Mathematics 6 Quarter 1 Module 9: Dividing Decimals and Mixed Decimals Up to 2 Decimal Places

Mathematics Quarter 1 – Module 9: Dividing Decimals Up To 2 Decimal Places by Whole Numbers And Dividing Mixed Decimals Up To 2 Decimal Places

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CO_Q1_Mathematics6_Module9

Mathematics – Grade 6 Alternative Delivery Mode Quarter 1 – Module 9: Dividing Decimals Up To 2 Decimal Places by Whole Numbers And Dividing Mixed Decimals Up To 2 Decimal Places First Edition, 2020

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Development Team of the Module Author: Virgilio C. Failanza Jr. Editors: Ma. Portia G. Galanto and Rebecca O. Billones, and Collin G. Sales Reviewers: Rosemarie D. Aclan and Collin G. Sales Illustrator: Virgilio C. Failanza Jr. Layout Artist: Felizardo S. Valdez III Management Team: Ramir B.Uytico, Pedro T. Escobarte, Jr., Elena P. Gonzaga, Donald T. Genine, Ma. Roselyn J. Palcat, Nordy D. Siason, Jr., Rowena S. Carillo, Rosemarie D. Aclan, Arthur J. Cotimo, Felizardo S. Valdez III, Marve E. Gelera

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Mathematics

Quarter 1 – Module 9: Dividing Decimals Up To 2 Decimal Places by Whole Numbers And Dividing of Mixed Decimals Up To 2 Decimal Places

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 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

This module was designed and written with you in mind. It is here to help you master dividing 2 decimal places by whole numbers, dividing decimals and mixed decimals up to 2 decimal places. 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 is divided into three lessons, namely:

• Lesson 1 – Dividing Decimals/Mixed Decimals Up to 2 Decimal Places by Whole Number
• Lesson 2 – Dividing Decimals Up to 2 Decimal Places
• Lesson 3 – Dividing Mixed Decimals Up to 2 Decimal Places

After going through this module, you are expected to:

1. divide decimals/mixed decimals up to 2 decimal places by whole numbers; (M6NS-Ig-116.3)
2. divide decimals up to 2 decimal places; (M6NS-Ig-116.4)
3. divide mixed decimals up to 2 decimal places; (M6NS-Ig-116.4) and
4. solve multi-step routine and non-routine problems involving division and any of the other operations of decimals, mixed decimals, and whole numbers including money using appropriate problem-solving strategies and tools. (M6NS-Ij-120.3)

What I Know

Find the value of N. Divide the following. Write your answer on your answer sheet.

1.) 4.44 ÷ 4 = N

2.) 0.12 ÷ 6 = N

3.) 1.8 ÷ 9 = N

4.) 16.24 ÷ 8 = N

5.) 3.12 ÷ 6 = N

6.) 39.26 ÷ 13 = N

7.) 60.75 ÷ 15 = N

8.) 281.40 ÷ 12 = N

9.) 501.84 ÷ 17 = N

10.) 1.17 ÷ 9 = N

Lesson 1: Dividing Decimals/Mixed Decimals Up To 2 Decimal Places by Whole Numbers

In this lesson you will learn how to divide decimals/mixed decimals up to 2 decimal places by whole numbers. To do this, divide them as whole numbers and write the decimal point of the quotient directly above the decimal point of the dividend. Moreover, you will solve routine and non-routine problems involving the skills you have learned in this lesson.

What’s In

Find the quotient. Write your answers on your answer sheet.

1.) 8 ÷ 0.64 = N

2.) 72 ÷ 0.96 = N

3.) 24 ÷ 0.15 = N

4.) 19 ÷ 0.38 = N

5.) 48 ÷ 0.32 = N

What’s New

Read and study the problem below.

Hazel and her 3 friends bought some food at the canteen. The total bill was ₱62.40. If they share the bill equally, how much will each one pay?

What is It

To solve the problem, divide ₱62.40 by 4. Follow the steps below.

Step 1: Divide the numbers the way you divide whole numbers.

    1
4 ) 62.40
  - 4
    2

a. Divide; 6 ÷ 4 → There is only one (1) group of 4 in 6, so we write 1 on the quotient b. Multiply: 1 x 4 = 4 c. Subtract: 6 – 4 = 2

Step 2: Bring down the next digit of the dividend 2 and annex it to the first remainder which is 2. This will form your new dividend which is 22.

    15
4 ) 62.40
  - 4 ↓
    22
  - 20
     2

a. Divide; 22 ÷ 4 → There are only five (5) groups of 4 in 22, so we write 5 on the quotient b. Multiply: 5 x 4 = 20 c. Subtract: 22 – 20 = 2

Step 3: Align the decimal point of the dividend to the quotient.

    15.
4 ) 62.
  - 4
    22
  - 20
     2

[transcriber’s note: the arrows in the printed Step 3 layout show the decimal point being aligned from the dividend to the quotient; they are not transcribed]

Step 4. Bring down the next digit of the dividend 4 and annex it to second remainder which is 2. This will form your next dividend which is 24.

        15.60
     4)62.40
       − 4
        22
       − 20
        24
        24
         0

a. Divide; 24 ÷ 4 → There are only six (6) groups of 4 in 24, so we write 6 on the quotient

b. Multiply: 6 x 4 = 24

c. Subtract: 24 – 24 = 0

d. Since your remainder is already 0 and the last digit in the dividend is 0, you need not to bring it down anymore, instead bring it up or copy it to your quotient.

Therefore, each of them will pay ₱15.60 for some food at the canteen.

What’s More

Find the quotient. Write your answer on your answer sheet.

1.) 28)326.20

2.) 12)62.40

3.) 8)122.40

4.) 14)229.25

5.) 15)187.50

What I Have Learned

In dividing decimals/mixed decimals up to 2 decimal places by a whole number, divide them the way you divide whole numbers and write the decimal point of the quotient directly above the decimal point of the dividend.

What I Can Do

A. Find the quotient and write your answer on your answer sheet.

1.) 43.75 ÷ 7 = N

2.) 107.40 ÷ 12 = N

3.) 320.40 ÷ 24 = N

4.) 208.25 ÷ 17 = N

5.) 79.92 ÷ 4 = N

B. Read and solve. Show your solution and answer on a separate sheet of paper.

6.) Vangie, a store owner, has 8.12 kilograms of candies. If she puts the candies into 7 jars equally, how many kilograms will each jar contain?

7.) On his birthday, Jessie receives a cash gift of P189.75. He wants to split the amount into three leisure activities namely: zoo tickets, game tickets and movie downloads. If he wants to budget the same amount for each activity, how much amount will he allot in each activity?

Assessment

Divide the following. Write your answer on your answer sheet.

1.) 0.08 ÷ 2 = N

2.) 0.14 ÷ 7 = N

3.) 1.17 ÷ 9 = N

4.) 0.24 ÷ 6 = N

5.) 3.24 ÷ 4 = N

6.) 36.36 ÷ 6 = N

7.) 22.40 ÷ 4 = N

8.) 126.24 ÷ 12 = N

9.) 20.41 ÷ 13 = N

10.) 2.16 ÷ 9 = N

Additional Activities

A. Divide the following. Write your answer on your answer sheet.

1.) 60.24 ÷ 12 = N

2.) 122.40 ÷ 8 = N

3.) 229.25 ÷ 35 = N

4.) 326.20 ÷ 28 = N

5.) 46.95 ÷ 3 = N

B. Solve the following problems. Show your solution and answers in your activity notebook.

6.) A restaurant owner bought 8 pieces of serving bowls for P302.80. How much each of the serving bowl cost?

7.) A mango juice manufacturer has 72.24 liters of mango puree. He plans to divide it equally into 12 containers for his 12 customers. How many liters does each one container hold?

8.) Rowena is buying 6 packs of cashew candies that cost ₱2.75 each. She wants to share these cashew candies with her two friends. She asks her 2 friends to pay her for their share. Including Rowena, how much does each one of them spend for a cashew candy?

9.) What is the average speed in kilometer per hour of a car that travels 390.45 kilometers in 15 hours?

10.) Edwin sold 15 kilos of calamansi and earned ₱431.25. How much each kilogram of calamansi cost?

Answer Key

[transcriber’s note: this page is printed upside down; the table below is transcribed upright, with its three columns in reading order from left to right]

What I Know	What’s More	Assessment
1) 1.11 2) 0.02 3) 0.2 4) 2.03 5) 0.52 6) 3.02 7) 4.05 8) 23.45 9) 29.52 10) 0.13 What’s In 1) 12.5 2) 75 3) 160 4) 50 5) 150	1) 11.65 2) 5.2 3) 15.3 4) 16.375 5) 12.5 What I Can Do A. 1) 6.25 2) 8.95 3) 13.35 4) 12.25 5) 19.98 B. 6) 1.16 kg 7) ₱63.25	1) 0.04 2) 0.2 3) 0.13 4) 0.04 5) 0.81 6) 6.06 7) 5.60 8) 10.52 9) 1.57 10) 0.24 Additional Activities A. 1) 5.02 2) 15.3 3) 6.55 4) 11.65 5) 15.65 B. 6) ₱37.85 7) 6.02 liters 8) ₱5.50 9) 26.03 kilometers 10) ₱28.75

What I Know

Find the quotient. Show the solutions on your answer sheet.

1.) 0.88 ÷ 0.22 = N

2.) 0.42 ÷ 0.21 = N

3.) 0.40 ÷ 0.05 = N

4.) 0.24 ÷ 0.08 = N

5.) 0.72 ÷ 0.04 = N

6.) 0.81 ÷ 0.09 = N

7.) 0.51 ÷ 0.17 = N

8.) 0.52 ÷ 0.13 = N

9.) 0.96 ÷ 0.32 = N

10.) 0.48 ÷ 0.12 = N

Lesson 2 Dividing Decimals up to 2 Decimal Places

In this lesson you will learn how to divide decimals up to 2 decimal places by following these steps:

1. change the divisor into whole numbers by moving the decimal point two places to the right;
2. move the decimal point of the dividend also two places to the right; and,
3. divide the way you divide whole numbers.

What’s In

Find the quotient. Write your answers on your answer sheet.

1.) 104.56 ÷ 8 = N

2.) 84.48 ÷ 12 = N

3.) 0.72 ÷ 6 = N

4.) 0.90 ÷ 15 = N

5.) 117.91 ÷ 13 = N

What’s New

Read and study the problem below.

Michael has 0.36 meter of string. He cuts it into pieces measuring 0.06 m. How many pieces of string will he get?

What is It

To find the number of pieces of string Michael will get, divide 0.36 by 0.06. Follow these steps:

Step 1: Change the divisor into whole numbers by moving the decimal point two places to the right.

divisor  →  0.06)0.36  →  6)0.36

Step 2: Move the decimal point of the dividend also two places to the right.

6)0.36  ← dividend  →  6)36

Step 3: Divide as whole numbers.

        6      ← quotient
     ______
  6)  36
      36
      --
       0

Therefore, Michael can get 6 pieces of string which measures 0.06 m out from the original 0.36 meters.

What’s More

This time find the quotient of the following mathematical expressions. Write the solutions on your answer sheet.

1.) 0.84 ÷ 0.21 = N

2.) 0.75 ÷ 0.25 = N

3.) 0.57 ÷ 0.03 = N

4.) 0.76 ÷ 0.19 = N

5.) 0.96 ÷ 0.48 = N

What I Have Learned

In dividing decimals up to 2 decimal places, follow these steps:

1. change the divisor into whole numbers means multiply it by 10 (for decimals up to tenths) or by 100 (for decimals up to hundredths); and
2. divide the way you divide whole numbers.

What I Can Do

A. On your answer sheet, divide the following.

1.) 0.90 ÷ 0.18 = N

2.) 0.66 ÷ 0.22 = N

3.) 0.58 ÷ 0.29 = N

4.) 0.87 ÷ 0.03 = N

5.) 0.80 ÷ 0.40 = N

B. Read and solve what is asked. Use sheet of paper for your answers.

6.) The thickness of a 120gsm bond paper is 0.14 millimeter. How many pieces is 0.98 millimeter thick?

7.) Margie has 0.85 grams of ground pepper. How many packs of 0.05 grams can she make from it?

Assessment

Divide the following. Show the solutions on your answer sheet.

1.) 0.77 ÷ 0.11 = N

2.) 0.60 ÷ 0.15 = N

3.) 0.80 ÷ 0.20 = N

4.) 0.24 ÷ 0.08 = N

5.) 0.36 ÷ 0.09 = N

6.) 0.86 ÷ 0.43 = N

7.) 0.92 ÷ 0.46 = N

8.) 0.54 ÷ 0.09 = N

9.) 0.63 ÷ 0.07 = N

10.) 0.95 ÷ 0.05 = N

Additional Activities

A. Find the quotient. Write your answers on your answer sheet.

1.) 0.91 ÷ 0.13 = N

2.) 0.84 ÷ 0.06 = N

3.) 0.99 ÷ 0.11 = N

4.) 0.72 ÷ 0.12 = N

5.) 0.88 ÷ 0.20 = N

B. Solve the following problems. Write your solution and answers on your answer sheet.

6.) Ray has a piece of wood that is 0.98 meter in length. He needs to cut pieces that are 0.07 meter in length. How many pieces of 0.07 meter in length Ray can cut from the piece of wood that is 0.98 meter?

7.) In a mango bars factory, they make bars in different sizes. The small bars are sold in pieces and the big ones are packaged in chunks. Identical chunks weighing 0.15 kilogram each are made from a big mango bar weighing 0.90 kilogram. How many chunks can be made from each big mango bars?

8.) Annabel and Lina are friends. One day, they went to a textile store to buy a piece of cloth that is 0.75 meter in length for face mask. How many pieces of 0.15-meter face mask can be made out of 0.75 meter piece of cloth?

9.) Joy has 0.96 kilogram of salted cashew nuts. She wanted to give these cashew nuts to her friends in school. How many packs measuring 0.12 kilogram can she make out of it?

10.) Jake has a 0.48-meter-long rope. How many pieces of 0.04 meter long can he cut from it?

Answer Key

[transcriber’s note: this page is printed rotated 180 degrees; the answer key is a three-part layout whose headers are printed at the foot of each part. The table below keeps those parts as columns in reading order.]

Assessment	Additional Activities	What’s More	What I Can Do	What I Know	What’s In
1) 7 2) 4 3) 4 4) 3 5) 4 6) 2 7) 2 8) 6 9) 9 10) 19	A. 1) 7 2) 14 3) 9 4) 6 5) 4.4 B. 6) 14 pieces 7) 6 chunks 8) 5 pieces 9) 8 packs 10) 12 pieces	1) 4 2) 3 3) 19 4) 4 5) 2	A. 1) 5 2) 3 3) 2 4) 29 5) 2 B. 6) 7 pieces 7) 17 packs	1) 4 2) 2 3) 8 4) 3 5) 18 6) 9 7) 3 8) 4 9) 3 10) 4	1) 13.07 2) 7.04 3) 0.12 4) 0.06 5) 9.07

What I Know

Divide the following. Show the solution on your answer sheet.

1.) 62.50 ÷ 1.25 = N

2.) 402.50 ÷ 80.50 = N

3.) 199.85 ÷ 28.55 = N

4.) 48.30 ÷ 3.45 = N

5.) 21.78 ÷ 1.21 = N

6.) 15.96 ÷ 1.33 = N

7.) 22.59 ÷ 2.51 = N

8.) 4.72 ÷ 2.36 = N

9.) 24.72 ÷ 6.18 = N

10.) 112.14 ÷ 5.34 = N

Lesson 3: Dividing Mixed Decimals up to 2 Decimal Places

In this lesson you will learn how to divide mixed decimals up to two (2) decimal places by following these steps:

1. Change the divisor into whole number by multiplying it by 10 (for decimals up to tenths) or by 100 (for decimals up to hundredths).
2. Multiply the dividend by the same number. Place the decimal point in the quotient.
3. Divide the dividend by the whole-number divisor.

What’s In

Find the quotient. Show your solution on your answer sheet.

1.) 0.96 ÷ 0.12 = N

2.) 0.38 ÷ 0.95 = N

3.) 0.87 ÷ 0.29 = N

4.) 0.68 ÷ 0.32 = N

5.) 0.78 ÷ 0.15 = N

What’s New

Study the situations below and find out how it is solved.

Christine bought 66.25 kilograms of mangoes. She packed these into packs containing 13.25 kilograms each. How many packs did she make?

What is It

To solve for the number of packs Christine made, divide 66.25 by 13.25. Follow the steps below:

Step 1: Change the divisor into a whole number by moving the decimal point two places to the right.

divisor → 13.25 ⟌ 66.25 ⟹ 1325 ⟌ 66.25

Step 2: Move the decimal point of the dividend the same number of places as the divisor as shown below.

1325 ⟌ 66.25 ⟸ dividend ⟹ 1325 ⟌ 6625

[transcriber’s note: a small arrow mark is printed under the decimal point of 66.25 in the first and second expressions]

Step 3: Divide the dividend by the divisor the way you divide whole numbers.

    5          ⟸ quotient
1325 ⟌ 6625    a. Divide; 6625 ÷ 1325 → There are only five (5) groups
  −6625           of 1325 in 6625, so we write 5 on the quotient.
    0          b. Multiply: 5 x 1325 = 6625
               c. Subtract: 6625 – 6625 = 0

Hence, Christine made 5 packs of mangoes containing 13.25 kilograms each.

The number 3.263 is divided by a 1-digit decimal number. It gives a quotient greater than 2 but less than 2.5. What is the number?

This kind of problem can be solved using Systematic Listing Strategy.

How to solve using Systematic Listing Strategy?

Note: Make sure you follow the conditions in the problem.

Conditions:

1. Your divisor should be a 1-digit decimal.
2. Your quotient should fall between 2 and 2.5.

In this case, to obtain a quotient greater than 2 but less than 2.5, assume that your divisor should be 1.6 or less.

Why divisor should be 1.6 or less?

If you narrow down your dividend to 3.2 only, the possible divisor is 1.6 to give you the quotient of 2. So, having a dividend greater than 3.2 which is 3.263 would give a result greater than 2 also if divided by 1.6. Notice that the number used for the quotient is slightly higher than 2 to fit the condition number 2.

Hence, possible divisors should be 1.6 or less to give an answer greater than 2.

Let’s try to divide 3.263 by 1.6 now.

3.263 ÷ 1.6 = 2.04 (✓)

Using 1.6 as divisor fits all the conditions stated above. So, it is a solution to this challenge.

Is there another solution to the problem?

Will there be other 1-digit decimal divisor as to condition number 1 to fit the range of quotient which is greater than 2 but less than 2.5?

Let’s try another divisor. How about 1.5?

3.263 ÷ 1.5 = 2.18 (✓)

Additional Activities

A. Divide the following. Write the solutions on your answer sheet.

1.) 47.36 ÷ 11.84 = N

2.) 264.18 ÷ 88.06 = N

3.) 66.15 ÷ 3.15 = N

4.) 175.76 ÷ 3.38 = N

5.) 63.48 ÷ 31.74 = N

B. Read and solve. Show your solution on your answer sheet.

6.) Ma’am Roselyn spends ₱87.65 for her snacks. If she takes her snacks twice a day, in how many days does her budget for snacks worth ₱1 051.80 last?

7.) Mario drove his car in going to his office and consumed 1.04 liters of crude oil for every kilometer. How far did he drive after he consumed 13.78 of crude oil?

8.) Aling Andet has 60.75 kilograms of cashew nuts. She repacked these in several bags. She put 2.25 kilograms in each bag. How many bags did she use to repack the cashew nuts?

9.) Trexie has 15.75 meters of ribbon. She wants to cut it into pieces of 1.75 meters long. How many pieces of ribbon will she get?

10.) The sum of all the rows, columns and the shaded diagonal only is 12. Complete the table and look for the value of A and B. Then, solve for the equation (A + B) ÷ 1.2.

	A
2.61	4.32
B		3.15

transcriber’s note: the grid has no printed header row; the shaded cells are the diagonal from the top-left to the bottom-right (the first cell of row 1, the center cell, and the last cell of row 3). The first row is shown here as the header row.

Answer Key

What I Know

1. 50 6) 12
2. 5 7) 9
3. 7 8) 2
4. 14 9) 4
5. 18 10) 21

What’s In

1. 8
2. 0.4
3. 3
4. 2.125
5. 5.2

What’s More

1. 13
2. 9
3. 5
4. 13
5. 5.1 and 5.2

What I Can Do

A.

1. 13
2. 11
3. 27
4. 9
5. 15

B. 6) 18 inches 7) 8.5

Assessment

1. 3 6) 7
2. 8 7) 8
3. 23 8) 17
4. 9 9) 4
5. 16 10) 4.1

Additional Activities

A.

1. 4
2. 3
3. 21
4. 52
5. 2

B. 6) 6 days 7) 13.25 kilometers 8) 27 bags 9) 9 pieces 10) 7.125

transcriber’s note: the answer key page is printed upside down; the answers above are transcribed in upright reading order.

References:

• Most Essential Learning Competencies (MELC) in Mathematics 6.

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