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- 1. 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
- 2. RULE To change a fraction to decimal, divide the numerator by the denominator up to the desired number of decimal places.
- 3. I. Give the meaning and explain the use of the following 1. How to change fractions to decimal? 2. What are the rules in changing fractions to decimals? 3. What is decimal? 4. Give some examples of fractions to decimals. 10 Worksheet
- 4. <ul><li>Change fractions to decimal __________________________________________ </li></ul><ul><li>2. Rules in changing fractions to decimals __________________________________________ </li></ul><ul><li>3. Decimal __________________________________________ </li></ul><ul><li>4. Examples of fractions to decimals __________________________________________ </li></ul>
- 5. II. Change the following fractions to decimals. Limit the number to tree decimal places. <ul><ul><li>2/3 =_____________ </li></ul></ul><ul><ul><li>2. ¾ =___________ </li></ul></ul><ul><ul><li>3. 6/7 =_____________ </li></ul></ul><ul><ul><li>4. 8/9 =_____________ </li></ul></ul><ul><ul><li>5. 2/15 =_____________- </li></ul></ul><ul><ul><li>6. 1/9 =_____________ </li></ul></ul><ul><ul><li>7. 5/6 =_____________ </li></ul></ul><ul><ul><li>9. 4/5 =_____________ </li></ul></ul><ul><li>10. 3/16 =_____________ </li></ul>
- 6. <ul><li>11. 13/14 =__________ </li></ul><ul><ul><li>12. ½ =__________ </li></ul></ul><ul><ul><li>13. 3/8 =__________ </li></ul></ul><ul><ul><li>14. 1/8 =__________ </li></ul></ul><ul><ul><li>15. 3/7 =__________ </li></ul></ul><ul><ul><li>16. 6/10 =__________ </li></ul></ul><ul><ul><li>17. 25/100 =__________ </li></ul></ul><ul><ul><li>18. 3/5 =__________ </li></ul></ul><ul><ul><li>19. 5/8 =__________ </li></ul></ul><ul><ul><li>20. 2/3 =__________ </li></ul></ul>
- 7. FUN WITH MATH!!! 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.
- 8. Can you guess the pseudonym that she used? Yes, you can. Simply follow the instruction.
- 9. 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)
- 10. Answers: A = 0.25 F = 0.65 K = 0.512 P = 0.27 B = 0.15 G = 0.28 L = 0.125 Q = 0.006 C = 0.6 H = 0.77 M = 0.333… R = 0.72 D = 0.54 I = 0.24 N = 0.40 S = 0.6 E = 0.76 J = 0.532 O = 0.75 T = 0.4113 U = 0.325
- 11. Lesson 11 EXPRESSING MIZED FRACTIONAL NUMBERS TO MIXED DECIMALS <ul><li>Lesson Objectives </li></ul><ul><li>After accomplishing this lesson, you are expected to: </li></ul><ul><ul><li>. Express mixed fractional numbers to mixed decimals. </li></ul></ul><ul><ul><li>. Know the rules in expressing mixed fractional numbers to mixed decimals. </li></ul></ul><ul><ul><li>. Interpret the mixed fractional numbers to mixed decimals. </li></ul></ul>
- 12. How can we change mixed fractional numbers to mixed decimals? See the following examples. 4 1/2 = 4.5 c. 21 1/8 = 21.125 14 3/8 = 14.375 d. 32 3/7 = 32.4285
- 13. From the examples given above, it can be seen that the rule in changing a mixed fractional number to mixed decimal is:
- 14. 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.
- 15. Worksheet I. Change the following mixed fractional numbers to mixed decimals. Limit the number to three decimal places. <ul><li>4 2/5 = _____________________ </li></ul><ul><li>2. 3 4/5 = ______________________ </li></ul><ul><li>3. 7 3/16 = ______________________ </li></ul><ul><li>4. 10 13/14 = ______________________ </li></ul><ul><li>5. 12 9/17 = ______________________ </li></ul><ul><li>6. 21 14/19 = ______________________ </li></ul><ul><li>7. 32 21/41 = ______________________ </li></ul><ul><li> </li></ul>11
- 16. 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 =_______________
- 17. II. Copy the correct mixed decimal to mixed fractional numbers. <ul><li>1 3/10 3. 31 503/100 </li></ul><ul><li>a. 1.03 a. 31.0503 </li></ul><ul><li>b. 1.30 b. 31.035 </li></ul><ul><li>c. 1.013 c. 31.00503 </li></ul><ul><li>d 1.13 d. 31.5030 </li></ul><ul><li>2. 8 420/1000 4. 8 143/1000 </li></ul><ul><li>a. 8.0420 a. 8.1430 </li></ul><ul><li>b. 8.240 b. 8.0143 </li></ul><ul><li>c. 8.420 c. 8.1043 </li></ul><ul><li>d. 8.0042 d. 8.00143 </li></ul>
- 18. 5. 9 6/100 a. 9.16 b. 9.600 c. 9.006 d. 9.06
- 19. Lesson 12 EXPRESSING DECIMALS TO FRACTIONS <ul><li>Lesson Objectives </li></ul><ul><li>At the end of the lesson, the students are expected to: </li></ul><ul><ul><li>. Change the decimals to fractions. </li></ul></ul><ul><ul><li>. Follow the rule in expressing decimals to fractions. </li></ul></ul><ul><ul><li>. Understand the equivalent decimals and fractions. </li></ul></ul>
- 20. As what we have learned earlier, decimals are common fractions written in different way.
- 21. 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.
- 22. 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) 18 25 = 72/100 or 18 25
- 23. 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.
- 24. 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 1 2 __ 5 __ 1000
- 25. The digit 2 is in the thousandths place so we write: 0.072 = 72/1000 = 9/125
- 26. <ul><li>Some Common Equivalent Decimals and Factions </li></ul><ul><ul><li>and 1/10 </li></ul></ul><ul><li>and 2/10 or 1/5 </li></ul><ul><li>1.5 and 1 ½ or 1 5/10 or 1 ½ </li></ul><ul><li>0.25 and 25/100 or ¼ </li></ul><ul><li>0.50 and 50/100 or ½ </li></ul><ul><li>0.75 and 75/100 or ¾ </li></ul>
- 27. 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.
- 28. It can be seen from the examples above the rule in changing a decimal to fraction is as follows:
- 29. 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.
- 30. Worksheet 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 = ________________ 12
- 31. 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 =_________________
- 32. FUN WITH MATH!!! 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.
- 33. 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 = _____ L 13. 0.2 = _____ E 14. 0.225 =______ O 15. 0.24 = _____ Y 16. 0.8 = _____ S 17. 0.5688=______ R
- 34. _____ _____ _____ ______ ______ _____ 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
- 35. Lesson 13 EXPRESSING MIXED DECIMAL NUMBERS TO MIXED FRACTIONAL NUMBERS <ul><li>Lesson Objectives </li></ul><ul><li>At the end of the lesson, the pupils should be able to </li></ul><ul><ul><li>. Express mixed decimal numbers to mixed fractional numbers. </li></ul></ul><ul><ul><li>. Follow the rules in expressing mixed decimal numbers to mixed fractions. </li></ul></ul><ul><li>3. Identify mixed decimals to mixed fractions. </li></ul>
- 36. How can we change mixed decimals to mixed fractions? Study the following examples:
- 37. <ul><ul><ul><li>5.03 = 5 3/100 </li></ul></ul></ul><ul><ul><ul><li>b. 6.2 = 6 2/10 = 6 1/5 </li></ul></ul></ul><ul><ul><ul><li>24.75 = 24 75/100 = 24 ¾ </li></ul></ul></ul><ul><ul><ul><li>d. 37.248 = 37 248/1000 = 37 31/125 </li></ul></ul></ul>The 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.
- 38. Worksheet 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 = __________ 13
- 39. 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
- 40. Unit III ADDITION AND SUBTRACTION OF DECIMALS NUMBERS
- 41. OVERVIEW OF THE MODULAR WORKBOOK This 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.
- 42. 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.
- 43. Lesson 14 MEANING OF ADDITION AND SUBTRACTION OF DECIMAL NUMBERS <ul><li>Lesson Objectives: </li></ul><ul><li>After accomplishing this lesson, you are expected to: </li></ul><ul><ul><li>. Define addition and Subtraction. </li></ul></ul><ul><li>2. Identify the parts of addition and subtraction. </li></ul><ul><li>3. Familiarize the language in addition and subtraction. </li></ul>
- 44. Addition is the process of combining together two or more decimal numbers. It is putting together two groups or sets of thing or people.
- 45. 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 (+).
- 46. 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.
- 47. <ul><li>Example: </li></ul><ul><ul><li> 14. 345 Minuend </li></ul></ul><ul><li>- 3.120 Subtrahend </li></ul><ul><li>11.232 Difference </li></ul>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 (-).
- 48. Worksheet I. Give the meaning and explain the use of the following. 1. What is addition? 2. What is subtraction? 3. What are the parts of addition? 4. What are the parts of subtraction? 14
- 49. 1. Addition ______________________________________________ 2 Subtraction ______________________________________________ 3. Parts of addition ______________________________________________ 4. Parts of subtraction ______________________________________________
- 50. 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 _______
- 51. 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 _______
- 52. 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.
- 53. 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.
- 54. 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.
- 55. Lesson 15 ADDITION AND SUBTRACTION OF DECIMAL NUMBERS WITHOUT REGROUPING <ul><li>Lesson Objectives: </li></ul><ul><ul><li>After finishing the lesson, the students are expected to: </li></ul></ul><ul><ul><ul><li>. Know how to add and subtract decimal numbers without regrouping. </li></ul></ul></ul><ul><li>2. Develop speed in adding and subtracting decimal number. </li></ul><ul><li>3. Follow the steps in adding and subtracting decimal numbers. </li></ul>
- 56. 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.
- 57. STEP 1 STEP 2 3+ 1 = 4 28. 143 + 11. 721 4 Add the thousandths place 4 + 2 = 6 28. 143 + 11. 721 64 Add the hundredths place
- 58. STEP 3 STEP 4 7 + 1 = 8 28. 143 + 11. 721 864 Add the tenths place 8 + 1 = 9 28. 143 + 11. 721 9. 864 Add the following up to the ones.
- 59. STEP 5 2 + 1 = 3 28. 143 + 11. 721 39. 864 Add the following up to the tens.
- 60. Now subtract 39. 864 to 11. 721. 39. 864 minuend - 11. 721 subtrahend 28. 143 difference
- 61. 2 Ways of Checking the Answer 1. minuend – difference = subtrahend 39. 864 minuend - 28. 143 difference 11. 721 subtrahend 2. difference + subtrahend = minuend 28. 143 difference + 11. 721 subtrahend 39. 864 minuend
- 62. 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.
- 63. <ul><li>As a procedure for adding or subtracting decimal numbers, we have the following: </li></ul><ul><li>Write the decimal numbers with the decimal points </li></ul><ul><li>falling in one column. </li></ul><ul><li>2. Add or subtract as if they were whole numbers. </li></ul><ul><li>3. Place the decimal point of the result in the same column </li></ul><ul><li>as the other numbers. </li></ul>
- 64. Worksheet Add and subtract as fast as you can. 15
- 66. FUN WITH MATH!!! 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).
- 67. <ul><li>85. 367 2. 645. 987 </li></ul><ul><li>+ 16. 252 - 314.625 </li></ul>R P <ul><li>74. 617 </li></ul><ul><li>+ 21. 721 </li></ul>O <ul><li>2,936. 475 </li></ul><ul><li>- 1,421.061 </li></ul>S <ul><li>51. 437 6. 658.325 </li></ul><ul><li>+ 18. 042 - 137.210 </li></ul>Y L <ul><li>895. 399 8. 945. 374 </li></ul><ul><li>- 471. 287 + 33. 161 </li></ul>A R 9. 32. 511 + 11. 621 R
- 68. <ul><li>7,649.251 11. 66.341 </li></ul><ul><li>- 36.030 + 12.412 </li></ul>E D _______ 521. 115 _______ 96. 338 _______ 44. 132 _______ 78. 753 _______ 1515. 414 _______ 331.362 _______ 101.619 _______ 424.112 _______ 69.478 _______ 7613.221 _______ 978.535
- 69. Lesson 16 ADDITION AND SUBTRACTION OF DECIMAL NUMBERS WITH REGROUPING <ul><li>Lesson Objectives: </li></ul><ul><ul><li>After accomplishing the lesson, the students are expected to be able to: </li></ul></ul><ul><ul><li>1. Define regrouping. </li></ul></ul><ul><li>2. Learn how to add and subtract decimal numbers with regrouping. </li></ul><ul><li>3. Answer and perform the operation critically and correctly. </li></ul>
- 70. 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.
- 71. 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.
- 72. Example 1: 0. 7 + 0. 5 0.7 + 0.5 = 12 10 tenths is regroup as ( 1 ) one. 2 . 1 7 5 . . 1 0 + 0 Tenths . Ones
- 73. Example 2: 0.09 + 0.06 0.9 + 0.6 = 15 hundredths 10 hundredths is 1 regrouped as 1 tenth. 5 1 . 0 9 6 0 0 . . 0 0 H T . O
- 74. Example 3: 0.065 + 0.008 5 + 8 = 13 thousandths 10 thousandths is regrouped as 1 hundredth. 3 7 0 0. 5 8 6 0 0 0 0. + 0. Th H T O
- 75. Subtract decimals like you were subtracting whole numbers.
- 76. Example 4: 0. 93 - 0. 28 9 is renamed as 8 + 1 tenths. 1 tenth is regrouped as 10 hundredths. 0. 9 3 - 0. 2 8 0. 6 5 <ul><li>Check: </li></ul><ul><ul><li>0. 28 </li></ul></ul><ul><ul><li>+ 0. 65 </li></ul></ul><ul><li> 0. 93 </li></ul>13 8 0. 3 8 0. 10 8 - 1 0. 3 9 0. hundredths tenths ones
- 77. Example 5: 0.730 - 0.518 2 10 0.730 - 0.518 0.212 Check: 0.518 + 0.212 0.730 Answer 2 1 2 0. 0. 0 - 8 2 - 1 7 - 5 0. 10 2+1 7 0. 0 3 7 0. thousandths hundredths tenths ones
- 78. Worksheet <ul><li>I. Answer the following. </li></ul><ul><ul><li>A. Add the following and check your answer on the Check Box below. </li></ul></ul><ul><li>0.6 2. 0.07 + 0.8 + 0.49 </li></ul><ul><li>0.36 4. 0.746 + 0.56 + 0.235 </li></ul>16
- 79. 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
- 80. II. Write on the blank ( + ) or ( - ) sign to make the statement TRUE. <ul><li>1. 4.793 ___ 3.549 = 8.342 </li></ul><ul><li>2. 72.685 ___ 45.726 ___ 13.493 = 104.918 </li></ul><ul><li>3. 1.45 ___ 0.50 ___ 3.95 ___ 5.66 = 11.56 </li></ul><ul><li>4. 36.58 ___ 35.789 ___ 354.587 = 426.956 </li></ul><ul><li>6.57 ___ 0.456 ___ 236.5 ___ 5 ___ 213.66 = 34.866 </li></ul><ul><li>6. 28. 625 ___ 25.361 = 3.264 </li></ul><ul><li>7. 57.54 ___ 0.25 = 57.29 </li></ul><ul><li>8. 86.3 ___ 0.456 ___ 32.58 = 118.424 </li></ul><ul><li>9. 39 ___ 5.65 = 33.35 </li></ul><ul><li>10. 53.654 ___ 5.236 = 48.418 </li></ul>
- 81. Lesson 17 ADDING AND SUBTRACTING MIXED DECIMALS <ul><li>Lesson Objectives: </li></ul><ul><ul><li>After finishing the lesson, the students are expected to: </li></ul></ul><ul><ul><li>1. Understand and know how to add and subtract mixed decimal numbers. </li></ul></ul><ul><li>2. Follow the rules in adding and subtracting mixed decimal numbers. </li></ul><ul><li>3. Perform the operation correctly. </li></ul>
- 82. 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? 1 3 2 9 4 . 4 5 2 4 1 4 7 1 1 8 6 7 2 9 5 3 1 3 8 2 . . . 1 1 1 +1 H Th T Th Th H T . 3
- 83. 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? 0 9 7 5 8 . 1 1 1 12 2 3 9 0 2 14 5 9 12 3 4 . . 5 6 -4 H Th T Th Th H T O
- 84. Ramon traveled 1.85790 kilometers more. In adding and subtracting mixed decimals, remember to align the decimal points and regroup when necessary.
- 85. Worksheet I. Add or subtract these mixed decimals. <ul><li>4.59804 2. 3.14879 3. 5.11788 </li></ul><ul><li> 7.81657 5.37896 1.93523 </li></ul><ul><li>+ 1.30493 + 2.95321 + 3.40175 </li></ul>4. 2.42814 5. 7.20453 6. 9.57128 - 1.19905 - 4.35712 - 2.89340 17
- 86. II. Rewrite with the correct alignment of decimal points on the space provided. Find the sum and difference. <ul><li>1. 4.930000 4. 18.17932 </li></ul><ul><li> 57.5244 + 2.41256 </li></ul><ul><li>+ 637.3672 </li></ul><ul><li>73.59203 5. 12.48004 </li></ul><ul><li>+ 154.38762 - 9.86327 </li></ul><ul><li> </li></ul><ul><li>3. 142.567021 6. 42.20239 - 85.791503 - 2.34876 </li></ul>
- 87. 4. 18.16532 9. 5.306321 - 4.01985 002.7509 + 4.952005 5. 951.235 7.18902 10. 103.93284 + 00.3 + 43.76895
- 88. Lesson 18 ESTIMATING SUM AND DIFFERENCE OF WHOLE NUMBERS AND DECIMALS <ul><li>Lesson Objectives: </li></ul><ul><ul><li>After understanding the lesson, you must be able to: </li></ul></ul><ul><ul><ul><li>. Define estimation. </li></ul></ul></ul><ul><li>2. Know the two methods in making estimates. </li></ul><ul><li>3. Learn how to estimate sum and difference and how it is done. </li></ul>
- 89. 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.
- 90. 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.
- 91. 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. <ul><li>Method 1: Sum of the First Digit only </li></ul><ul><li>Estimate in Addition </li></ul><ul><ul><li>3.455 + 2.672 + 5.135 </li></ul></ul>
- 92. <ul><li>Rounded off to the </li></ul><ul><li>nearest ones </li></ul><ul><ul><li>3 .455 3.000 </li></ul></ul><ul><ul><li>2 .672 3.000 </li></ul></ul><ul><li>+ 5 .134 + 5.000 </li></ul><ul><ul><li> 11.000 </li></ul></ul>first estimate Rounded off to the nearest tenths 3. 4 55 0.500 2. 6 72 0.700 + 5. 1 34 + 0.100 1.300 to be added the first estimate if desired or required.
- 93. 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.
- 94. Estimate 5.472147 – 2.976543 Rounded to the nearest ones Actual Subtraction 5.472147 5.000000 5.472147 - 2.976543 - 3.000000 - 2.976543 2.000000 2.495604
- 95. Method 2: Rounding Method <ul><li>Estimate the sum by rounding method in place of whole numbers. </li></ul><ul><li>Example: 6.567 7.000 </li></ul><ul><li> 5.482 5.000 </li></ul><ul><li> + 4.619 + 5.000 17.000 </li></ul>
- 96. 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.
- 97. 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.
- 98. Worksheet 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 Sum 1. 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. 18
- 99. 3. 648.937 649.000 4. 871.055 871.000 214.562 215.000 276.386 276.000 + 450.211 + 450.000 + 107.891 + 108.000 A.S. E.S. A.S. E.S. 5. 374.738 375.000 6. 342.165 342.000 469.345 469.000 178.627 179.000 + 213.543 + 213.500 + 748.715 + 749.000 A.S. E.S. A.S. E.S.
- 100. B. Actual Difference/ Estimated Difference 7. 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. 9.2875 9.0000 - 17.928 - 18.000 - 6.8340 - 7.0000 A.D. E.D. A.D. E.D.
- 101. FUN WITH MATH!!! 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.
- 102. 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. 939.00 2. 639.27-422.30 S. 216.00 3. 48.21+168.2 P. 2.0000 4. 285.15+27.35+627.30 E. 146.000 5. 8.941-8.149 W. 28.10 6. 18.95+9.25 J. 111.00 7. 129.235+16.41 T. 537.00 8. 9.2875-6.834 S. 1.000 9. 989.15-451.85 E. 217.00
- 103. _____ ______ ______ ______ ______ 1 2 3 4 5 _____ ______ ______ ______ 6 7 8 9
- 104. Lesson 19 MINUEND WITH TWO ZEROS <ul><li>Lesson Objectives: </li></ul><ul><ul><li>After accomplishing the lesson, the students are expected to be able to: </li></ul></ul><ul><ul><ul><li>. Know how to subtract decimal numbers with two zeros in minuend. </li></ul></ul></ul><ul><li>2. Follow the steps in subtraction of numbers involving zeros. </li></ul><ul><li>3. Check the answer and perform the operation correctly. </li></ul>
- 105. 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.
- 106. <ul><li>STEPS IN SUBTRACTION OF DECIMAL NUMBER INVOLVING ZEROS </li></ul><ul><ul><li>. Arrange the digits in column. </li></ul></ul><ul><ul><li>. Regroup from one place to the next until all successive zeros are renamed. </li></ul></ul><ul><ul><li>. Subtract to find the answer. </li></ul></ul><ul><ul><li>. Check the answer. </li></ul></ul>
- 107. Example: 0.8005 - 0.6372 3 3 6 1 0. 2 7 3 6 0. 5 10 9 7 0. 10 9+1 10 7+1 0. 5 0 0 8 0. T Th Th H T O
- 108. Rewriting: 0.8005 - 0.6372 Difference 0.1633 Checking: 0.6372 + 0.1633 0.8005
- 109. Worksheet 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 <ul><li>0.10013 </li></ul><ul><li>- 0.00011 </li></ul><ul><li>7. 2.00143 </li></ul><ul><li>- 0.88043 </li></ul><ul><li>0.7008 </li></ul><ul><li>- 0.5383 </li></ul><ul><li>9. 0.8008 </li></ul><ul><li>- 0.0880 </li></ul><ul><li>10. 0.14003 </li></ul><ul><li>- 0.03333 </li></ul>19
- 110. FUN WITH MATH!!! 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.
- 112. Lesson 20 PROBLEM SOLVING INVOLVING ADDITION AND SUBTRACTION OF DECIMALS <ul><li>Lesson Objectives: </li></ul><ul><ul><li>After accomplishing the lesson, the students are expected to be able to: </li></ul></ul><ul><ul><ul><li>. Follow the step of solving problem. </li></ul></ul></ul><ul><li>2. Analyze the problem critically. </li></ul><ul><li>3. Develop interest in solving word problem. </li></ul>
- 113. 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
- 114. 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 = N 5. What is the solution? Php. 82.60 Php. 100.05 + Php. 96.10 Php. 278.75 Solve Decide Show
- 115. Check 6. How do you check your answer? We add downward. Php. 82.60 Php. 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.
- 116. Worksheet 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? __________________________________________________________________________________________ 20
- 117. 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? ______________________________________________________________________________________________
- 118. 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?
- 119. 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?
- 120. 6. What is the answer? __________________________________________________________________________________________ 7. How do you check the answer?
- 121. 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? __________________________________________________________________________________________ 2. What are the given facts? __________________________________________________________________________________________
- 122. 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? _________________________________________________________________________________________
- 123. 7. How do you check 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?
- 124. 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?
- 125. 6. What is the answer? __________________________________________________________________________________________ 7. How do you check the answer?
- 126. 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? __________________________________________________________________________________________ 2. What are the given facts? __________________________________________________________________________________________ 3. What is the process to be used? __________________________________________________________________________________________
- 127. 4. What is the mathematical sentence? ______________________________________________________________________________________________ 5. How the solution is done? 6. What is the answer? ______________________________________________________________________________________________ 7. How do you check the answer?
- 128. UNIT IV MULTIPLICATION OF DECIMALS
- 129. 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.
- 130. 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.
- 131. Lesson 21 MEANING OF MULTIPLICATION OF DECIMAL NUMBERS <ul><li>Lesson Objectives: </li></ul><ul><li>After learning this lesson, you are expected to: </li></ul><ul><li>Define multiplication. </li></ul><ul><li>2. Locate where the multiplicand, multiplier and product are. </li></ul><ul><li>3. Familiarize the terms in multiplication. </li></ul>
- 132. 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. .4 + .4 + .4 + .4 + .4 + .4 = 2.4 In multiplication, it is written as: .4 -> multiplicand x 6 -> multiplier 2.4 -> product (answer in multiplication) factors
- 133. 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 0.007 x 0.5 x 3 x 2 x 4 4.5 0.24 2.48 0.028
- 134. 1. What is multiplication? 2. What are factors? 3. What are products? 4. Give some examples of multiplication decimals. I. Give the meaning and explain the use of the following. 21 Worksheet
- 135. <ul><li>multiplication ________________________________________________________________________________ </li></ul><ul><li>2. factors ________________________________________________________________________________ </li></ul><ul><li>3. products ________________________________________________________________________________ </li></ul><ul><li>4. Examples of multiplication decimals ________________________________________________________________________________ </li></ul>
- 136. <ul><li>Identify the words by looping vertically ,horizontally and diagonally directions. (Word – Puzzle) </li></ul>

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