

2 𝑚𝑒𝑡𝑒𝑟𝑠 C. 4

5

8 𝑚𝑒𝑡𝑒𝑟𝑠 D. 10

1

2𝑚𝑒𝑡𝑒𝑟𝑠

14. Thomas worked 18 hours to finish his project. If he worked 𝟐

𝟑𝒉𝒐𝒖𝒓𝒔 every day,

how many days did he spend in doing his project?

A. 27 B. 12 C. 1

27 D.

1

12

15. What is 𝟖𝟏

𝟐 divided by the sum of 𝟐

𝟑

𝟒 𝒂𝒏𝒅

𝟐

𝟑 ?

A. 35

38 B. 2

20

41 C. 2

11

20 D. 1

3

82

Solve each problem.

1. For a hand towel, Joana uses 1

7𝑚𝑒𝑡𝑒𝑟 of cloth. If she has 4

4

5𝑚𝑒𝑡𝑒𝑟𝑠 of cloth, how

many hand towels can she make?

2. The area of a rectangle is 5

10𝑜𝑓 𝑎 𝑠𝑞𝑢𝑎𝑟𝑒 𝑚𝑒𝑡𝑒𝑟. If the width is

1

5𝑜𝑓 𝑎 𝑚𝑒𝑡𝑒𝑟, what is

the length?

3. Danica needs to repack 601

2 𝑘𝑔 of rice in plastic bags containing 1

1

2 𝑘𝑔 each. How

many packs of rice will she make?

4. What is 101

4 more than the quotient of 16 𝑎𝑛𝑑 1

1

3 ?

5. What is the average speed of a vehicle that runs 21

3 𝑘𝑖𝑙𝑜𝑚𝑒𝑡𝑒𝑟𝑠 an hour for 140

kilometers?


Mathematics


Addition and Subtraction of

Decimals

6

2

Mathematics - Grade 6 Alternative Delivery Mode Quarter 1 - Module 4: Addition and Subtraction of Decimals Second Edition, 2021 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 OIC-Schools Division Superintendent: Carleen S. Sedilla CESE OIC-Assistant Schools Division Superintendent and OIC-Chief, CID: Jay F. Macasieb DEM, CESE

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Telefax: (632) 8882-5861 / 8882-5862



Writer: Alex P. Geronimo Editor: Patricia Ulynne F. Garvida Reviewer: Michael R. Lee Layout: Ma. Fatima D. Delfin and Michiko Remyflor V. Trangia Management Team: Neil Vincent C. Sandoval Education Program Supervisor, LRMS Michael R. Lee Education Program Supervisor, Mathematics

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This module was designed and written with you in mind. It is here to help you master the operations of addition and subtraction of decimals. The scope of this module uses different engaging learning situations that are within your ability and grade level expectations to ensure understanding and mastery of the skills. Learning activities, such as drills, exercises, evaluation, and problem solving sets, utilized simple numbers and word problems to at least lessen the time spent for this module. The module is divided into lessons, namely:

Lesson 1 - Adds and subtracts decimals and mixed decimals through ten thousandths without or with regrouping

Lesson 2 - Solves 1 or more steps routine and non-routine problems involving addition and/or subtraction of decimals and mixed decimals using appropriate problem solving strategies and tools

After going through this module, you are expected to: 1. add decimal and mixed decimals without and with regrouping with two or more

addends; 2. subtract decimal and mixed decimals without and with regrouping; 3. determine the different steps in solving word problems; and 4. solves routine and non-routine problems involving addition and subtraction of

decimals using appropriate problem solving strategies and tools.

What I Know


1. Find the sum of 0.5 + 0.3 A. 0.8 B. 0.08 C. 0.53 D. 0.35

2. Find the sum of 0.37 + 0.42 A. 0.3742 B. 0.79 C. 0.079 D. 0.97

3. Add 2.25 + 7.129 A. 10.379 B. 9.479 C. 9.389 D. 9.379

4. Find the sum of 0.2 + 5.45 + 1.001 A. 6.651 B. 6.561 C. 6.615 D. 7.651

5. What is the answer when you add 6.95 + 9.42? A. 15.37 B. 16.37 C. 18.37 D. 19.37

Lesson

1 Addition and Subtraction

of Decimals

This lesson deals with addition and subtraction of decimal numbers. Skills with these two basic operations help you resolve mathematical problems and real-life situations involving decimals. The concept is illustrated using the number lines to show adding decimal numbers between 0 and 1, such as 0.1, 0.2, 0.3, and so on, and mixed decimal numbers between 1 and 2 which composed of a whole number and decimal

number, such as 1.1, 1.2, 1.3, and so on. The decimal point (.) separates the whole

number from the decimal part.

What I Need to Know

4

The number line shows how we add and subtract decimals.

Adding or subtracting decimal numbers is the same way as adding or subtracting whole numbers. You just need to arrange the numbers vertically where the decimal points are aligned and then add the digits of the same place value.

0.5 0.7 0.9

+ 0.3 - 0.3 + 0.5

0.8 0.4 1.4

What’s In

Let’s have a brief drill and review of addition and subtraction of whole numbers.

In an addition sentence, the numbers being added are the addends and the answer is called sum. In the example below, 12 and 8 are the addends and 20 is the sum. The position of the addends is not important as supported by the commutative property of addition where the order of the addends does not affect the sum. That is, the sum of 12+8 is the same as 8+12.

On the other hand, a subtraction sentence is composed of the minuend, subtrahend, and difference. The minuend is a number from which another (subtrahend) is to be subtracted, while subtrahend is the number being subtracted. Usually, the minuend has the bigger value than the subtrahend. The answer in a subtraction process is called difference.

0.5 + 0.3 = 0.8

0.7 - 0.3 = 0.4

0.9 + 0.5 = 1.4

Horizontal Form Vertical Form

12 + 8 = 20 12 addends

+ 8

addends sum 20 sum

Horizontal Form Vertical Form

15 - 9 = 6 15 Minuend

- 9 Subtrahend

6 Difference Difference

5

In addition or subtraction of whole numbers, vertically arrange the numbers then add or subtract from the right most digit to the left, depending on the operation asked in the problem. If the sum of two or more digits belong to the same place value is more than 10, we regroup the tens digit to the next place value. When subtracting numbers and the digit of minuend is smaller than the subtrahend, we regroup or borrow from the next digit of the minuend.

What’s New

Addition and Subtraction of Decimal Numbers Without Regrouping

Here are the steps in adding or subtracting decimal numbers without regrouping:

Step 1: Arrange the decimal numbers vertically. Align the decimal points in one column as well as the digits belonging to the same place values. You may put zeroes (0) as place holder to the empty place value position in the decimal part. Step 2: Add or subtract from right to left. Step 3: Put the decimal point in your answer right below the decimal point of the number being added or subtracted.

Decimal numbers

Example a1. 0.35 + 0.41 = Example s1. 0.96 – 0.55 =

Step 1: Arrange in vertical form Step 1: Arrange in vertical form

0.35 0.96

+ 0.41 - 0.55

0.76 0.41

Step 2: Add 5+1 and then 3+4 Step 2: Subtract 6-5 and then 9-5

Step 3: Put decimal point Step 3: Put decimal point

Answer: 0.76 Answer: 0.41

Mixed Decimal Numbers

Example a2. 16.38 + 52.41 = Example s2. 67.45 –31.14 =

Step 1: Arrange in vertical form Step 1: Arrange vertical form

16.38 67.45

+ 52.41 -31.14

Step 2: Add 68.79 Step 2: Subtract 36.31

Step 3: Put decimal point Step 3: Put decimal point

Answer: 68.79 Answer: 36.31

6

1

13 1

1

10 9 3

Decimals and Mixed Decimals

Ex. a3. Ex. s3.

Arrange Put 0 on empty Arrange Put 0 on empty vertically place value and vertically place value and then add. then subtract.

Answer : 5.539 Answer : 18.214

Observe that in addition without regrouping, the sum of the digits in one column is always less than 10, while in subtraction without regrouping, notice that the digits in the minuend is always bigger than the subtrahend.

Addition and Subtraction of Decimal Numbers With Regrouping Addition and subtraction with regrouping follow the same steps as in addition and subtraction without regrouping. Regrouping happens in addition when the sum of the digits in a column is 10 or more. In this case, the tens digit will be regrouped to the next column of digits to the left while the ones digit will be retained at bottom. An example is shown below.

Ex. 1: 0.8 0.8 -Add 8+9 = 17. + 0.9 + 0.9 -1 will be regroup to the next column to the

1.7 left while 7 will be retained at the bottom

-Add 1 + 0 + 0 =1 The answer is 1.7 and not 0.17

Regrouping happens in subtraction when the digit in the minuend is smaller than the digit in the subtrahend. In this case, the minuend will borrow 1 from the digit on the left. An example is shown to illustrate this process.

Ex. 2: 7.23 7 . 2 3 3 minus 7 is not possible so you

- 2.57 - 2 . 5 7 need to borrow from 2 to make 3

6 equal to 13. Hence 13-7=6

7 . 2 3 next step is 1 minus 5 which is - 2 . 5 7 not possible so borrow 1 from 7

4 . 6 6 to make 1 equal to 11. Thus

11-5 =6. The digit 7 became 6 The answer is 4.66 The final step is 6 - 2 = 4

Ex. 3: 15.4 15.400 Put two zeroes to the empty

- 12.327 - 12.327 place value

1 5 . 4 0 0 Perform subtraction

- 1 2 . 3 2 7 with regrouping as shown

0 3 . 0 7 3 in Ex. 2

The answer is 3.073

0.3 + 5.23 +0.009 = 18.964 – 0.75 =

0.3

+ 5.23

0.009

0.300

+ 5.230

0.009

5. 539

18.964

- 0.75

18.964

- 0.750

18.214

13 11

6

1

2

1

2

7

What is It

In adding or subtracting decimals, you just need to follow these simple steps:

Arrange the numbers in a column. Align the decimal points. Use 0 as placeholder, if needed.

Add or subtract as you would add or subtract whole numbers from right to left. If the sum is 10 or more, regroup to the next place value, and if the minuend is smaller than the subtrahend, regroup by borrowing 1 from the digit on the left.

Place a decimal point in the sum or difference. Align this with the other decimal points

What’s More

Activity 1: Understanding Addition and Subtraction of Decimals Rewrite the numbers in column and then perform the indicated operations:

1) 0.36 + 0.22 6) 3.58 + 5.61 2) 5.34 + 2.63 7) 8.123 + 0.3 + 0.54 3) 0.87 – 0.54 8) 0.78 – 0.4 4) 7.59 – 2.48 9) 0.455 – 0.273 5) 0.8 + 0.3 + 0.5 10) 0.6 – 0.249

What I Have Learned

Steps in Addition and Subtraction of Decimals

Arrange the numbers in a column. Align the decimal points. Use 0 as placeholder, if needed.

Add or subtract as you would add or subtract whole numbers from right to left. Place a decimal point in the sum or difference. Align this with the other decimal

points.

What I Can Do

A. Rewrite the given mathematical sentence on the space provided

1) 2.5 + 3.4 = 5.9 2) 6.7 – 5.5 = 1.2 3) 0.2 + 3.5 + 10.176 = 13.876

Step 1

Step 2

Step 3

8

B. Rewrite the given problem vertically on the space provided then perform the indicated operation

1) 6.4 + 1.5 = 2) 9.6 – 7.4 = 3) 15.1 + 0.113 + 4.81 =

C. Solve the following story problems.

1. Mary bought 0.5 kilogram of carrots, 0.7 kilogram of potato, and 1.1 kilograms of cauliflower. What is the total weight of the vegetables Mary bought?

2. During the weekend, mother bought 2.5 kilograms of pork meat. She cooked 1.3 kilogram on Sunday for lunch. How much pork was left?

Assessment

A. Solve for the sum or difference.

1. 5.35 2. 6.487 3. 31.578 4. 12. 67 +2.33 - 2.355 - 11.26 + 96.35

5. 0.163 6. 51. 92 7. 45.9 8. 58.749 + 8.18 - 17. 58 - 12.164 + 57.221

9. 70.542 10. 59. 647 11. 0.9 + 2.35 + 25.3 + 8.225 =

- 53.891 - 27.958 12 . 63.5 – 14.289 =

Lesson

2 Routine and Non-routine

Problems Involving Addition and Subtraction of Decimals

Problem Solving Strategy Problem solving with decimals is like solving word problems in your previous mathematics lessons. Here are the basic steps in solving word problems:

Understand

You need to understand the given problem and note the following: a. What is asked in the problem? b. What are the facts and information given?

Plan Determine the operations to be used and formulate your number sentence. You

may draw a model or illustration to help you visualize your plan.

Solve

Compute and show your solutions.

Check and look back

Review and re-check your answer. You may use your calculator to check the accuracy of your computations. You may also use estimation technique for a speedy check of your answer.

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ROUTINE WORD PROBLEMS Problem 1

Study the solution below:

Problem 2

Study the solution.

NON-ROUTINE WORD PROBLEMS

Problem 1 Problem 2

Solution: Solution:

Solution:

Understand Know what is asked: Total cups of ingredients needed

Know the given facts: Whole milk-1.75 cups, Heavy cream-0.5 cup, Granulated sugar-0.5

cup, Cornstarch -0.25 cup, Banana-2.25 cups

Plan

Determine the operation to be used: addition

Write the number sentence: 1.75+0.5+0.5+0.25+2.25=n Solve

Show your solution: 1.75+0.5+0.5+0.25+2.25=5.25 cups

Check and look back

Review and re-check your answer: you can use calculator to add 1.75+0.5+0.5+0.25+2.25

Jennifer needs the following ingredients in baking a banana pie: 1.75 cups of whole milk, 0.5 cup of heavy cream, 0.5 cup of granulated sugar, 0.25 cup of cornstarch, and

2.25 cups of banana. How many cups of ingredients does she need in all?

Understand

Know what is asked: How many kilograms heavier is Cardo than Daniel? Know the given facts: Cardo’s Weight- 48.6 kg Daniel’s Weight-42.5 kg

Plan

Determine the operation to be used: Subtraction

Write the number sentence: 48.6 – 42.5 =n

Solve

Show your solution: 48.6 – 42.5 = 6.1 kg Check and look back

Review and re-check your answer: review the accuracy of the given and the unit of

measure for the answer. Apply inverse operation that is adding 42.5 + 6.1 = 48.6

Cardo’s weight is 48.6 kilograms while his younger brother Daniel weight is 42.5 kilograms.

How many kilograms heavier is Cardo than his younger brother Daniel?

A rectangular table has a length of 7.35

feet and a width of 3.70 feet. Find the

perimeter of table.

The combined weight of John and George is

118.54 kilograms. If John is heavier by 4.54

kilograms, how much do each of them weigh?

Understand Know what is asked: Find the perimeter of the table Know the given facts: Length-7.35 ft Width-3.70ft

Plan Determine the operation to be used: Addition

Visualize that a rectangle has 2 lengths and 2 widths and perimeter is the distance around the rectangle Perimeter =Length + Length +Width +Width

Write the number sentence: 7.35 + 7.35 + 3.70 +3.70=n

Solve Show your solution: 7.35 + 7.35 + 3.70 +3.70= 22.10 or 22.1 ft.

Check and look back Review and re-check your answer: formula for the perimeter of a rectangle. Always check the unit of measure of the answer

Understand

Know what is asked: Find the weight of each.

Know the given facts: 118.54kg-total 4.54 kg

– John’s weight more than George

Plan Determine the operation to be used: Subtract

and divide

Represent: George’s weight = n

John’s weight = n+4.54

Write the number sentence:

George weight =(118.54 – 4.54)÷2 John’s weight = George weight +4.54

Solve

Show your solution: G= (118.54 – 4.54)÷2

G= 114 ÷ 2 =57kg

J = 57 + 4.54 = 61.54kg

Check and look back Review and re-check your answer: G + J =

118.54 kg and J – G = 4.54 kg

10

Problem 3

Solution:

What is It

The basic steps in analyzing and solving word problems are:

Understand the problem

Plan for the solution

Solve or compute

Check and look back

What I Can Do

Solve each problem. Show all the steps. 1. During the school nutrition month, the school clinic recorded the weights of

Sofia, Angela, and Ishi. Sofia’s weight is 31.63 kilograms. Angela’s weight is 35.15 kilograms while Ishi’s weight is 33.86 kilograms. What is the total weight of the three pupils?

2. During year-end sale, the cost of a TV set is ₱ 18,355.35. Its price has been

reduced by ₱ 5,000.00. What was the price of the TV set before the sale?

3. For the month, the electric bill costs ₱ 2,124.87 while water bill costs ₱ 655.15.

How much will be needed to pay for the bills? 4. Henry went to the bookstore to buy some school art materials. He bought a water

color worth ₱ 65.75 and a drawing pad worth ₱ 115.45. If he gave the cashier

two 100-peso bills, how much change will he receive?

5. The cost of a Davao pomelo is ₱ 125.75 while the cost of a watermelon is ₱ 80

more than the cost of a Davao pomelo. What is the total cost of the pomelo and watermelon?

Use the following information to answer the question below

Chocolate bar ₱ 18.75

Slice of Pizza ₱ 35.50

Can of Juice ₱ 20.00

Burger Sandwich ₱ 23.25

A customer bought 2 chocolate bars, 1 slice of pizza, 1 can of juice, and 2 burger

sandwich. How much is his change if he gave the cashier two 100-peso bills?

Understand Know what is asked: How much is the change?

Know the given facts: Chocolate bar=18.75 Slice of pizza= 35.50

Can of Juice = 20.00 Burger sandwich = 23.25

2 chocolate bar, 1 slice pizza, 1 can of juice, 2 burger sandwich, P200

Plan Determine the operation to be used: addition and subtraction

Write the number sentence: Step 1: 2choco bar + 1 pizza + 1 Juice + 2 burger = n

18.75+18.75 +35.50+20.00+23.25+23.25=n

Step 2: 200 – n = Change

Show your solution: Step 1: 18.75+18.75 +35.50+20.00+23.25+23.25= 139.50 Step 2: 200 – 139.50 = Php 60.50

Check and look back

Review and re-check your answer: you can use your calculator to check accuracy of the

answer. Peso is also important as unit of currency for the problem.

6 mathematics modules

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