Decimal Numbers Part 2

On the other hand, fractions can also be expressed as a decimal without using the equality principle. Instead we have to think of a fraction as a quotient of two integers that is a/b=a = a b.

Example 3:

Express 2/5 as a decimal.

Expressing 2/5 as quotient of 2 and 5 we have 2/5 = 0.4

RULE

To change a fraction to decimal, divide the numerator by the denominator up to the desired number of decimal places.

I. Give the meaning and explain the use of the following

1. How to change

fractions to

decimal?

1. How to change

fractions to

decimal?

2. What are the rules in changing fractions to decimals?

2. What are the rules in changing fractions to decimals?

3. What is decimal?3. What is decimal?

4. Give some

examples of

fractions to decimals.

4. Give some

examples of

fractions to decimals.

1. Change fractions to decimal __________________________________________

2. Rules in changing fractions to decimals __________________________________________

3. Decimal __________________________________________

4. Examples of fractions to decimals __________________________________________

II. Change the following fractions to decimals. Limit the number to tree decimal places.

1. 2/3 =_____________2. 2. ¾ =___________3. 6/7 =_____________4. 8/9 =_____________5. 2/15 =_____________-6. 1/9 =_____________7. 5/6 =_____________9. 4/5 =_____________

10. 3/16 =_____________

11. 13/14 =__________12. ½ =__________ 13. 3/8 =__________ 14. 1/8 =__________ 15. 3/7 =__________ 16. 6/10 =__________ 17. 25/100 =__________18. 3/5 =__________19. 5/8 =__________ 20. 2/3 =__________

It was very fortunate that Sophie Germain, a woman mathematician was born at a time when people looked down on women. In 1776, women then were not allowed to study formal, higher level mathematics. Thus, this persistent woman reads books of famous mathematicians and studied on her own. Aware of her situation, she shared her theorems and mathematical formulae to other mathematicians and teachers through correspondence using a pseudonym.

Can you guess the pseudonym that she used?Yes, you can. Simply follow the instruction.

Select the right answer to the equation below. Write the letter of the correct answer on the respective number decode pseudonym that she used. You may use the letter twice.

______ ______ ______ ______ (1) (2) (3) (4)

______ ______ ______ ______ (5) (6) (7) (8)

______ ______ ______ (9) (10) (11)

______ ______ ______ ______ (12) (13) (14) (15)

Answers:A = 0.25 F = 0.65 K = 0.512 P = 0.27B = 0.15 G = 0.28 L = 0.125 Q = 0.006C = 0.6 H = 0.77 M = 0.333… R = 0.72D = 0.54 I = 0.24 N = 0.40 S = 0.6E = 0.76 J = 0.532O = 0.75 T = 0.4113

U = 0.325

Lesson 11EXPRESSING MIZED FRACTIONAL NUMBERS TO MIXED DECIMALS

Lesson ObjectivesAfter accomplishing this lesson, you are expected to:

1. Express mixed fractional numbers to mixed decimals.2. Know the rules in expressing mixed fractional numbers to mixed decimals.3. Interpret the mixed fractional numbers to mixed decimals.

Lesson ObjectivesAfter accomplishing this lesson, you are expected to:

1. Express mixed fractional numbers to mixed decimals.2. Know the rules in expressing mixed fractional numbers to mixed decimals.3. Interpret the mixed fractional numbers to mixed decimals.

How can we change mixed fractional numbers to mixed decimals?See the following examples.

4 1/2 = 4.5 c. 21 1/8 = 21.12514 3/8 = 14.375 d. 32 3/7 =

32.4285

From the examples given above, it can be seen that the rule in changing a mixed fractional number to mixed decimal is:

RULE

To change a mixed fractional number to a mixed decimal, change the fraction to decimal up to the number of decimal places desired and then annex it to the integral part.

I. Change the following mixed fractional numbers to mixed decimals. Limit the number to three decimal places.

1. 4 2/5 = _____________________

2. 2. 3 4/5 = ______________________

3. 7 3/16= ______________________

4. 10 13/14 = ______________________

5. 12 9/17 = ______________________

6. 21 14/19 = ______________________

7. 32 21/41 = ______________________

8. 2 ¼ = _______________9. 3 5/7 = _______________ 10. 4 ½ = _______________11. 8 ¼ = _______________ 12. 2 1/3 = _______________13. 5 4/6 = _______________14. 10 4/5 = _______________15. 3 ¼ = _______________16. 10 3/7 = _______________ 17.10 11/20 = _______________18. 8 3/10 = _______________19. 6 15/16 = _______________20. 8 1/10 =_______________

II. Copy the correct mixed decimal to mixed fractional numbers.

1. 1 3/10 3. 31 503/100a. 1.03 a. 31.0503b. 1.30 b. 31.035c. 1.013 c. 31.00503d 1.13 d. 31.5030

2. 8 420/1000 4. 8 143/1000a. 8.0420 a. 8.1430b. 8.240 b. 8.0143c. 8.420 c. 8.1043d. 8.0042 d. 8.00143

5. 9 6/100a. 9.16b. 9.600c. 9.006d. 9.06

Lesson 12EXPRESSING DECIMALS TO FRACTIONS

Lesson ObjectivesAt the end of the lesson, the students are expected to:

1. Change the decimals to fractions.2. Follow the rule in expressing decimals to fractions.3. Understand the equivalent decimals and fractions.

Lesson ObjectivesAt the end of the lesson, the students are expected to:

1. Change the decimals to fractions.2. Follow the rule in expressing decimals to fractions.3. Understand the equivalent decimals and fractions.

As what we have learned earlier, decimals are common fractions written in different way.

There are certain instances when it becomes necessary to change decimal into fraction. Hence, it is necessary to acquire skill in changing a decimal to faction.

Now we will study how to write decimals in fractions.

Example 1: Write 0.5 in a faction form.5 or 1 10 2

0.5 = 5(1/10) Example 2: Write 0.72 in a fraction form.

0.72 = 7(1/10) + 2(1/100)1825

= 72/100 or 1825

On the other hand, a simple way of expressing decimal to factions is possible without writing the numeral in expanded form. What we need is only to determine the place value of the last digit as we read if from left to right.

Example 1: Write 0.5 in a faction form.

Notice that the digit 5 is in the tenth place, we can write immediately:

0.5 = or 12

__5__1000

The digit 2 is in the thousandths place so we write:

0.072 = 72/1000 = 9/125

Some Common Equivalent Decimals and

Factions0and 1/10

0and 2/10 or 1/51.5 and 1 ½ or 1 5/10 or 1

½0.25 and 25/100 or ¼0.50 and 50/100 or ½0.75 and 75/100 or ¾

Identifying Equivalent Decimals and Fractions

Decimals are a type of fractional number. The decimal 0.5 represents the fraction 5/10. The decimal 0.25 represents the

fraction 25/100. Decimal fractions always have a denominator based on a power of

10.We know that 5/10 is equivalent to 1/2 since 1/2 times 5/5 is 5/10. Therefore, the decimal 0.5 is equivalent to 1/2 or 2/4, etc.

It can be seen from the examples above the rule in changing a decimal to fraction is as follows:

RULE

To change a decimal number to a fraction, discard the decimal point and the zeros at the left of the left-most non-zero digit and write the remaining digits over the indicated denominator and reduce the resulting fraction to its lowest terms. (The number of zeros in the denominator is equal to the number of decimal places in the decimal number.

Change the following decimals to factional form and simplify them.

1. 0.4 = ________________

2. 0.007 = ________________3. 0.603 = ________________4. 0896 = ________________5. 056 =

________________6. 0.06 = ________________7. 0.125 = ________________8. 0.5 =

________________9. 0.42857 =

________________10. 0.375 =

________________

11. 0.54 = ________________12. 0.14 = ________________13. 0.8187 = ________________14. 0.956 = ________________15. 0.3567 = ________________16. 0.578 =_________________17. 0.34878 =_________________18. 0.47891 =_________________19. 0.12489 =_________________10. 0.14789 =_________________

How can you make a tall man short?

To find the answer, change the following decimal number to lowest factional form. Each time an answer is given in the code, write the letter for that exercise.

1. 0.6 = A 6. 0.24 = _______ O 2. 0.5 = _______B 7. 0.125 = _______ H 3. 0.7 = _______N 8. 0.55 = _______ L 4. 0.4 = _______I 9. 0.3 = _______W 5. 0.75 = _______ O 10. 0.048 = _______R 11. 0.25 = ______O

12. 0.75 = _____ L13. 0.2 = _____ E 14. 0.225 =______O 15. 0.24 = _____Y16. 0.8 = _____S17. 0.5688=______R

_____ _____ _____ ______ ______ _____ ½ 6/25 6/125 711/1250 225/ 1000 3/10

__A___ ______ ______ 3/5 ¾ 11/20

_____ ______ ______ 1/8 4/10 12/15

_____ _____ _____ _____ _______ 8/32 12/16 14/20 18/90 36/150

Lesson 13EXPRESSING MIXED DECIMAL NUMBERS TO

MIXED FRACTIONAL NUMBERS

Lesson Objectives At the end of the lesson, the pupils should be able to

1. Express mixed decimal numbers to mixed fractional numbers.2. Follow the rules in expressing mixed decimal numbers to mixed fractions.

3. Identify mixed decimals to mixed fractions.

Lesson Objectives At the end of the lesson, the pupils should be able to

1. Express mixed decimal numbers to mixed fractional numbers.2. Follow the rules in expressing mixed decimal numbers to mixed fractions.

3. Identify mixed decimals to mixed fractions.

How can we change mixed decimals to mixed fractions? Study the following examples:

a. 5.03 = 5 3/100b. b. 6.2 = 6 2/10 = 6 1/5c. 24.75 = 24 75/100 = 24 ¾d. 37.248 = 37 248/1000 = 37

31/125The rule applied to the above example is:

RULE

To change a mixed decimal number to a mixed fractional number, do not change the integral part, change the decimal part to a fraction according to the rule, and write the result as a mixed fractional number.

Change the following mixed decimals to mixed fractional numbers. (First is an example.)

1. 3.06 = 3 6/10 6. 67.7362 = ___________2. 5.72 = ________ 7. 62.72 = ___________3. 11.302 = ________ 8. 71.4684 = ___________4. 10.642 = ________ 9. 92.5896 = __________5. 51.136 = ________ 10. 4.789 = __________

II. Identify the following by writing D if it is mixed decimals and F if it is mixed fractional numbers.

_____1. 1 217/100 _____ 11. 14.3245_____ 2. 1.0124 _____ 12. 18 18/24_____ 3. 1.4568 _____ 13. 9.28_____ 4. 32 8/18 _____ 14. 1.0406_____ 5. 2.510 _____ 15. 4 235/1000_____ 6. 10.01 _____ 16. 450 11 /111_____ 7. 39 45/100 _____ 17. 1.5345_____ 8. 45 105/265 _____ 18. 143.445254_____ 9. 101 81/411 _____ 19. 12 34/91_____ 10. 1.01123 _____ 20. 653 185/1124

OVERVIEW OF THE MODULAR WORKBOOKThis modular workbook provides you greater understanding in all aspects of addition and subtraction of decimal numbers. It enables you to perform the operation correctly and critically. It includes all the needed information about the addition and subtraction of decimal numbers, its terminologists to remember, how to add and how to subtract decimals with or without regrouping, how to estimate sum and differences, and subtracting decimal numbers involving zeros in minuends. This modular work will help you to enhance your minds and ability in answering problems deeper understanding and analysis regarding all aspects of adding and subtracting decimal numbers.

OBJECTIVES OF THE MODULAR WORKBOOK

After completing this Unit, you are expected to:1. Familiarize the language in addition and subtraction.2. Learn how to add and subtract decimal numbers with or without regrouping.3. Know how to check the answers.4. Estimate the sum and differences and how it is done.5. Know how to subtract decimal numbers with zeros in the minuend.6. Develop speed in adding and subtracting decimal numbers.7. Analyze problems critically.

Lesson 14MEANING OF ADDITION AND SUBTRACTION OF

DECIMAL NUMBERS

Lesson Objectives:After accomplishing this lesson, you are expected

to:1. Define addition and Subtraction.

2. Identify the parts of addition and subtraction. 3. Familiarize the language in addition and subtraction.

Lesson Objectives:After accomplishing this lesson, you are expected

to:1. Define addition and Subtraction.

2. Identify the parts of addition and subtraction. 3. Familiarize the language in addition and subtraction.

Addition is the process of combining together two or more decimal numbers. It is putting together two groups or sets of thing or people.

Example: 0.5 + 0.3 = 0.8

Addends Sum or Total

Addends are the decimal numbers that are added. Sum is the answer in addition. The symbol used for addition is the plus sign (+).

The process of taking one number or quantity from another is called Subtraction. It is undoing process or inverse operation of addition. It is an operation of taking away a part of a set or group of things or people.

Note: Decimal points is arrange in one column like in addition of decimals.

Example: 14. 345 Minuend

- 3.120 Subtrahend11.232 Difference

Minuend is in the top place and the bigger number in subtraction. The number subtracted from the minuend is called subtrahend. It is the smaller number in subtraction. The subtrahend is subtracted or taken from the minuend to find the difference. Difference is the answer in subtraction. The symbol used for subtraction is the minus sign (-).

I. Give the meaning and explain the use of the following.

1. What is addition?1. What is addition?

2. What is subtraction?2. What is

subtraction?

3. What are the parts of addition?

3. What are the parts of addition?

4. What are the parts of subtraction?

4. What are the parts of subtraction?

1. Addition ______________________________________________2 Subtraction ______________________________________________3. Parts of addition ______________________________________________4. Parts of subtraction______________________________________________

II. Identify the following decimal numbers whether it is addends, sum, minuend, subtrahend or difference. Put an if addends, if sum, if minuend, if subtrahend and if difference.

1. 0.9 _______ + 0.8 _______

1.7 _______

2. 2.24 _______ + 2.38 _______ 4.62 _______

3. 12.85 _______ - 0. 87 _______ 11.98 _______

4. 7.602 _______ - 2.664 _______ 4.938 _______

5. 0.312 _______ + 0.050 _______ 0.362 _______

6. 6.781 _______ - 1.89 _______

8.676 _______

7. 0.215 _______ + 0.001 _______ 0.216 _______

8. 0.156 _______ + 1.811 _______ 1.967 _______

9. 0.113 _______ + 0.009 _______ 0.122 _______

10. 0.689 _______ - 1.510 _______ 2.199 _______

III. Answer the following by completing the letter in each box which indicate the parts of addition and subtraction of decimals.

1. It is the numbers that are added.

2. The answer in addition.

3. It is the process of combining together two or more numbers.

4. Sign used for addition.

5. It is undoing process or inverse operation of addition.

6. Sign used for subtraction.

7. It is the answer in subtraction.

8. It is in the top place and the bigger number in subtraction.

9. It is the smaller number in subtraction.

10. Subtraction is an operation of _________ a part of a set or group of things or people.

Lesson 15ADDITION AND SUBTRACTION OF DECIMAL

NUMBERS WITHOUT REGROUPING

Lesson Objectives: After finishing the lesson, the students are expected to:

1. Know how to add and subtract decimal numbers without regrouping.2. Develop speed in adding and subtracting

decimal number.3. Follow the steps in adding and subtracting decimal numbers.

Lesson Objectives: After finishing the lesson, the students are expected to:

1. Know how to add and subtract decimal numbers without regrouping.2. Develop speed in adding and subtracting

decimal number.3. Follow the steps in adding and subtracting decimal numbers.

Add the following decimals: 28. 143 and 11.721.

If you added them this way, you are

right.

28. 143 + 11. 721

39. 864

Let us add the decimals by following these steps.

STEP 1 STEP 2

Add the thousandths place

3+ 1 = 4 28. 143 + 11. 721 4

Add the hundredths place

4 + 2 = 6 28. 143 + 11. 721

64

STEP 3

Add the tenths place

7 + 1 = 8 28. 143 + 11. 721 864

STEP 4

Add the following up to the ones.

8 + 1 = 9 28. 143 + 11. 721 9. 864

STEP 5

Add the following up to the tens.

2 + 1 = 3 28. 143 + 11. 721 39. 864

Now subtract 39. 864 to 11. 721.

39. 864 minuend - 11. 721 subtrahend 28. 143 difference

2 Ways of Checking the Answer

1. minuend – difference = subtrahend39. 864 minuend

- 28. 143 difference11. 721 subtrahend

2. difference + subtrahend = minuend28. 143 difference

+ 11. 721 subtrahend39. 864 minuend

If you subtract the difference from minuend and the answer is subtrahend the answer is correct. Also, adding the difference and subtrahend will the result to the minuend: it is also correct.

As a procedure for adding or subtracting decimal numbers, we have the following:

1. Write the decimal numbers with the decimal points falling in one column.2. Add or subtract as if they were whole numbers.3. Place the decimal point of the result in the same column as the other numbers.

Add and subtract as fast as you can.

Add and subtract the following to find the mystery words and write the letter of each answer in the code below.

This appears twice in the Bible (In Matthew VI and Luke II).

1. 85. 367 2. 645. 987

+ 16. 252 - 314.625 R P

3. 74. 617

+ 21. 721 O

4. 2,936. 475

- 1,421.061 S

5. 51. 437 6. 658.325

+ 18. 042 - 137.210 Y L

7. 895. 399 8. 945. 374

- 471. 287 + 33. 161 A R

9. 32. 511

+ 11. 621 R

10. 7,649.251 11. 66.341

- 36.030 + 12.412 E D

_______

521. 115

_______

96. 338

_______

44. 132

_______

78. 753

_______

1515. 414

_______

331.362

_______

101.619

_______

424.112

_______

69.478

_______

7613.221

_______

978.535

Lesson 16ADDITION AND SUBTRACTION OF DECIMAL

NUMBERS WITH REGROUPING

Lesson Objectives: After accomplishing the lesson, the students are expected to be able to:

1. Define regrouping.2. Learn how to add and subtract decimal

numbers with regrouping.3. Answer and perform the operation critically and correctly.


1. Define regrouping.2. Learn how to add and subtract decimal

numbers with regrouping.3. Answer and perform the operation critically and correctly.

In the past lesson, you’ve learned how to add and subtract decimal numbers without regrouping. The only difference in this lesson is that it involves regrouping and borrowing. It is easy to add and subtract decimal numbers without regrouping.

Regrouping is a process of putting numbers in their proper place values in our number system to make it easier to add and subtract.

Here’s how to add decimal numbers with regrouping.

Example 1: 0. 7

+ 0. 5

Ones . Tenths

1 0+ 0

.

.75

1 . 2

0.7 + 0.5 = 1210 tenths is regroup as

(1) one.

Example 2: 0.09

+ 0.06

O . T H

00

.

.00

96

0 . 1 5

0.9 + 0.6 = 15 hundredths10 hundredths is 1 regrouped as 1 tenth.

Example 3: 0.065

+ 0.008

O T H Th

0.+ 0.

00

60

58

0. 0 7 3

5 + 8 = 13 thousandths 10 thousandths is regrouped as 1

hundredth.

Subtract decimals like you were subtracting whole numbers.

Example 4: 0. 93- 0. 28

ones tenths hundredths

0. 9 3

0. 8 - 1 10

0. 8 3

0. 8 13

9 is renamed as 8 + 1 tenths. 1

tenth is regrouped as

10 hundredths.

0. 9 3 - 0. 2 8 0. 6 5

Check: 0. 28+ 0. 65

0. 93

Example 5: 0.730

- 0.518

2 10

0.730 - 0.518 0.212

ones tenths hundredths thousandths

0. 7 3 0

0. 7 2+1 10

0. 7 - 5

2 - 1

0 - 80.

0. 2 1 2

Check: 0.518

+ 0.212 0.730

I. Answer the following.A. Add the following and check your answer

on the Check Box below.

1. 0.6 2. 0.07 + 0.8 + 0.49

3. 0.36 4. 0.746 + 0.56 + 0.235

B. Subtract the following and check your answer on the Check Box below.

1. 0.62 2. 0.762 - 0.58 - 0.325

3. 0.850 4. 0.452 - 0.328 - 0.235

II. Write on the blank (+) or (-) sign to make the statement TRUE.

1. 4.793 ___ 3.549 = 8.3422. 72.685 ___ 45.726 ___ 13.493 = 104.9183. 1.45 ___ 0.50 ___ 3.95 ___ 5.66 = 11.564. 36.58 ___ 35.789 ___ 354.587 = 426.9565. 6.57 ___ 0.456 ___ 236.5 ___ 5 ___ 213.66 = 34.8666. 28. 625 ___ 25.361 = 3.2647. 57.54 ___ 0.25 = 57.298. 86.3 ___ 0.456 ___ 32.58 = 118.4249. 39 ___ 5.65 = 33.3510. 53.654 ___ 5.236 = 48.418

Lesson 17 ADDING AND SUBTRACTING MIXED

DECIMALS

Lesson Objectives: After finishing the lesson, the students are expected to:1. Understand and know how to add and subtract

mixed decimal numbers. 2. Follow the rules in adding and subtracting mixed decimal numbers. 3. Perform the operation correctly.

Lesson Objectives: After finishing the lesson, the students are expected to:1. Understand and know how to add and subtract

mixed decimal numbers. 2. Follow the rules in adding and subtracting mixed decimal numbers. 3. Perform the operation correctly.

Ramon traveled from his house to school, a distance of 1.39845 kilometers. After class, he traveled to his friend’s house 1.85672 kilometer away in another direction. From his friends to his own house, he rode another 1.23714 km over. How many kilometers did Ramon traveled?

3 . T H Th T Th H Th

1 1 1+1

.

.

.

1382

2953

1867

1471

524

4 . 4 9 2 3 1

He traveled a total of 4.49231 km. The following day, he traveled to the school and the seashore for a total of 6.35021 km. How many more kilometers did Ramon traveled than previous day?

O T H Th T Th H Th5

6-4

.

.

12

34

14

59

9

02

12

23

11

1 . 8 5 7 9 0

Ramon traveled 1.85790 kilometers more.

In adding and subtracting mixed decimals, remember to align the decimal points and regroup when necessary.

I. Add or subtract these mixed decimals.

1. 4.59804 2. 3.14879 3. 5.11788

7.81657 5.37896 1.93523

+ 1.30493 + 2.95321 + 3.40175

4. 2.42814 5. 7.20453 6. 9.57128 - 1.19905 - 4.35712 - 2.89340

II. Rewrite with the correct alignment of decimal points on the space provided. Find the sum and difference.

1. 4.930000 4. 18.17932 57.5244 + 2.41256

+ 637.3672

2. 73.59203 5. 12.48004 + 154.38762 - 9.86327

3. 142.567021 6. 42.20239

- 85.791503 - 2.34876

4. 18.16532 9. 5.306321 - 4.01985 002.7509

+ 4.952005

5. 951.235 7.18902 10. 103.93284 + 00.3 + 43.76895

Lesson 18ESTIMATING SUM AND DIFFERENCE OF

WHOLE NUMBERS AND DECIMALSLesson Objectives:

After understanding the lesson, you must be able to:

1. Define estimation. 2. Know the two methods in making estimates.

3. Learn how to estimate sum and difference and how it is done.

Lesson Objectives: After understanding the lesson, you must be able to:

1. Define estimation. 2. Know the two methods in making estimates.

3. Learn how to estimate sum and difference and how it is done.

Estimation is a way of answering a problem which does not require an exact answer. An estimate is all that is needed when an exact value is not possible. Estimation is easy to use and or to compute. Rounding is one way of making estimation. Each decimal number is rounding to some place value, usually to the greatest value and the necessary operation is performance on the rounded decimal numbers.

Two methods are used in making estimation, the rounding off the desired

digit one and finding the sum of the first digit only. We have learned how to round decimal numbers in this section, first only the front digits are used. If an improved or refined estimate is desired,

the next digits are used.

When large decimal numbers are involved, it is wise to estimate before computing the exact and user is expected to be about or close to the estimate.

Method 1: Sum of the First Digit only

Estimate in Addition3.455 + 2.672 + 5.135

Rounded off to the nearest ones

3.455 3.0002.672 3.000

+ 5.134 + 5.000 11.000

Rounded off to the nearest tenths

3.455 0.500 2.672 0.700 + 5.134 + 0.100

1.300

to be added the first estimate if desired or required.

Thus the sum 3.455 + 2.672 + 5.134 can be roughly estimated by 11.000. If a better estimate is required or desired, then add 1.300 to get 11.300.

Estimate 5.472147 – 2.976543

Rounded to the nearest onesActual Subtraction

5.472147 5.000000 5.472147 - 2.976543 - 3.000000 - 2.976543

2.000000 2.495604

Method 2: Rounding Method

a. Estimate the sum by rounding method in place of whole numbers.Example: 6.567 7.000

5.482 5.000 + 4.619 +5.000

17.000

b. Estimate the difference by rounding method.

Example: 14.525 15.000 - 11.018 - 11.000 4.000

By the rounding method, the first example is estimated by 17.000 and the second one by 4.000. The actual value of the sum of example no.1 is 16.668 and the difference of example no. 2 is 3.507 respectively. Both methods give a reasonable estimate.

Remember:In estimating the sums, first round each addend

to its greatest place value position. Then add. If the estimate is close to the exact sum, it is a good estimate. Estimating helps you expect the exact answer to be about a little less or a little more than the estimate.

However, in estimating difference, first round the decimal number to the nearest place value asked for. Then subtract the rounded decimal numbers. Check the result by actual subtraction.

I. Estimates the sum and difference to the greatest place value. Check how close the estimated sum (E.S.) / estimated difference (E.D.) by getting the actual sum (A.S.) and actual difference (A.D.).

A. Actual Sum/ Estimated Sum1. 3.417 3.000 2. 36.243 36.000

2.719 3.000 29.641 30.000 + 1.829 + 2.00 + 110.278 + 110.000 A.S. E.S. A.S. E.S.

3. 648.937 649.000 4. 871.055 871.000214.562 215.000 276.386 276.000

+ 450.211 + 450.000 + 107.891 + 108.000 A.S. E.S. A.S. E.S.

5. 374.738 375.000 6. 342.165 342.000469.345 469.000 178.627 179.000

+ 213.543 + 213.500 + 748.715 + 749.000 A.S. E.S. A.S. E.S.

B. Actual Difference/ Estimated Difference7. 14.255 14.000 8. 28.267 28.000 - 11.812 - 12.000 - 16.380 - 16.000 A.D. E.D A.D. E.D.

9. 345.678 346.000 10. 92.365 92.000 - 212.792 - 213.000 - 75.647 -

76.000 A.D. E.D. A.D.

E.D.

11. 62.495 62.000 12. 9.28759.0000

- 17.928 - 18.000 - 6.8340 - 7.0000A.D. E.D. A.D. E.D.

Match a given decimals with the correct estimated sum / difference to the greatest place – value.

The shortest verse in the Bible consists of two words.

To find out, connect each decimals with he correct estimated sum / difference to the greatest place – value. Write the letter that corresponds to the correct answer below it.

1. 36.5+18.91+55.41 U. 939.002. 639.27-422.30 S. 216.003. 48.21+168.2 P. 2.00004. 285.15+27.35+627.30 E. 146.0005. 8.941-8.149 W. 28.106. 18.95+9.25 J. 111.007. 129.235+16.41 T. 537.008. 9.2875-6.834 S. 1.0009. 989.15-451.85 E. 217.00

_____ ______ ______ ______ ______ 1 2 3 4 5

_____ ______ ______ ______ 6 7 8 9

Lesson 19MINUEND WITH TWO ZEROS


1. Know how to subtract decimal numbers with two zeros in minuend.

2. Follow the steps in subtraction of numbers involving zeros.

3. Check the answer and perform the operation correctly.


1. Know how to subtract decimal numbers with two zeros in minuend.

2. Follow the steps in subtraction of numbers involving zeros.

3. Check the answer and perform the operation correctly.

You always have to regroup in subtracting decimal numbers with zeros. You will have to

regroup from one place to the next until all successive zeros

are renamed and ready for subtraction.

STEPS IN SUBTRACTION OF DECIMAL NUMBER INVOLVING ZEROS

1. Arrange the digits in column.2. Regroup from one place to the next until all

successive zeros are renamed.3. Subtract to find the answer.4. Check the answer.

Example:

0.8005

- 0.6372

O T H Th T Th

0. 8 0 0 5

0. 7+1 10

9+1 10

0. 7 9 10 5

0. 6 3 7 2

0. 1 6 3 3

Rewriting: 0.8005- 0.6372

Difference 0.1633

Checking:0.6372

+ 0.16330.8005

I. Subtract the following and check.1. 16.004 - 2.875

2. 28.009 - 11.226

3. 18.003 - 5.739

4. 11.001 - 9.291

5. 4.0075 - 2.9876

6. 0.10013 - 0.00011

7. 2.00143 - 0.88043

8. 0.7008 - 0.5383

9. 0.8008 - 0.0880

10. 0.14003 - 0.03333

Answer the following to find the mystery words.

In what type of ball can you carry?

To find the answer, draw a line connecting each decimal number with its equal difference. The lines pass through a box with a letter on it. Write what is in the box on the blank next to the answer.

Lesson 20PROBLEM SOLVING INVOLVING ADDITION AND

SUBTRACTION OF DECIMALS


1. Follow the step of solving problem.2. Analyze the problem critically.3. Develop interest in solving word problem.


1. Follow the step of solving problem.2. Analyze the problem critically.3. Develop interest in solving word problem.

Kristina saves her extra money to buy a pair of shoes for Christmas. Last week she saved Php. 82.60; two weeks ago, she saved Php. 100.05. This week she saved Php. 92.60. How much did she save in three weeks?

Steps in Solving a Problem

1. Analyze the problem

2. What is asked? Total amount did Kristina save in three weeks.3. What are the given facts? Php. 82.60, Php. 100.05, and Php. 96.10

Know

3. What is the word clue? Save.

What operation will you use? We use addition.4. What is the number sentence? Php. 82.60 + Php. 100.05 + Php. 96.10 = N5. What is the solution? Php. 82.60

Php. 100.05 + Php. 96.10

Php. 278.75

Solve

Decide

Show

Check

6. How do you check your answer?We add downward.Php. 82.60Php. 100.05

+ Php. 96.10 Php. 278.75

“Kristina saves Php. 278.75 in three weeks.”

It is easy to solve word

problems by simply

following the steps in

solving word problem.

I. Read the problem below and analyze it.

A. Baranggay Maligaya is 28.5 km from the town proper. In going there Angelo traveled 12.75 km by jeep, 8.5 km by tricycle and the rest by hiking. How many km did Angelo hike?

1. What is asked?_____________________________________________

_____________________________________________

2. What are the given facts?_____________________________________________

_____________________________________________

3. What is the process to be used?_______________________________________________

_______________________________________________

4. What is the mathematical sentence?_______________________________________________

_______________________________________________

5. How the solution is done?

6. What is the answer?_______________________________________________

_______________________________________________

7. How do you check the answer?

B. Faye filled the basin with 2.95 liters of water. Her brother used 0.21 liter when he washed his hands and her sister used 0.8 liter when she washed her face. How much water was left in the basin?

1. What is asked?_____________________________________________

_____________________________________________


_____________________________________________

3. What is the process to be used?_____________________________________________

_____________________________________________

4. What is the mathematical sentence?_____________________________________________

_____________________________________________


6. What is the answer?__________________________________________________________________________________________


C. Ron cut four pieces of bamboo. The first piece was 0.75 meter; the second was 2.278 meters; the third was 6.11 meters and the fourth was 6.72 meters. How much longer were the third and fourth pieces put together than the first and second pieces put together?

1. What is asked?_____________________________________________

_____________________________________________


_____________________________________________

3. What is the process to be used?

__________________________________________________________________________________________

4. What is the mathematical sentence?

__________________________________________________________________________________________


6. What is the answer?

_________________________________________________________________________________________


D. Pamn and Hazel went to a book fair. Pamn found 2 good books which cost Php. 45.00 and Php. 67.50. She only had Php.85.00 in her purse but she wanted to buy the books. Hazel offered to give her money. How much did Hazel share to Pamn?

1. What is asked?_____________________________________________

_____________________________________________


_____________________________________________


_____________________________________________

4. What is the mathematical sentence?_____________________________________________

_____________________________________________


6. What is the answer?__________________________________________________________________________________________


E. Marlene wants to buy a bag that cost Php. 375.95. If she has saved Php. 148.50 for it, how much more does she need?

1. What is asked?_____________________________________________

_____________________________________________


_____________________________________________


_____________________________________________

4. What is the mathematical sentence?_______________________________________________

_______________________________________________


6. What is the answer?_______________________________________________

_______________________________________________


OVERVIEW OF THE MODULAR WORKBOOK

This modular workbook provides you with the understanding of the meaning of multiplication of decimals, multiply decimals in different form and how to estimate products. It will develop the ability of the students in multiplying decimal numbers. This modular workbook will help you to solve problems accurately and systematically.

OBJECTIVES OF THE MODULAR WORKBOOK

After completing this Unit, you are expected to:1. Define multiplication, multiplicand, multiplier, products and factors.2. Know the ways of multiplying decimal numbers.3. Learn the ways of multiplying decimal numbers involving zeros.4. Learn how to make an estimate and know the ways of making estimates.

Lesson 21MEANING OF MULTIPLICATION OF DECIMAL

NUMBERS

Lesson Objectives: After learning this lesson, you are expected

to:1.Define multiplication.2.Locate where the multiplicand, multiplier and

product are.3.Familiarize the terms in multiplication.

.4 + .4 + .4 + .4 + .4 + .4 = 2.4In multiplication, it is written as:

.4 → multiplicand x 6 → multiplier 2.4 → product (answer in multiplication)

factors

Multiplication is a short cut for repeated addition. It is a

short way of adding the same decimal number. It is the

inverse if division.

The decimal numbers we multiply are called multiplicand and multiplier is the decimal number that multiplies. The answer in the multiplication is the product. The decimal numbers multiplied together are factors.

Another examples:

9 0.08 1.24 0.007x 0.5 x 3 x 2 x 4

4.5 0.24 2.48 0.028

1. What is multiplication

?

1. What is multiplication

?

2. What are

factors?

2. What are

factors?

3. What are

products?

3. What are

products?4. Give some examples of multiplication

decimals.

4. Give some examples of multiplication

decimals.

I. Give the meaning and explain the use of the following.

1.multiplication ________________________________________________________________________________

2. factors ________________________________________________________________________________

3. products ________________________________________________________________________________

4. Examples of multiplication decimals ________________________________________________________________________________

II. Identify the words by looping vertically ,horizontally and diagonally directions. (Word – Puzzle)

Decimal Numbers Part 2

Technology

Transcript of Decimal Numbers Part 2