Math Module First Quarter

1WORKBOOK

IN MATHEMATICSVI

( First Quarter )

May Ester M. Rubio

Master Teacher I

2CHAPTER ONE

Whole Numbers

Lesson No. 1 .. Expression or Equation

Lesson No. 2 Base, Exponent and Power

Lesson No. 3. Power

Lesson No. 4 Evaluating Expression

Lesson No. 5.. Two to Three Step Word

Problem Involving Whole Numbers

Lesson No. 1

EXPRESSION OR EQUATIONExpression it may consist of one number of more numbers with operation and

3grouping symbols without the equals (=) symbol

Equation it may consist of numbers with operation and grouping symbols with equals

( -) symbol.

Identify which set is an expression and which set is an equation.

Set A Set B5147 + 75 5 147 + 75 = 5 222

1663 1 843 985 = 858547 + (1 843 985 ) ( 2 147 X 50 ) 50 = 2 147

PRACTICEDirections: Write EX if it is an expression or EQ if it is an equation.

_____ 1. 82 X 4 + ( 28 7)

_____ 2. ( 9510 10 ) + ( 2 848 4 ) = N

_____ 3 . ( 2 147 X 50 ) 50

_____ 4. 5 202 X 4

_____ 5. 47 + 32 = 79

_____ 6. ( 1 X 3 ) + 8 = 12

_____ 7. 95 ( 2 + 5 )

_____ 8. ( 6 + 7 ) + ( 100 4 ) = 38

_____ 9. 9510 10

_____ 10. 305

Lesson No. 2

BASE, EXPONENT AND POWER

423 = 8BASE is the number that is multiplied repeatedly or the

factor

Exponent is a number written at the upper right hand of a

number. It tells the number of times the number

is multiplied by itself .

Power is the product obtained after multiplying a number

by itself as many times as indicated by its exponent

PRACTICEDirections: Identify the base, exponent and the power

Equation Base Exponent Power1) 52 = 252) 72 = 493) 24 = 164) ( 4+5)2 = 815) (15 9)4 = 1296

MORE PRACTICEDirections: Write the equation.

Equation Base Exponent Power1. 7 2 492. 4 3 643. 6 2 364. 2 5 325. ( 20 2 ) 3 1000

Lesson No. 3

POWER

5To find the power, multiply the base by itself as many times as indicated by itsexponent.

Example

23 = 2 X 2 X 2 42 = 4 X 4

= 4 X 2 =

=

PRACTICEDirections: Find the power.

1. 36 = _____ 6. ( 10 7 ) 2 = _____

2. 45 = _____ 7. ( 9 5 ) 2 = _____

3. 210 = _____ 8. 252 = _____

4. 112 = _____ 9. 93 = _____

5. ( 3 + 4 ) 3 = _____ 10. 54 = _____

MORE PRACTICEDirections: Match column B to column A.

Column A Column B

_____ 1. 1 024 a) 12 2

_____ 2. 125 b) ( 45 5 ) 3

_____ 3. 144 c) ( 2 + 2 ) 5

_____ 4. 1 000 d) ( 8 3 ) 3

_____ 5. 729 e) ( 2 X 5 ) 3

Lesson No. 4

EVALUATING EXPRESSION

8

166

6To evaluate an expression means to find its value in the simplest form byfollowing the PEMDAS rule.

P simplify the expression enclosed by the parenthesis ( ) or other grouping symbolslike the brace [ ] and the bracket { }

E simplify the number with an exponent

M perform the operation of multiplication

D perform the operation of division

A perform the operation of addition

S perform the operation of subtraction

Example:

( 20 16 ) 2 + 10 ( 8 2 ) = N

42 + 10 4 = N P

4 X 4 + 10 - 4 = N E

16 + 10 - 4 = N M

26 - 4 = N A

22 = N S

More Examples

Evaluate Solution

1. 92 = N 9 X 9 =

2. 2 + 33 2 + ( 3 X 3 X 3 )

2 + 27

3. ( 5 1 ) 22 4 ( 2 X 2 )

4 4

4. 15 X 2 ( 32 3 ) 15 X 2 [ ( 3 X 3 ) 3 ]

15 X 2 ( 9 3 )

81

29

1

715 X 2 6

30 6

PRACTICEDirections: Evaluate the following expressions.

1. 24 = _____

2. 32 + 22 = _____

3. ( 45 8 ) + 42 = _____

4. 38 + 12 ( 42 + 12 ) = _____

5. 10 X 12 6 + 52 = _____

MORE PRACTICEDirections: Evaluate the following expressions.

1. 28 2 + 7 32 = _____

2. 82 X 4 + ( 28 7 ) = _____

3. ( 69 12 ) + ( 83 47 ) 2 = _____

4. ( 150 75 ) 2 + ( 290 5 ) = _____

5. 5 X ( 13 7 )2 + [ ( 4 2 ) + 5 ] = _____

6. 43 + 34 52 = _____

7. ( 5 3 ) 3 + ( 2 1 ) 4 ( 4 2 ) 3 = _____

8. 6 + ( 12 5 ) 2 ( 9 3 ) 3 = _____

9. 18 X ( 15 9 ) 2 17 ( 9 5 ) 2 = _____

10. ( 516 412 ) ( 15 ) ( 45 36 ) 2 + ( 8 5 ) 3 = _____

HOMEWORK

5

8Evaluate the following expressions. Follow the PEMDAS rule.

1. ( 47 321 + 27 385 ) x 21 6 = N

2. [ ( 96 000 + 282 000 ) 2 ] X 36 = N

3. 90 5 + ( 63 800 20 000 ) = N

4. ( 37 254 X 20 14 252 ) 2 = N

5. ( 85 200 + 9 250 ) X ( 47 243 8 198 ) = N

MIND ENHANCERChange the following descriptions into numerical expressions then evaluate.

1. The second power of 10 plus 15

2. Fourteen cubed minus 28

3. The second power of the sum of 250 and 25

4. The difference between 1 000 and the third power of 10

5. The product of 12 and the third power of the quotient of 9 and 3

6. The square of the sum of 20 and 3

7. The product of 6 and 5 raised to the third power

8. The square of the quotient of 15 divided by 3

9. The sun of the square of 100 and the square of 10

10. The difference between the fourth power of 3 and 3 squared

11. The sun of 6 and 9 added to the difference of 19 and 16

12. Twice the difference of 15 and 11 subtracted from the product of 14 and 5

13.The quotient of 48 and 8 multiplied by the sum of 4 and 8

14.The difference of 114 and 86 divided by the difference of 56 and 49

15.Twice the sum of 8 and 9 subtracted from the product of 9 and 8

Lesson No. 5

Two Three Step Word Problems

9Involving Whole Numbers

When solving word problems on whole numbers, use the RSTUVW Approach.

The letters stand for :

R Read the problem carefully

S Study the given facts

T Think of the operation/s to be used

U Use the operation/s to solve the problem

V Verify your answer

W Write your answer to the problem in a complete sentence

Example:

A five star hotel charges Php 38 000 a month from a foreigner who staysin one unit of the hotel. If the foreigner stays in the hotel for two years, how much

should be charged from him ?

Now analyze the problem. Follow the RSTUVW Approach

Step 1 : Read the problem carefully.

Step 2 : Study the given facts.

Step 3 : Think of the operation/s

To be used.

Step 4 : Use the operation/s

to solve the problem

Step 5 : Verify your answer.

Given :______________________________________________________________________________________

Operation/s:______________________________________________________________________________________Solve :______________________________________________________________________________________

Use your calculator to check the answer.

10

Step 6 : Write the answer in

a complete answer

PRACTICEAnalyze and then solve the problems following the steps in the RSTUVW Approach.

1. Mother earns Php 38 000 less than fathers monthly salary. If father earnsPhp 22 000 a month, how much is the combines salary of mother and father ?

2. James gives Php 12 000 to her mother every month. He has been giving thisamount for 18 months. If mother spends only Php 10 000 of James money andsaves the rest, how much would mother save after 18 months ?

3. The serial number of a bundle of Php 1 000 bills starts from MN 370003 andends at MN 370255. How much is the total amount of the bundle ?

4. Mr. Reyes bought 30 boxes of ponkan. Each box costs Php 200. If there are 50pieces of ponkans per box, how much did Mr. Reyes earn from selling all theponkans at 3 for Php 25 ?

5. A house is rented at Php 2 500 a month. If a family rented it for 2 and a halfyears, how much did they pay ?

MORE PRACTICEAnalyze and then solve the problems following the steps in the RSTUVW Approach.

1. A fisherman caught 134 kls of bangus, if a kilo cost Php 65.00 how much did hesold if there are 29 kls left ?

2. Cyril took note of the scores of his five friends in a 100-item test in spelling. Raffyscored 84; Louie, 88; Mac, 81; Bogie, 85; and Tony, 87. If Cyril scored 91; whatwas the average score of the six boys ?

3. Mr. Hernandez paid Php 1, 720, 000 for a house and lot last year. This year hesold it for Php 2, 488, 500. How much profit did he make after paying Php 18,742 to the sales agent ?

4. The area of the Pacific Ocean is about 165 760 000 square kilometers ( km2 )and that of the Atlantic Ocean is about 82 400 000 km2. How much bigger is thePacific Ocean than the Atlantic Ocean ?

5. The reading on an electric meter for the month of September was 5 124 kWh.The next month, the reading was 5 332 kWh. How much electricity was used ?

11

HOMEWORKAnalyze and then solve the problems following the steps in the RSTUVW Approach.

1. Nida took 36 pictures with her new camera. Four of the pictures wereoverexposed and were not developed. If it cost Php 4 to print each picture, whatwas the total cost of the pictures ?

2. A parking lot has 28 rows with 25 car spaces in each row. If 3 rows are removedand used as a driveway, how many cars can be parked in the lot ?

3. Find Jennas average grade if her grades were 86, 89, 92, 94, 88, 93, 87, 90 and91.

4. A university charges Php 136 tuition fee per unit in college. If Kate takes 21 unitsand is given a discount of Php 278, how much should she pay ?

5. Eight parishes collected a total of Php 95 488 for the fire victims. What was theaverage collection from each parish ?

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CHAPTER TWO

DECIMALS

Lesson No. 1 .. Visualizing and Renaming Decimals

Lesson No. 2 Place Value of Decimals

Lesson No. 3. Reading and Writing Decimals

Lesson No. 4 Writing Decimals in Standard and

Expanded Notation

Lesson No. 5.. Comparing and Ordering Decimals

Lesson No. 6 . Rounding Off Decimals Through Ten

Thousandths

Lesson No. 1

Visualizing and Renaming Decimals

13

Study the numbers inside the box. What are they ?

Lets visualize these decimals. Which figure represents 0.01 , 1.0 and 0.1.

a) b)

c)

Decimal fraction is just another way ofwriting tenths, hundredths and other powersof ten parts of a unit.

110 = 0.1 - read as one- tenth

1100 = 0.01 - read as one hundredth

11 000 = 0.001 - read as one thousandth

110 000 =0.0001 - read as one- ten thousandth

PRACTICEComplete the table below.

Fractions Decimal Read as

1.0 0.1 0.01

0.001 0.0001 0.10001

14

1. 110

2.Five - tenths

3.0.8

4. 3100

5.0.08

6.0.19

7.Fifteen thousandths

8.Twenty five thousandths

9. 1251 000

10.0.0120

MORE PRACTICEDo you know the name of the spaceship used by Neil A. Armstrong, Edwin Aldrin

and Michael Collins during their flight to the moon called Apollo 11 ?

Find out the name of the spaceship by changing the fractions below intodecimals. After getting the answer, change it to its corresponding letter. Then formthose letters to know the name of the spaceship.

1. 15 4. 347 7. 5 432100 = _____ 1 000 = _____ 10 000 = ___

2. 24 5. 182100 = _____ 10 000 = _____

3. 124 6. 4 7341000 = _____ 10 000 = _____

The spaceship used in Apollo 11 is ___________________________.

Lesson No. 2

Place Value of Decimals

A = 0.24 R = 0.0182 U = 0.347 N = 0.4734

B = 0.04734 S = 0.15 V = 0.5432 T = 0.124

W = 0.05432

15

Look at the figure and study the place value of decimals.

1 2 . 5 6 8 2Tenths

Hundredths

Thousandths

Ten thousandths

In a decimal, the value of the digits to the right of the decimal point is always lessthan one. The value of a digit starts from tenths then hundredths, thousandths , ten-thousandths , and so on.

PRACTICEIdentify the place value of the underlined digit.

1) 98.2035 = _________________ 6) 32.8116 = ____________________

2) 5.3910 = _________________ 7) 5.2 = ____________________

3) 6348.9045= _________________ 8) 62.3887 = ____________________

4) 1000.3857= _________________ 9) 3.5276 = ____________________

5) 638.5294 = _________________ 10) 6.3421 = ____________________

MORE PRACTICEIdentify the place value of the number three digit in the following expressions.

1) 8.314 ____________________ 6) 1.5283 ________________________

2) 295.6378 _________________ 7) 58.4385 _______________________

3) 125.9563 ________________ 8) 98.7635 _______________________

4) 85.6372 _________________ 9) 18.347 ________________________

5) 1.5234 __________________ 10) 11.03 ________________________

HOMEWORK

16

Identify the place value of the underlined digit.

1) 267.249 6) 725 703.825 2

2) 1 388.561 3 7) 2 140.725 3

3) 39 347.06 8) 65.182 9

4) 811 329.502 6 9) 52 385.042 1

5) 15 347.403 9 10) 629.315 6

Lesson No. 3

Reading and Writing Decimals

17

The decimal fraction has a value that is always less than one. Let us examine thevalue of each digit in this number.

TenThousands

Thousands hundreds tens ones tenths hundredths thousandths Tenthousandths

1 5 2 7 8 4 3 9 6

Whole Number

Decimal point

4 3 9 610 100 1 000 10 000

Decimal Fraction

Note that as we go to the right, the value of the digit becomes smaller.

Lets read more decimals.

Decimal read as5.2058 Five and two thousand fifty-eight ten thousandths3.0035 Three and thirty-five ten thousandths4.0005 Four and five ten thousandths0.3002 Three thousand two ten thousandths

PRACTICEWrite in words the decimal numbers below.

1) 12.5438_____________________________________________________________

2) 40.0538_____________________________________________________________

3) 19.0054_____________________________________________________________

4) 254.0309____________________________________________________________

5) 143.2800____________________________________________________________

6) 15.29 _______________________________________________________________

7) .006 ________________________________________________________________

8) 85.3000 _____________________________________________________________

9) 52.33781 ____________________________________________________________

10) 5.00005 ____________________________________________________________

MORE PRACTICEWrite these words in symbols.

18

1.Five hundred two and two ten-thousandths _____________________________

2. three and forty-five ten-thousandths __________________________________

3. twenty two and one hundred fifteen ten-thousandths ____________________

4. four and five hundred forty-two ten-thousandths_________________________

5. eight ten thousandths _____________________________________________

6. eleven and thirteen ten-thousandths _________________________________

7. one hundred forty and seventeen thousandths __________________________

8. five hundred six and seven hundred eight thousandths ____________________

9. one thousand four and five hundred eight thousandths _____________________

10. eight hundred one and eighteen ten-thousandths ________________________

11. one thousand thirty-seven ten thousandths _____________________________

12. sixty-four and one hundred forty-six thousandths ________________________

13. four thousand five and six thousand one ten thousandths __________________

14. twenty-seven and seven hundred two thousandths _______________________

15. sixteen and seven thousand forty-eight ten thousandths ___________________

HOMEWORKWrite the decimals for these fractions then write in words how you read them.

1) 5 Read: _____________________________________________________10 000 Write: _____________________________________________________

2) 52 Read: _____________________________________________________10 000 Write: _____________________________________________________

3) 143 Read: ______________________________________________________10 000 Write: ______________________________________________________

4) 2048 Read: ______________________________________________________10 000 Write: ______________________________________________________

5) 1 002 Read: ______________________________________________________10 000 Write: ______________________________________________________

Lesson No. 4

Writing Decimals in Standard and Expanded Notations

19

Study how the decimals written in standard notation can be written in expandednotation.

Standard Notation Expanded Notation1) 87.97 8 X 101 + 7 X 100 + 9 X 10-1 + 7 X 10-2

where:8 X 101 = 807 X 100 = 79 X 10-1 = .97 X 10-2 = .07

2) 265.256 2 X 102 + 6 X 101 + 5 X 100 + 2 X 10-1 + 5 X 10-2 +6X 10-3

Where:2 X 102 = 2006 X 101 = 605 X 100 = 52 X 10-1 = .25 X 10-2 = .056 X 10-3 = .006

PRACTICEWrite the following decimals in expanded notation.

1) 47.8234 = __________________________________________________________

2) 108.9672 = __________________________________________________________

3) 347.8371 = __________________________________________________________

4) 638.2439 = __________________________________________________________

5) 901.4318 = __________________________________________________________

6) 1 892.7325 = ________________________________________________________

7) 6 934.8253 = ________________________________________________________

8) 9 849.4772 = ________________________________________________________

9) 89 415.3473 = _______________________________________________________

10) 183 219.1827 = _____________________________________________________

MORE PRACTICEWrite these decimals written in words in their standard and expanded notations.

Decimals in Words Standard Notation Expanded Notation

1) eight ten thousandths

20

2) twenty-three tenthousandths

3) one hundred two tenthousandths

4) one and seven hundredeighteen ten thousandths

5) forty-five and ninety-seven ten thousandths

6) nineteen and ninety tenthousandths

7) sixty-two and twenty-sixten thousandths

8) ninety-four and onethousand eight tenthousandths

9) one hundred four andfifty-six thousandths

10) four hundred seventeenand ninety-five tenthousandths

HOMEWORKWrite the following in expanded notation.

1) 125.698 4) 6.3840

2) 6 284.08 5) 8 230.239 5

3) 64 238.1658

Lesson No. 5

Comparing and Ordering Decimals

21

In the decimal 11.86 which has a larger place value, the digit 8 or 6 ? Study thefigure below to find the answer.

The shaded part is 8 or 0.810

The dotted part is 6 or 0.06.100

Now, can you tell which is bigger, 0.8 or 0.06 ?

______________________________

Study more examples on how to compare decimals.

1) 4.9 > 4.09 > 4.009 > 4.0009

2) 1.1273 < 1.1274 < 1.1275 < 1.1276

3) 1.1 = 1.10 = 1.100 = 1.1000

PRACTICEA. Compare the decimals by writing > , < or =.

1) 14.07 _____ 14.17 6) 102.135 _____ 102.035

2) 1.1273 _____ 1.1274 7) 1.008 _____ 1.08

3) 843.010 _____ 843.0100 8) 19.354 _____ 19.35400

4) 5.09 _____ 5.0009 9) 20.2000 _____ 20.20

5) 10.600 _____ 10.601 10) 09.10 _____ 9.1

B. Arrange the given decimals from greatest to least.

1.238 2.476 8.983 1.2 2.4760

22

1)

2)

3)

4)

5)

MORE PRACTICEA. Compare these decimals by writing < , > or = in the blank.1) 0.162 _____ 0.106

2) 0.036 _____ 0.031

3) 0.4 _____ 0.40

4) 3.53 _____ 3.59

5) 7.01 _____ 7.103

6) 0.61 _____ 0.601

7) 9.2 _____ 9.200

8) 10.021 _____ 0.045

9) 0.7562 _____ 0.7559

10) 8.627 _____ 8.649

B. Order the decimals from the least to the greatest.

1) 0.5 0.49 0.53 0.51 __________________________________

2) 0.03 0.029 0.3 0.305 __________________________________

3) 1.237 1.273 1.027 1.230 __________________________________

4) 7.0 7.326 7.3 7.320 __________________________________

5) 0.0101 0.0099 0.011 0.0019 __________________________________

HOMEWORKA. Compare these decimals by writing < , > or = in the blank.

9.002 8.102 9.200 8.0102 8.1

12.0001 12.0010 12.0100 12.1000 12.1

25.1235 25.2235 25.0125 25.1 25.123

40.05 40.04 40.041 40.055 40.045

23

1) 0.008 _____ 0.0009

2) 0.19321 _____ 0.19231

3) 0.0019 _____ 0.0002

4) 12.7 _____ 12.7000

5) 0.999 _____ 0.99

6) 0.1 _____ 0.01

7) 0.2 _____ 0.02

8) 0.03 _____ 0.04

9) 0.21 _____ 0.021

10) 0.003 _____ 0.0003

B. Order the decimals from the least to the greatest.

1) 0.07 0.64 0.73 0.7 ____________________________________

2) 0.45 0.405 0.5 0.54 ____________________________________

3) 0.031 0.301 0.310 0.03 ____________________________________

4) 1.628 1.476 1.528 2.025 ____________________________________

5) 4.285 4.258 4.396 4.187 ____________________________________

Lesson No. 6

Rounding Off Decimals Through Ten Thousandths

24

Here are the rules in rounding off decimals.

1) If the nearest digit at the right of the digit to be rounded off is 5 or above, add 1 tothe digit to be rounded off and drop all the other digits to its right.

2) If the nearest digit at the right of the digit to be rounded off is 4 and below retainthe digit to be rounded off and drop all the digits at the right of the digit to berounded off.

Here are examples

NumberRounded to the Nearest

tenths hundredths thousandths Ten thousandths2.01234 2.0 2.01 2.012 2.01235.12344 5.1 5.12 5.123 5.12343.43211 3.4 3.43 3.432 3.43217.56789 7.6 7.57 7.568 7.56798.98765 9.0 8.99 8.988 8.9877

PRACTICEComplete the table below.

NumberRounded to the Nearest

tenths hundredths thousandths Ten thousandths1) 4.3815762) 2.9143253) 3.4354384) 9.0235425) 10.0203876) 15.3540327) 18.4390028) 20.3543899) 25.03010510) 30.438298

MORE PRACTICEA. Round off the following decimals to the nearest tenth.

1) 13.726 4 _____________________

2) 280.094 7 _____________________

3) 311.150 0 _____________________

4) 526.949 8 _____________________

5) 419.899 1 _____________________

6) 2 114.981 _______________________

7) 3 760.075 1 _______________________

8) 825.346 7 _______________________

9) 4 008.019 9 _______________________

25

10) 15 903.158 2 _______________________

B. Round off the above decimals to the nearest hundredth.

1) __________________________ 6) _________________________

2) __________________________ 7) _________________________

3) __________________________ 8) _________________________

4) __________________________ 9) _________________________

5) __________________________ 10) ________________________

HOMEWORKComplete the chart.

NumberRound off to the nearest

WholeNumber

Tenth Hundredth Thousandth TenThousandth

1) 4.237 692) 28.912 473) 88.004 564) 92.308 475) 108.206 396) 207.159 537) 398.204 188) 562.555 559) 712.897 6410) 899.125 30

26

CHAPTER THREE

Addition and Subtraction ofDecimals

Lesson No. 1 .. Estimate Sums and Differences of

Whole Numbers and Decimals

Lesson No. 2 Addition and Subtraction of

Decimals

Lesson No. 3. Addition and Subtraction of Mixed

Decimals

Lesson No. 4... Problem Solving Involving Addition

and Subtraction of Decimals

Lesson No. 1

ESTIMATE SUMS AND DIFFERENCES OF WHOLENUMBERS AND DECIMALS

27

Study how to estimate the sum of my money in the bank to the nearest hundredths.

Initial deposit P 15 278 . 4386 = P 15 278 . 44

Additional deposit 253 . 2500 = 253 . 25________________________________ __________________________

P 15 531 . 69

Study how to estimate the sum to the nearest tenths.



P 15 531 . 70

Study how to estimate the sum to the nearest ones.



P 15 531 . 00

PRACTICEEstimate the sum and difference to the indicated place value.

Given Ones Tenths1) 24.84397+ 123.29824

2) 476.19438+ 1 937.99825

3) 143.25376+ 22.14398

4) 6 725.58354+ 1 276.52145

5) 10 478.08238+ 11 725.97438

6) 473.8279- 121.2781

7) 921.8198- 141.3124

8) 1 763.9254- 651.9835

9) 4 381.1494- 1 211.9999

10) 14 738.9154- 1 488.1815

When estimating sums and differences, round off the given numbersfirst to the desired place value.

28

MORE PRACTICEEstimate the sum and difference to the indicated place value.

Given Ones Tenths1) 10 478.08238

+ 11 725.97438

2) 63.1345+ 94.76315

3) 51.048+ 36.78904

4) 6 391.4132+ 3 955.84761

5) 86 325.147+ 75 431.85623

6) 24.4812- 18.5769

7) 286.5718- 269.7923

8) 42 800.1443- 39 765.2576

9) 391 865.4579- 287 648.3651

10) 82 101.63578- 79 143.54651

Lesson No. 2

Addition and Subtraction of DECIMALS

29

In adding or subtracting decimals, remember to align the decimal points.To add or subtract, follow the process of adding or subtracting whole numbers.

Example:

0.5 + 0.687 + 0.16 + 0.8932 = n 0 . 8 0 0 0 ------- insert 3 zeros

0 . 6 8 7 0 ------- insert 1 zero

+ 0 . 1 6 0 0 ------- insert 2 zeros

0 . 8 9 3 2

2 . 5 4 0 2

Example:

0 . 5 - 0 . 2 8 7 3 = n 0 . 5 0 0 0 ----- insert 3 zeros

- 0 . 2 8 7 3

0 . 2 1 2 7

PRACTICEA. Add or subtract.

1) 0.38 + 0.47 = n 6) 0.23 0.16 = n

2) 0.412 + 0.638 = n 7) 0.97 0.178 = n

3) 0.529 + 0.646 = n 8) 0.232 0.046 = n

4) 0.4129 + 0.4738 = n 9) 0.76 0.057 = n

5) 0.284 + 0.325 = n 10) 0. 200 0.099 = n

B. Arrange the numbers vertically then add or subtract.

1) 0.048 + 0.027 + 0.049

2) 0.78 + 0.3621 + 0.691 + 0.3

3) 0.349 + 0.7005 + 0.2421 + 0.8 + 0.32

4) 0.45 0.2185

5) 0.83 0.52983

C. Arrange the numbers vertically then subtract.

1) 0.203 0.16 6) 5.7 3.276

2) 0.133 0.0857 7) 6 - 4.767

30

3) 0.9 0.41078 8) 9.0 4.73

4) 6.4 4.32 9) 3.4 1.26

5) 8.27 4.163 10) 47.6 9.06

MORE PRACTICEA. Add or subtract the following.

1) 0.8756 + 0.6872 11) 0.9265 0.7157

2) 0.7393+ 0.1877 12) 0.2457 0.2349

3) 0.3576 + 0.8546 13) 0.8765 0.5678

4) 0.2917 + +0.6358 14) 0.1542 0.1435

5) 0.6483 + 0.2529 15) 0.5937 0.3788

6) 0.5365 + 0.7325 16) 0.6911 0.3695

7) 0.5176 + 0.4958 17) 0.3276 0.1178

8) 0.3985 + 0.6358 18) 0.3361 0.1163

9) 0.3961 + 0.5559 19) 0.1473 0.1437

10) 0.3758 + 0.5898 20) 0.9154 0.2515

B. Add or subtract the following.

1) 0.3749 2) 0.6085 3) 0.7583

+ 0.4572 + 0.3937 + 0.2658

4) 0.5056 5) 0.3835

+ 0.3935 + 0.2786

6) 0.9651 7) 0.8570 8) 0.6593

- 0.5237 - 0.5356 - 0.3247

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9) 0.5635 10) 0.7651

- 0.1418 - 0.4239

HOMEWORKFind the sum or difference.

1) 0.684 2) 0.83 3) 0.73 4) 0.9002

+ 0.295 + 0.567 + 0.3073 + 0.8634

5) 0.84 6) 0.84 7) 0.540 8) 0.3

+ 0.8056 - 0.6358 - 0.2365 - 0.076

9) 0.6 10) 0.9702

- 0.1858 - 0.1694

Lesson No. 3

Addition and Subtraction of Mixed DecimalsA. Addition or subtraction of whole numbers and decimals.

32

Add 851 and 0.325 8 5 1. 0 0 0 ---- insert 3 zeros

+ 0. 3 2 5

8 5 1. 3 2 5

Subtract 0.61 from 12 1 2.0 0

- . 6 1

1 1.3 9

B. Addition or subtraction of mixed decimals

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

PRACTICEA Find the sum.

1) 38.07 + 2 = _____

2) 9.721 + 0.015 = _____

3) 9.4 + 11.2 + 8.75 = _____

4) 3.21 + 1.7 +6 + 3.749 = _____

5) 21.7 + 10.05 + 6.3 + 0.43 = _____

6) 453.029 + 319.84 + 95.23 = _____

7) 24.640 3 + 9.408 + 36.3 = _____

8) 16.52 + 4.311 + 8.591 + 8.846 = _____

9) 317.48 + 46.238 9 + 445 + 39.482 2 = _____

10) 143.217 + 9.45 + 307.020 + 258.726 = _____

11) 29.18 0.12 = _____

12) 8 7.256 1 = _____

13) 254.604 38 = _____

14) 342.16 79.7 = _____

15) 715.08 546.9 = _____

16) 237.2 84.317 = _____

17) 363 4.281 = _____

33

18) 157.546 148.347 = _____

19) 354.36 93.208 6 = _____

20) 1.000 43 0.065 18 = _____

B. Add or subtract these mixed decimals.

1) 82.4385 2) 5.435 3) 637.4 4) 82.19

+ 65.9685 + 6.762 + 389.85 + 45.02

48.3914 3.84 781.432 8.9

5) 43.16 6) 891.7 7) 38.6709 8) 15.84

+ 9.9 + 188.43 + .4388 + 1.467

16.432 870.108 5.67 87.432

9) 2.893 10) 523.4 11) 392 12) 3.806

- 1.8432 - 79.329 - 82.685 - 1.481

13) 9.36 14) 15.84 15) 324.5

- 7.1316 - 12.635 - 168.95

MORE PRACTICEAdd and subtract these decimals.

1) 14.39847 2) 38.217601 3) 7.38254 4) 9.76582

+35.10121 +31.421354 +2.10300 + 3.20000

5) 8.2 6) 9.36782 7) 18.25835 8) 67.43284

+ 5.73824 + 4.13299 + 21.23149 + 39.00355

34

9) 25.49003 10) 189.2542 11) 62.35 12) 87.218

+89.25405 + 352.53589 + 84.23617 + 69.56376

13) 25.29685 14) 187.38415 15) 128.39084 16) 256.7834

+ 60.0362 + 100.06398 + 657.67604 + 50.76

17) 35.17849 18) 245.65085 19) 63.385268 20) 761.16658

+ 34.067581 + 334.409574 +169.871834 + 88.08288

21) 4.38295 22) 43.438251 23) 87.43825 24) 83.70385

- 2.14174 - 24.317101 - 21.21432 - 44.28

25) 76.43479 26) 143.25376 27) 176.34321 28) 1 276.35439

- 61.32248 - 22.14398 - 174.12432 - 192.19999

29) 243.82 30) 63.9 31) 32.56878 32) 435.631

- 12.41254 - 1.8345 - 17.45986 - 315.9476

33) 8.5104 34) 639.1432 35) 68.235 36) 824.31

- 3.6789 - 395.5548 - 59.3596 - 487.6529

37) 78.5682 38) 40.208 39) 568.391 40) 735.38

- 69.47931 - 24.9564 - 487.45881 - 187.93345

HOMEWORKA. Add the following. B. Subtract the following

1) 7.6458 + 2.4936 = 1) 47.0143 - 19.2336 =

35

2) 38.256 + 27.967 = 2) 26.9206 - 9.8769 =

3) 48.7435 + 21.6950 = 3) 8.0008 - 5.4569 =

4) 15.614 + 7.9965 = 4) 10.9200 - 4.7513 =

5) 26.4579 + 48.9536 = 5) 35.4070 - 16.2135 =

6) 7.9192 + 4.1918 = 6) 58.0675 - 52.3679 =

7) 3.7586 + 2.5965= 7) 7.6000 - 3.5947 =

8) 54.6059 + 17.5064 = 8) 19.2143 - 13.3465 =

9) 76.5432 + 12.3654 = 9) 22.190 - 18.621 =

10) 89.765 + 5.438 = 10) 74.6401 - 29.8536 =

11) 57.6854 + 38.7543 = 11) 63.5397 - 30.7499 =

12) 67.8925 + 5.0308 = 12) 36.0070 - 23.2159 =

13) 6.9786 + 2.6143 = 13) 89.3005 - 59.7869 =

14) 68.0645 + 45.6321 = 14) 90.2763 - 44.6875 =

15) 34.1625 + 15.0809 = 15) 76.0000 - 67.8721 =

Lesson No. 4

Word Problems Involving DecimalsProblem No. 1

If mothers money of P 102 130.53 earned an interest of P 617.04 on November30, how much is her balance on that date after it was deducted P 123.41 for the tax ?

36

Let us analyze the problem together using the RSTUVW Approach.

PRACTICEAnswer the word problems.

1) During a vacation, Bens records showed gasoline purchases of 19.75 gallons , 15.4

gallons, 13.85 gallons and 21.06 gallons. How many gallons of gasoline did he buy ?

Asked: _____________________________________________________________

Given : ____________________________________________________________

Operation: __________________________________________________________

Number Sentence: ___________________________________________________

Answer: ____________________________________________________________

Read and analyze the problem carefully

Study the details of the problem.

Think of the operation or the processto be used.

Use the operation or the processthought of to answer the problem.

Verify the accuracy of the answer.

Write the final answer to the problem.

Problem: Mothers balance onNovember 30.

Solution:P 102 130.53 P 102 747.57+ 617.04 - 123.41P 102 747.57 102 624.16

Addition and Subtraction

Given:P 102 130.53 P 123.41P 617.04

Mother has a remaining balance ofP 102 624.16 in the bank on Nov. 30

Use the calculator to verify youranswer.

37

2) The perimeter of a triangle is equal to the sum of the length of its sides. Find the

perimeter of a triangle whose sides are 8.75 cm, 9.6 cm and 10.375 cm.

Asked: ___________________________________________________________

Given: ___________________________________________________________

Operation : ________________________________________________________

Number Sentence: _________________________________________________

Answer: __________________________________________________________

3) Rachel has P 3 316.40 in her savings account. If she made withdrawals of P 285.00,

P 472.46 and P 1 042.25, how much money is left in her account ?

Asked: _____________________________________________________________

Given: _____________________________________________________________

Operation: __________________________________________________________

Number Sentence: ___________________________________________________

Answer: ___________________________________________________________

4) One week a jogger ran the following distances : 15.3 km , 18.75 km , 19 km , 21.5 km

,25.375 km and 30.25 km. If his weekly average is 150 km, did he run less or more ?

Answer: ______________________________________________________________

5) Romeo has P 20 000 in available credit on his Visa charge card. If she purchases a

portable CD player for P 8 139.55, a boom box for P 399.95 and two way speakers

for P 3 425.05, how much available credit does she have left ?

Asked: _____________________________________________________________

Given: ______________________________________________________________

Operation: ___________________________________________________________

Number Sentence: ____________________________________________________

Answer: _____________________________________________________________

38

MORE PRACTICEAnalyze and solve the problems below. Choose the letter of the correct answer.

1) Two tourists traveled a total of 6 102.67 km during a tour. If they traveled 3 713.79

km by airplane and completed the rest of the tour by car, how many kilometers did

they travel by car ?

A) 9816.46 km B) 98164.6 km C) 2388.88 km D) 238.888 km

2) What is the perimeter of a triangle whose sides measure 27.15 cm, 36.8 cm and 39

cm ?

A) 102.95 cm B) 1029.5 cm C) 38965.68 cm D) 3896.568 cm

3) Mrs. Sta. Agueda spent the following amounts while shopping for her children: P

246.75 for an umbrella, P384.95 for a pair of shoes, P306.25 for a bag and P 311.10

for some small items.If she initially had P 1 500.00, how much money does she have

now ?

A) P 1 249.05 B) P 250.95 C) P 2 749.05 D) P 562.05

4) A barangay has a total road length of 184.75 km. If 99.54 km of this road had been

paved by the previous administration and 36.8 km by the present administration, how

much more remains to be paved ?

A) 321.09 km B) 173.14 km C) 136.34 km D) 48.41 km

5) Rosa wanted to give her mother a Bible which costs P 195.75 but she has saved

P 150.00 only. If her older sister gives her P 30.00 more, would Rosa be able to buy

the Bible ?

A) YES B) NO C) MAYBE D) CANNOT SAY

6) Junjun bought a backpack for P 165.50, notebooks for P 55.75 and other school

things for P 68.60. How much change should he get from P 500 ?

A) P 210.15 B) P 289.85 C) P 789.85 D) P 289.05

39

7) A triangle has sides that measure 26.718 m and 28.6 m. If its perimeter is 85.608 m,

what is the measure of the third side ?

A) 55.318 m B) 678.5268 m C) 30.29 m D) 64.62 m

8) Mac had two baggage that weighed 20.75 kg and 13.8 kg. The airplane he would

take allowed only 30 kg of baggage per person. By how much were his baggage

overweight ?

A) 6.95 kg B) 4.55 kg C) 64.55 kg D) 34.55 kg

9) Jill bought a kilo of rice at P 21.50 and 2.5 kg of sugar at P 55.90. How much change

should she get from P 100.00 ?

A) P 77.40 B) P 20.10 C) P 22.37 D) P 22.60

10) Lucille paid P 98.95 for a book, P 65.90 for a ream of bond paper, P 256.90 for a

pen set, and P 179.75 for a drawing set. How much change should she get if she

gave the salesclerk P 650 ?

A) P 601.50 B) P 1 201.50 C) P 48.50 D) P 327.20

HOMEWORK1) How much should the following pay for their orders ?

A) Rafael 2 kutsinta, tea

B) Tedjoy 1 suman, soft drink

C) Macky 2 banana cue, milk

D) Bernie 3 puto, coffee

Mc Jays Native Kakanin

kutsinta P 7.75 banana cue P 5.30 coffee P 11.25puto P 4.50 soft drink P 9.50 milk P 10.75suman P 5.25 tea P 10.85

40

E) Dawn 3 kutsinta, coffee

2) This year, a school parade was 4.06 km. Last year, the route was 3.97 km. How

much shorter was the parade last year ?

3) Edna saved P 0.95 on Friday and P 0.87 on Saturday. How much did Edna save in

two days ?

4) Father gave mother five hundred peso bill for marketing. Mother spent P 112.50 for

rice and P 161.75 for fish and meat. How much was left of the five hundred pesos ?

5) Aubrey had P 86.70 in savings. Her mom gave her P 50.00 more. After buying

materials for her project she had P 26.75 left. How much did the material cost ?

CHAPTER FOUR

41

Multiplying DecimalsLesson No. 1 .. Multiplying Decimals

Lesson No. 2 Multiplying Mixed Decimals by

Whole Numbers

Lesson No. 3. Multiplying Mixed Decimals by Mixed

Decimals

Lesson No. 4 Multiplying Decimals by 10, 100 and

1 000

Lesson No. 5.. Multiplying Decimals by 0.1 , 0.01

and 0.001

Lesson No. 6 . Problem Solving Involving

Multiplication of Decimals

Lesson No. 1

Multiplying Decimals Through Ten Thousandths

42

An easy way of multiplying decimals is to multiply the factors as if they are wholenumbers. Then count the number of decimal places of the factors and the total is thenumber of the decimal places in the product.

Here is an example of multiplying decimals :

. 4 5 2 decimal places

X . 3 8 2 decimal places

3 6 0

1 3 5

0. 1 7 1 0 4 decimal places

PRACTICEMultiply these.

1) 0.83 2) 0.38 3) 0.23 4) 0.49 5) 0.54

X 0.7 X 0.2 X 0.3 X 0.8 X 0.4

6) 0.374 7) 0.827 8) 0.395 9) 0.826 10) 0.934

X 0.9 X 0.8 X 0.6 X 0.4 X 0.2

11) 0.9855 12) 0.8246 13) 0.2796 14) 0.9288 15) 0.2541

X 0.8 X 0.3 X 0.4 X 0.6 X 0.7

16) 0.64 17) 0.35 18) 0.89 19) 0.75 20) 0.27

X 0.84 X 0.78 X 0.26 X 0.98 X 0.61

21) 0.583 22) 0.614 23) 0.279 24) 0.428 25) 0.549

X 0.15 X 0.34 X 0.25 X 0.84 X 0.62

26) 0.1257 27) 0.8249 28) 0.3277 29) 0.3641 30) 0.9421

43

X 0.42 X 0.82 X 0.79 X 0.32 X 0.54

31) 0.95 32) 0.65 33) 0.41 34) 0.78 35) 0.64

X 0.218 X 0.279 X 0.824 X 0.527 X 0.348

36) 0.826 37) 0.729 38) 0.342 39) 0.518 40) 0.394

X 0.984 X 0.349 X 0.378 X 0.824 X 0.964

41) 0.8942 42) 0.6499 43) 0.4782 44) 0.5297 45) 0.5279

X 0.824 X 0.961 X 0.341 X 0.671 X 0.946

46) 0.2846 47) 0.9277 48) 0.6382 49) 0.8266 50) 0.8394

X 0.8247 X 0.9352 X 0.8645 X 0.3213 X 0.6152

MORE PRACTICEMultiply the following decimals.

1) 0.23 2) 0.59 3) 0.89 4) 0.91 5) 0.57

X 0.08 X 0.06 X 0.05 X 0.07 X 0.09

6) 0.17 7) 0.97 8) 0.64 9) 0.63 10) 0.58

X 0.84 X 0.31 X 0.87 X 0.42 X 0.46

11) 0.589 12) 0.284 13) 0.349 14) 0.389 15) 0.642

X 0.37 X 0.45 X 0.37 X 0.21 X 0.96

11) 0.641 12) 0.272 13) 0.645 14) 0.542 15) 0.319

X 0.507 X 0.219 X 0.197 X 0.342 X 0.247

16) 0.8441 17) 0.5186 18) 0.1224 19) 0.2135 20) 0.2187

44

X 0.2184 X 0.2581 X 0.8156 X 0.2415 X 0.5318

HOMEWORKMultiply the following decimals.

1) 0.32 2) 0.826 3) 0.9578 4) 0.3527 5) 0.1852

X 0.5 X 0.27 X 0.824 X 0.2759 X 0.52

Lesson No. 2

Multiplying Mixed Decimals by Whole Number

45

Here is an example of multiplying mixed decimals by a whole number.

3 . 2 4 ( two decimal places )

X 5

1 6.2 0 ( two decimal places )An easy way of multiplying decimals is to multiply the factors as if they are whole

numbers. Then count the number of decimal places of the factors and the total is thenumber of decimal places in the product.

PRACTICEMultiply the following.

1) 4.24 2) 7.84 3) 3.65 4) 8.29 5) 5.17

X 6 X 4 X 7 X 3 X 9

6) 9.236 7) 2.743 8) 1.615 9) 6.893 10)5.398

X 12 X 54 X 28 X 91 X 72

11) 8.0165 12) 7.9503 13) 1.4187 14) 3.2346 15) 4.7860

X 6 X 9 X 5 X 7 X 3

16) 6.3702 17) 5.5921 18) 2.9150 19) 8.0703 20) 4.1658

X 52 X 34 X 14 X 37 X 69

MORE PRACTICEMultiply the following.

1) 1.38 2) 2.67 3) 35.08 4) 35.08 5) 14.34

X 18 X 3 X 23 X 71 X 35

6) 45.379 7) 41.327 8) 35.633 9) 83.621 10) 52.674

46

X 85 X 96 X 27 X 33 X 94

11) 6.3278 12) 2.3975 13) 6.8214 14) 5.2288 15) 6.3419

X 6 X 1 X 9 X 5 X 7

16) 351.2895 17) 234.1822 18) 159.3164 19) 321.2854 20) 217.3189

X 8 X 3 X 4 X 9 X 2

HOMEWORKMultiply the following.

1) 2.89 2) 3.84 3) 6.33 4) 7.28 5) 9.31

X 2 X 8 X 4 X 5 X 7

6) 12.567 7) 34.285 8) 51.611 9) 57.319 10) 61.379

X 5 X 6 X 9 X 3 X 8

11) 3.2894 12) 6.8279 13) 5.2377 14) 9.1622 15) 3.7755

X 21 X 34 X 52 X 97 X 68

Lesson No. 3

Multiplying Mixed Decimals by Mixed DecimalsStudy the example below.

47

23.68 ( 2 decimal places )X 3.1 ( 1 decimal place )23 68

71 0473.408 ( 3 decimal places )

PRACTICEMultiply the following.

1) 2.7 2) 3.8 3) 9.4 4) 3.1 5) 5.7

X 2.4 X 6.1 X 1.1 X 6.7 X 9.2

6) 3.65 7) 6.28 8) 9.27 9) 3.71 10) 5.61

X 5.2 X 7.1 X 8.4 X 5.4 X 6.3

11) 32.891 12) 52.894 13) 63.821 14) 54.375 15) 61.975

X 5.21 X 6.21 X 5.37 X 8.74 X 6.25

16) 63.2189 17) 63.2877 18)95.2118 19)58.3122 20) 14.2975

X 6.2 X 1.55 X 3.218 X 7.9 X 6.34


48

1) 3.8 2) 9.8 3) 4.7 4) 6.7 5) 3.1

X 2.8 X 6.7 X 5.9 X 8.1 X 7.2

6) 6.34 7) 8.19 8) 9.27 9) 8.63 10) 9.34

X 6.4 X 7.5 X 9.4 X 4.2 X 6.5

11) 8.52 12) 6.34 13) 7.88 14) 4.22 15) 9.12

X 6.21 X 2.54 X 1.94 X 7.54 X 9.35

16) 7.254 17) 6.934 18) 4.213 19) 9.212 20) 2.643

X 5.62 X 3.21 X 3.96 X 6.24 X 5.11

21) 3.5218 22) 6.3124 23) 8.2941 24) 6.3227 25) 6.2174

X 3.8 X 5.21 X 5.46 X 6.315 X 6.41

HOMEWORKMultiply the following.

1) 6.9 2) 9.234 3) 6.2491 4) 57.82 5) 22.143

X 2.8 X 2.5 X 1.56 X 8.7 X 6.4

6) 6.9724 7) 5.61 8) 6.41 9) 621.34 10) 521.8216

X 3.21 X 3.1 X 9.2 X 6.94 X 7.9

Lesson No. 4

Multiplying Decimals by 10, 100 and 1 000Study the following examples:

A B C

49

0.8 X 10 = 8 0.8 X 100 = 80 0.8 X 1 000 = 8000.34 X 10 = 3.4 0.34 X 100 = 34 0.34 X 1 000 = 3400.215 X 10 = 2.15 0.215 X 100 = 21.5 0.215 X 1 000 = 2150.5432 X 10 = 5.432 0.5432 X 100 = 54.32 0.5432 X 1 000 = 543.2

Now, can you give a short cut for multiplying a decimal number by number like10, 100 and 1 000 ?

Multiplying decimals by 10 , 100 and 1 000 makes a greater number, so movethe decimal point to the right.

When multiplying decimals by powers of 10, move the decimal point to the rightas many places as there are zeros in the multiplier. Add zero or zeros when needed.

PRACTICEComplete the table.

Decimal X 10 X 100 X 1 0001) 0.9342) 0.543) 0.0764) 3.2485) 73.64896) 676.54987) 835.9678) 1245.386759) 2106.277610) 6790.28345Complete the table below by supplying the product of the given factors.

Decimal X 10 X 100 X 1 0001) 213.0492) 235.1353) 841.2094) 732.1435) 123.45616) 234.56747) 892.02038) 412.05329) 925.214510) 373.8214


1) 0.386 2) 0.86 3) 0.36 4) 0.473 5) 0.496

X 10 X 100 X 1000 X 1000 X 10

50

6) 0.85 7) 0.7 8) 0.512 9) 0.93 10) 0.51

X 1000 X 1000 X 100 X 100 X 10

11) 0.289 12) 0.009 13) 0.23 14) 0.956 15) 0.365

X 1000 X 1000 X 1000 X 100 X 10

16) 0.39 17) 0.871 18) 0.004 19) 0.70 20) 0.603

X 1000 X 1000 X 1000 X 100 X 10

Multiply these orally.

1) 0.826 x 10 = _____ 0.826 X 100 = _____ 0.826 X 1000 = _____

2) 0.632 X 10 = _____ 0.632 X 100 = _____ 0.632 X 1000 = _____

3) 0.068 X 10 = _____ 0.068 X 100 = _____ 0.068 X 1000 = _____

4) 0.9 X 10 = _____ 0.9 X 100 = _____ 0.9 X 1000 = _____

5) 0.43 X 10 = _____ 0.43 X 100 = _____ 0.43 X 1000 = _____

HOMEWORKComplete the table.

Decimal X 10 X 100 X 1 0001) 2.56722) 32.183) 0.94234) 3.88165) 21.672116) 63.218947) 0.21948) 6.285459) 364.2816410) 6.38411

Lesson No. 5

Multiplying Decimals by 0.1, 0.01 and 0.001 We move the decimal point 1 place to the left when the decimal number is

multiplied by 0.1. Example:

51

18.2 X 0.1 = 1 8 . 2 = 1.82

We move the decimal point 2 places to the left when the decimal number ismultiplied by 0.01. Example:

18.2 X 0.01 = 1 8 . 2 = 0.182

We move the decimal point 3 places to the left when the decimal number ismultiplied by 0.001.Example:

18.2 X 0.01 = 01 8 . 2 = 0.0182

PRACTICEMultiply these numbers by:

Factors 0.1 0.01 0.0011) 38.42) 397.83) 4 128.764) 178.735) 839.256) 1 473.637) 4 472.1988) 81 813.4189) 21 934.147310) 58 254.034511) 788.085412) 1 666.76513) 5 795.27514) 7 351.37915) 75 582.14516) 7 851.9817) 95.3318) 5 678.43219) 859.59620) 6 785.034

MORE PRACTICEGive the missing numbers in the table.

52

Factors 0.1 0.01 0.0011) 8.314 831.42) 478.2 47.823) 9 354 93.544) 7 638.2 76.3825) 9 876.35 987.6356) 3 468.4 34.6847) 975.13 9.75138) 635.4279) 1 025.631 10.2563110) 49 875.42 498.7542

Multiply the following.

1) 3256.1978 2) 63.2194 3) 0.52 4) 1.375 5) 621.32

X 0.001 X 0.01 X 0.1 X 0.001 X 0.01

6) 0.342 7) 12.3 8) 1457.36 9) 921.3 10) 8245.3214

X 0.001 X 0.01 X 0.1 X 0.01 X 0.001

HOMEWORKComplete the table by multiplying the decimals with 0.1, 0.01 and 0.001.

Decimals X 0.1 X 0.01 X 0.0011) 324.122) 9 625.33) 634.0574) 0.2185) 2.316) 361.2117) 348.968) 6325.129) 85.3210) 6.3

Lesson No. 6

Problem Solving Involving Multiplication ofDecimals

Analyze the problem below.

53

Rosemarie sent two packages, each weighing 1.85 kg, to her brothers in Hong Kong. Ifshe paid P 175.00 per kg of the package, how much did she pay in all ?

What is asked ? What are given ? What are the operations to be used ? Write the equation to solve the problem ? What is your answer ?

Answer more problems !

PRACTICEAnswer the problems below .

1) Edna needs 0.95 m of ribbon to trim a shirt. If a ribbon costs P 0.75 metre how much

will the ribbon cost ?

Asked: ______________________________________________________________

Given : ______________________________________________________________

Operations: __________________________________________________________

Equation: ____________________________________________________________

Answer: _____________________________________________________________

2) Carmen can swim 12 meters in one minute. How far can she swim in 30 minutes ?

Asked: ______________________________________________________________

Given : ______________________________________________________________

Operations: __________________________________________________________

Equation: ____________________________________________________________

Answer: _____________________________________________________________

3) Milagros bought 6 siopao worth P 9.50 each. How much did she pay in all ?

Asked: ______________________________________________________________

Given : ______________________________________________________________

Operations: __________________________________________________________

Equation: ____________________________________________________________

54

Answer: _____________________________________________________________

4) If she added 13 large soft drinks for her friends which cost P 15.50 each, what is the

total cost of the softdrinks ?

Asked: ______________________________________________________________

Given : ______________________________________________________________

Operations: __________________________________________________________

Equation: ____________________________________________________________

Answer: _____________________________________________________________

5) What is the area of Aidas backyard if it is 15.935 m long and 6.45 m wide ?

Asked: ______________________________________________________________

Given : ______________________________________________________________

Operations: __________________________________________________________

Equation: ____________________________________________________________

Answer: _____________________________________________________________

6) Dante measured their dining table. Its length is 2.643 m while its width is 1.45 m.

What is the area of the dining table ?

Asked: ______________________________________________________________

Given : ______________________________________________________________

Operations: __________________________________________________________

Equation: ____________________________________________________________

Answer: _____________________________________________________________

7) In Marikina Elementary, 100 pupil in Grade IV, V, VI joined the field trip in Tagaytay

City. If each pupil paid P 182.25 , how much is the total collection ?

Asked: ______________________________________________________________

Given : ______________________________________________________________

55

Operations: __________________________________________________________

Equation: ____________________________________________________________

Answer: _____________________________________________________________

8) A soft drinks company gave out 1 000 free t-shirts to those who patronage their

products. Each t-shirt costs P 35.83. How much did the soft drinks company pay for

the t-shirts?

Asked: ______________________________________________________________

Given : ______________________________________________________________

Operations: __________________________________________________________

Equation: ____________________________________________________________

Answer: _____________________________________________________________

9) A coach buys 19 pairs of socks at P 68.75 per pair. What is the total cost of the

socks?

Asked: ______________________________________________________________

Given : ______________________________________________________________

Operations: __________________________________________________________

Equation: ____________________________________________________________

Answer: _____________________________________________________________

10) Ellen buys 53 gallons of gasoline at P 79.09 per gallon. What is the total cost of the

gasoline ?

Asked: ______________________________________________________________

Given : ______________________________________________________________

Operations: __________________________________________________________

Equation: ____________________________________________________________

Answer: _____________________________________________________________

MORE PRACTICEAnalyze and solve the following problems.

56

1) Kenny made a down payment of P 1 750 on a camcorder and agreed to make

payments of P 520.85 per month for one year. Find the total cost of the camcorder.

2) Joel earns P 8 355.35 per month. If Karen earns twice as much as Joel, how much

do they earn together ?

3) The cost of a photocopy in store A is P 0.35 while in store B it costs P 0.53. How

much do I save if I had 317 pages photocopied at store A instead of store B ?

4) The Avis Car Rental Company charges P 1 243.45 per day and P 20 per km to rent

their cars. The ABC Car Rental Company charges P 1 048.25 per day and P 21.25

per km. Which company will you choose if you rent a car for two days and travel 325

km ?

5) If a meter of cloth cost P 72.95 , how much would 6.4 meters cost ?

HOMEWORKSolve the following problems .

1) Mang Elo, a balut vendor, bought 100 new duck eggs at P 3.65 each. How much did

he pay for all the eggs ?

2) Mrs. Pasana baked 1 000 pineapple pie for a party. If a pie costs P 17.85, how much

did the 1 000 pie cost ?

3) A cone of ice cream cost P 16.25, how much in all did the 6 children spend on ice

57

cream ?

4) Mang Juan sold 46 cotton candies at P 2.15 each. How much altogether is the cost of

the cotton candies ?

5) A rope measures 4.63 m. How long is it in centimeters ?

6) The peso dollar exchange rate is P 39.25. If Justin had $ 27.50, how much would

this amount in pesos ?

7) A factory needs 0.085 ton of glass and 0.012 of rubber to build a truck. How many

tons to glass and rubber are needed for 295 trucks ?

8) A car designed for use as a police car is priced at P 502 200. For municipalities

buying 10 or more units, the price is P 475 500.25. What would be the total cost of 25

cars ?

9) If a car travels 55.6 km an hour, how far will it travel in 8 hours ?

10) Rosemarie sent two packages, each weighing 1.85 kg, to her brothers in Hong

Kong. If she paid P 175.00 per kg of the package, how much did she pay in all ?

58

Chapter FiveDivision of Decimals

Lesson No. 1 Kinds of DecimalsLesson No. 2 Divide Whole Numbers by DecimalsLesson No. 3 Divide Decimals by DecimalsLesson No. 4 Divide Mixed Decimals and Whole

NumbersLesson No. 5 Divide Mixed Decimals by Mixed DecimalsLesson No. 6 Divide Decimals by 10 , 100 1,000 MentallyLesson No. 7 Divide Decimals by 0.1, 0.01, 0.001

MentallyLesson No. 8 Solve Word Problems Involving Division of

Decimals

Lesson No. 1

KINDS OF DECIMALSDecimals can be classified as terminating or non terminating.

59

1) TERMINATING Decimal is one that has a definite ending decimal place value.

Example:

_ 515 / 255

25550

2) NON TERMINATING Decimal have an infinite number of decimal places

a) Repeating example 0.333333333333

b) Non repeating example 0.325841562

Lesson No. 2

Divide Whole Numbers by Decimals and Vice VersaCheck whether you can divide correctly all the numbers given below.

1) 4 / 6 484 2) 6 / 7 044 3) 7 / 9 185 4) 22 / 4850

How about when you divide decimals. Study the example below.

60

1) 0.9 / 63 - move the decimal one place to the right

9 / 630 - add one zero to the dividend

0709 /630 - divide

06363

00X

____2) 2/0.24 - write a decimal directly above the dividend

.122/0.24 - divide

244X

PRACTICEA. Divide the following.

1) 72 0.8 = _____ 6) 210 0.12 = _____

2) 455 0.5 = _____ 7) 800 0.20 = _____

3) 826 0.4 = _____ 8) 564 0.25 = _____

4) 49 0.7 = _____ 9) 1256 0.16 = _____

5) 936 0.3 = _____ 10) 981 0.3 = _____

61

B. Divide the following.

1) 0.756 9 = _____ 6) 0.846 6 = _____

2) 0.966 6 = _____ 7) 0.434 7 = _____

3) 0.686 2 = _____ 8) 0.775 5 = _____

4) 0.714 7 =_____ 9) 0.872 8 = _____

5) 0.305 5 = _____ 10) 0.316 2 = _____

MORE PRACTICEDivide the following.

1) 696 0.09 = _____ 6) 0.936 78 = _____

2) 888 0.37 = _____ 7) 0.924 66 = _____

3) 975 0.25 = _____ 8) 0.939 69 = _____

4) 595 0.85 = _____ 9) 0.832 34 = _____

5) 684 0.04 = _____ 10) 0.833 49 = _____

HOMEWORKDivide the following.

1) 183 0.61 = _____ 6) 0.241 2 = _____

2) 900 0.45 = _____ 7) 0.2564 80 = _____

3) 598 0.22 = _____ 8) 0.98324 16 = _____

4) 775 0.15 = _____ 9) 0.925 5 = _____

5) 828 0.92 = _____ 10) 0.821 4 = _____

Lesson No. 3

Divide Decimals by DecimalsWhen dividing decimals, move the decimal point of the divisor until it becomes a

whole number. Move also the decimal of the dividend the same number of places the

decimal point of the divisor has been moved. When the divisor is already a whole

number, you can proceed to division. Make sure the decimal point of the quotient is

directly above the newly placed decimal point of the dividend.

Example:

62

_______ ______0.52 / 0.85241 52 / 85.241 2 moves

_______ ______0.238 / 0.25419 238 / 254.19 3 moves

______ _____0.5 / 0.351 5 / 3.51 1 move

PRACTICEDivide the following.

1) 0.72 0.3 = _____ 6) 0.96 0.8 = _____

2) 0.96 0.4 = _____ 7) 0.441 0.07 = _____

3) 0.387 0.09 = _____ 8) 0.558 0.06 = _____

4) 0.516 0.6 = _____ 9) 0.218 0.02 = _____

5) 0.81 0.9 = _____ 10) 0.61284 0.04 = _____


1) 0.96 0.6 = _____ 4) 0.381 0.5 = _____

2) 0.32 0.04 = _____ 5) 0.867 0.05 = _____

3) 0.212 0.08 = _____


1) 0.24 0.012 = _____ 4) 0.55 0.011 = _____

2) 0.36 0.6 = _____ 5) 0.75 0.25 = _____

3) 0.42 0.14 = _____

Lesson No. 4

Division of Mixed Decimals and WholeNumbers

Study the example below.

Example 1:

_______

3.2 / 160 - move the decimal of the divisor one place to the right and add

63

one zero to the dividend

____5032 / 1600 - divide

160000

Example 2:

____4 / 2.4 - place a decimal point in the quotient directly above the decimal

point in the dividend

0.64 / 2.4 - divide

024240

PRACTICEDivide the following.

___ ____ ___1) 7.4 / 15 2) 9.6 / 541 3) 8.5 / 22

___ ____ ____4) 1.5 / 49 5) 2.5 / 475 6) 3 / 9.6

_____ _____ _____ _____7) 9 / 1.89 8) 5 / 36.5 9) 16 / 28.80 10) 8 / 5.60


____ _____1) 1.84 / 273 6) 9 / 1.42

____ ____2) 1.4 / 24 7) 42 / 4.31

_____ ____3) 2.9 / 4 365 8) 19 / 14.2

____ ____4) 2.1 / 342 9) 48 / 16.3

64

______ _____5) 7.8 / 3 568 10) 15 / 28.5


______ _____1) 3.5 / 241.5 6) 92 / 579.6

_____ ____2) 4.3 / 51.6 7) 18 / 85.3

______ _____3) 5.16 / 206.41 8) 51 / 36.51

______ ____4) 10.9 / 62.981 9) 13 / 58.5

_______ ____5) 6.5 / 374.21 10) 21 / 75.6

Lesson No. 5

Division of Mixed Decimals and MixedDecimals

Mixed decimals are divided in the same way as whole numbers. In dividing mixed

decimals by mixed decimals, the decimal point in the divisor is moved to the right to

make it a whole number. You only have to move the decimal place of the dividend the

same number the decimal point was moved in the divisor, unless if the dividend in a

65

whole number then you add zero. Align the decimal point of the quotient to that of the

dividend.

PRACTICE

Divide. Classify the quotient as to terminating or non terminating. If it is non terminating,

classify if it is repeating or non repeating. Write only the letter on the space before the

number.

A. terminating decimal C. non terminating non repeating

B. non terminating, repeating decimal decimal

____ ___________1) 4.2 / 12.4 _____6) 1.52 / 395.2

____ _________2) 4.1 / 16.4 _____7) 4.5 / 4.28

______ _________3) 3.12 / 7.3008 _____8) 6.3 /55.2

______ ___________4) 3.60 / 311.04 _____9) 7.42 / 244.86

______ __________5) 25.4 / 171.45 _____10) 2.4 / 873.5

MORE PRACTICE

Divide. Classify the quotient as to terminating or non terminating. If it is non terminating,


number.



66

_____1) 13.5 4.5 = ____ _____6) 501.6 62.7 = ____

_____2) 6.08 7.6 = ____ _____7) 122.1 11.1 = ____

_____3) 73.5 24.5 = ____ _____8) 4.278 34.5 = ____

_____4) 112.2 1.87 = ____ _____9) 2.06 10.3 = ____

_____5) 2.12 21.2 = ____ _____10) 14.629 92 4.8 = _____

HOMEWORKDivide. Classify the quotient as to terminating or non terminating. If it is non terminating,


number.



_____ 1) 26.645 7.3 = ____ _____ 6) 389.45 4.4 = ____

_____ 2) 21.505 4.25 = ____ _____ 7) 892.52 2.06 = ____

_____ 3) 72.4 3.62 = ____ _____ 8) 9 182.17 8.005 = ____

_____ 4) 147.82 2.3 = ____ _____ 9) 431.6 1.3 = ____

_____ 5) 473.09 3.9 = ____ _____ 10) 5 045.9 1.8 = ____

Lesson No. 6

Divide Decimals by 10 , 100 1,000 MentallyWhen a decimal is to be divided by:

10, move the decimal point 1 place to the left to get the quotient 100, move the decimal point 2 places to the left to get the quotient 1 000, move the decimal point 3 places to the left to get the quotient

EXAMPLES:

148.2 10 = 14.82

67

148.2 100 = 1.482

148.2 1 000 = 0.1482

The number of zeros in the divisor will tell you the number of places to the left ofthe decimal point that would be skipped.

PRACTICEDivide these numbers by 10, 100 and 1 000.

DIVIDEND 10 100 1 0001) 5 147.42) 2 183.63) 3 452.24) 8 318.185) 9 493.376) 27 345.497) 39 146.328) 54 987.189) 176 347.4510) 882 963.7411) 330 153.112) 418 253.1813) 651 210.5414) 531 053.4915) 781 255.3116) 2.36417) 8.34218) 52.621719) 614.3284120) 6.328

MORE PRACTICE

Give the missing numbers in the table.

FACTORS 10 100 1 0001) 4 381.2 43.8122) 963.47 9.63473) 157.293 15.72934) 6 768.39 676.8395) 1 982.418 198.24186) 3 562.1 43.812

68

7) 5 327.8 532.788) 91 025.83 9 102.5839) 6 232.4 62.32410) 8 135.87 81.3587

HOMEWORK

Divide these numbers as fast as you can.

1) 43.8 10 = __________ 11) 59 378.14 100 = __________

2) 196.47 10 = __________ 12) 41 821.36 100 = __________

3) 343.18 10 = __________ 13) 97 415.43 100 = __________

4) 456.39 10 = __________ 14) 186 244.35 1 000 = __________

5) 1 415.43 10 = __________ 15) 246 132.89 1 000 = __________

6) 9 823.93 10 = __________ 16) 655 421.37 1 000 = __________

7) 47 383.2 100 = __________ 17) 198 257.13 1 000 = __________

8) 91 413.73 100 = __________ 18) 888 345.39 1 000 = __________

9) 47 413.73 100 = __________ 19) 197 463.84 1 000 = __________

10) 49 215.88 100 = __________ 20) 546 217.54 1 000 = __________

Lesson No. 7

Divide Decimals by 0.1 , 0.01 , 0.001 MentallyWhen dividing decimal by:

0.1, move the decimal point of the dividend to one place to the right to get the

quotient

0.01, move the decimal point of the dividend to two places to the right to get the

quotient

69

0.001, move the decimal point of the dividend to three places to the right to get

the quotient

EXAMPLE:

43.2 0.1 = 432 5.2371 0.1 = 52.371

43.2 0.01 = 4320 5.2371 0.01 = 523.71

43.2 0.001 = 43200 5.2371 0.001 = 5237.1

PRACTICEDivide these mentally.

DIVIDEND 0.1 0.01 0.0011) 4.84712) 15.32213) 18.19624) 35.43255) 95.21476) 12.17327) 89.24738) 381.19259) 473.154310) 2 135.218411) 2 529.68512) 1 283.91213) 7 568.40514) 2 567.83415) 2 456.585216) 632.1217) 1284.318) 82.619) 6.220) 1285.34

MORE PRACTICEGive the mixing numbers in the table.

DIVIDEND 0.1 0.01 0.0011) 15.39432) 417.21533) 934.24764) 81 529.45) 4 192.15766) 351.847) 90.8048) 3 344.95

70

9) 4 376.37 81 529.410) 7 611.663

HOMEWORKDivide the following mentally.

1) 6.32 0.001 = __________ 11) 8.2 0.01 = __________

2) 85.32 0.001 = __________ 12) 985.21 0.001 = __________

3) 125.4 0.01 = __________ 13) 9.21 0.1 = __________

4) 854.3671 0.1 = ___________ 14) 2.1 0.1 = __________

5) 641.237 0.1 = __________ 15) 5.24 0.001 = __________

6) 6.3218 0.01 = __________ 16) 85.21 0.1 = __________

7) 954.2 0.1 = __________ 17) 96.315 0.01 = __________

8) 9.2174 0.001 = __________ 18) 6.12 0.01 = __________

9) 6.8 0.001 = __________ 19) 6.2457 0.01 = __________

10) 96.2485 0.1 = __________ 20) 5.2 0.01 = __________

Lesson No. 8

PROBLEM SOLVING INVOLVING DIVISIONOF DECIMALS

Analyze the problem below.

A customer of Aling Letty paid Php 217.50 for 3 kilos of chicken. How muchdid Aling Letty charge for each kilo of chicken ? What is asked ? What are given ? What are the operations to be used ?

71

Write the equation to solve the problem ? What is your answer ?

Answer more problems!

PRACTICEAnswer the word problems below.

1) Mrs. Lituanias class has to raise Php 287.50 for a globe in Hekasi class. There are50 pupils in the class. How much will each pupil contribute ?

Asked: ________________________________________________________________

Given: ________________________________________________________________

Operation: _____________________________________________________________

Number Sentence: ______________________________________________________

Answer: _______________________________________________________________

2) Mrs. Malabanan bought 5 reams of coupon bond worth Php 447.50. How much dideach ream of coupon bond cost ?

Asked: ________________________________________________________________

Given: ________________________________________________________________

Operation: _____________________________________________________________

Number Sentence: ______________________________________________________

Answer: _______________________________________________________________

3) Zaldy cut a bamboo 12 meters long. If he were to cut it into pieces 1.2 m long, howmany pieces of bamboo will there be ?

Asked: ________________________________________________________________

Given: ________________________________________________________________

Operation: _____________________________________________________________

Number Sentence: ______________________________________________________

Answer: _______________________________________________________________

4) How many pieces of cloth each 4.2 m long can be cut from a 24 meter piece ?

Asked: ________________________________________________________________

Given: ________________________________________________________________

Operation: _____________________________________________________________

Number Sentence: ______________________________________________________

Answer: _______________________________________________________________

72

5) Mylene bought 7.5 meters of tetoron at Php 198.75. How much does a meter cost ?

Asked: ________________________________________________________________

Given: ________________________________________________________________

Operation: _____________________________________________________________

Number Sentence: ______________________________________________________

Answer: _______________________________________________________________

MORE PRACTICEAnswer the word problem below.

1) A container full of papayas weigh 22.1 kilograms. If each papaya weighs 1.2kilograms and the container weighs 0.5 kg, how many pieces were in the container ?

Asked: ________________________________________________________________

Given: ________________________________________________________________

Operation: _____________________________________________________________

Number Sentence: ______________________________________________________

Answer: _______________________________________________________________

2) Mrs. Dela Paz bought eggs for Php 686.40. If eggs cost Php 26.40 per dozen, howmany dozen did she buy ?

Asked: ________________________________________________________________

Given: ________________________________________________________________

Operation: _____________________________________________________________

Number Sentence: ______________________________________________________

Answer: _______________________________________________________________

3) Dianne sold 166.25 kg of grapes. If each grapes weighed about 1.75 kg, how manypacks of grapes did Dianne sell ?

Asked: ________________________________________________________________

Given: ________________________________________________________________

Operation: _____________________________________________________________

Number Sentence: ______________________________________________________

Answer: _______________________________________________________________

4) Ana earns Php 43.25 per hour. If her salary for one week was Php 2 335.50 , howmany hours did she work ?

Asked: ________________________________________________________________

73

Given: ________________________________________________________________

Operation: _____________________________________________________________

Number Sentence: ______________________________________________________

Answer: _______________________________________________________________

5) Three men paid a total of P 1 026 for lunch and the cost of the meal is dividedequally. How much did each men pay ?

Asked: ________________________________________________________________

Given: ________________________________________________________________

Operation: _____________________________________________________________

Number Sentence: ______________________________________________________

Answer: _______________________________________________________________

HOMEWORKAnswer the word problem below.

1) Juans odometer read 38 796.1 km at the beginning of his trip. When the trip ended, it

read 39 365.8 km. If he used 31.5 gallons of gasoline, for the whole travel, how many

kilometers did he travel per gallon of gasoline ?

Asked: ________________________________________________________________

Given: ________________________________________________________________

Operation: _____________________________________________________________

Number Sentence: ______________________________________________________

Answer: _______________________________________________________________

2) A ream of bond paper is 6.21 cm thick. If each sheet of paper is 0.003 cm thick, how

many sheets of paper are there in two reams ?

Asked: ________________________________________________________________

Given: ________________________________________________________________

Operation: _____________________________________________________________

Number Sentence: ______________________________________________________

Answer: _______________________________________________________________

3) Rosa found out that she had read 3 618 words in 4.02 minutes. How many words did

she read per minute ?

Asked: ________________________________________________________________

74

Given: ________________________________________________________________

Operation: _____________________________________________________________

Number Sentence: ______________________________________________________

Answer: _______________________________________________________________

4) If my watch is late by 4.5 seconds per hour, by how many minutes will it be late in two

days ?

Asked: ________________________________________________________________

Given: ________________________________________________________________

Operation: _____________________________________________________________

Number Sentence: ______________________________________________________

Answer: _______________________________________________________________

5) A contractor finished 4.75 kilometers for a new highway in 5 days. On the average,

how many kilometers of the highway were finished each day ?

Asked: ________________________________________________________________

Given: ________________________________________________________________

Operation: _____________________________________________________________

Number Sentence: ______________________________________________________

Answer: _______________________________________________________________

Math Module First Quarter

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