MATH 5

ON YOUR OWNSolve for the sum or difference. Write your answers in your notebook.1) 0.267 6) 0.924 - 0.122 - 0.2132) 0.246 7) 0.657 - 0.132 - 0.253) 0.823 8) 0.342 - 0.51 + 0.1534) 0.576 9) 0.542 + 0.123 + 0.325) 0.364 10) 0.647 + 0.225 - 0.214 5

ADDITION AND SUBTRACGTRIAODNE VOF DECIMALS THROUGH ADDITTIOHNOUASNADNSDUTBHTSRPALCATCIOENWOITFHDERCEIGMRAOLUSPTINHGROUGH THOUSANDTHS PLACE WITH REGROUPINGObjective: Add and subtract decimals through thousandths place with regrouping REVIEW Do as indicated. 1) 0.278 + 0.32 + 0.101 2) 0.834 – 0.212 3) 0.431 + 0.425 + 0.14 4) 0.674 – 0.313 5) 0.352 + 0.213 + 0.134 STUDY AND LEARN There are 2 bottles of milk in the refrigerator. If we are to combine the contents of the 2 bottles in a container, how much milk will there be in all? To find the total amount of milk in the 2 bottles, we add 0.625 to 0.29. 1

Let’s solve this step by step. 0.625 + 0.290 1 Write the numbers in column. Make sure to align the decimal points. Use a placeholder 1 when needed. 0.625 2 Subtract as you would subtract whole + 0.290 numbers. Regroup if necessary. 0 915 3 Place the decimal point in the sum. Align this with the decimal points of the addends. 1 0.625 + 0.290 0.915The total amount of milk in the 2 bottles is 0.915 liters.Let’s have some more examples.1) 0.934 + 0.38 = n 11 0.934 0.934 + 0.380 + 0.380 We place 0 as a 1.314 place holder. Place the decimal point exactly below the decimal points of the addends.2) 0.562 + 0.237 + 0.36 = n Use 0 as placeholder. 11 0.562 0.237 + 0.360 1.159Look at the 2 bottles of milk again.How much milk does bottle A contain?How about bottle B?How much more milk than bottle B does bottle A contain?To solve this, we subtract the amount of milk in bottle B from that of bottle A. Thuswe subtract 0.29 from 0.625. 2

Let’s solve. 0.625 - 0.290 1 Write the numbers in a column. Make sure to align the decimal points. Use a 5 12 placeholder when needed. 0.625 2 Subtract as you would have done with - 0.290 whole numbers. Regroup if necessary. 0 335 3 Place the decimal point exactly below the other decimal points. 5 12Bottle A has 0.335 liters more milk than bottle B. 0.625Below are other examples for you to study. - 0.290 1) 0.79 - 0.365 = n 0.335 0.790 Use 0 as placeholder - 0.365 0.425 2) 0.634 – 0.27 0.634 - 0.270 Use 0 as placeholder 0.3643

TRY THESEA. Find the sums of the decimals along the rows, columns and the diagonals by adding across, down and diagonally.  0.45 0.432 0.38  0.065 0.361 0.18  0.23 0.349 0.245B. Find the difference between the two quantities. Look for the difference in Column B. AB 1) a. 0.1420.796 L 0.248 L2) 0.39 kg b. 0.057 0.532 kg c. 0.6353)0.823 m 0.546 m 4

4) 0.249 kg d. 0.548 0.306 kg 0.295 m e. 0.2775) 0.93 m WRAP UPIn adding/subtracting decimals with regrouping we undertake thefollowing steps Step 1: Write the decimals in columns, aligning the decimal points. Use 0 as place holder when needed. Step 2: Add/subtract as we would add/subtract whole numbers. Regroup if necessary. Step 3: Place the decimal point in the result aligned with the other decimal points. 5

ON YOUR OWNFind the sum or difference. Write your solutions and answers in your notebook.1) 0.657 6) 0.342 + 0.39 + 0.282) 0.593 7) 0.257 + 0.369 + 0.27 - 0.216 8) 0.935 – 0.2873) 0.832 + 0.0494) 0.433 9) 0.27 + 0.394 + 0.421 - 0.129 10) 0.748 – 0.4995) 0.306 + 0.118 6

ADDITION AND SUBTRAGRCATDIEOVN OF MIXED DECIMALSADDITION ANDWSITUHBTORUATCRTEIGORNOOUFPMINIGXED DECIMALS WITHOUT REGROUPING Objective: Add and subtract mixed decimals without regroupingREVIEWRound off the following decimal numbers.1) 4.623 (tenths) ______2) 13.846 (hundredths) ______3) 115.2834 (thousandths) ______4) 6.409 (tenths) ______5) 14.3239 (thousandths) ______ STUDY AND LEARNRead and understand the story problem below. Freddie is a Grade V pupil of Gregoria de Jesus Elementary School. He sells icecandy after class. On Monday he earned 61.75 and on Tuesday 52.00. How muchdid he earn in two days?What is asked in the problem?How much did he earn in two days?What shall we do to solve the problem?We shall add. 1

Let’s solve for the sum following the steps below.1. Align the decimal points 61.75 + 52.002. Add as you would add whole numbers. 61.75 + 52.00 113 75 3. Place the decimal point in the sum in line with the 61.75 decimal points of the addends. + 52.00 113.75Freddie earned 113.75 in two days.If Freddie spent 12.75 from his earnings, how much will be left?What process shall we use to solve the problem? SubtractionWhat is the number sentence? 113.75 - 12.75 = NLet’s solve this together following the steps below:1. Align the decimal points. Use zero as place holder 113.75 if necessary. - 12.752. Subtract the same way as we subtract whole 113.75 numbers. - 12.75 101 003. Place the decimal point in line with the decimal 113.75 points of the minuend and subtrahend. - 12.75 101.00Below are other samples for you to study.Addition: Subtraction:12.3621 + 24.723 + 3.461 = N 45.72 – 13.694 = N12.0621 Align the decimal points. 45.89624.7030 Use zero as place holder if - 13.694+ 3.1110 necessary. 2

12.0621 Add/subtract as you would 45.89624.7030 add/subtract whole numbers. - 13.694+ 3.1110 Regroup if necessary. 32 202 12.0621 Align the decimal point of 45.896 24.7030 the result with the decimal - 13.694+ 3.1110 point of the addends/minuend39.8761 and subtrahend. 32.202Were you able to follow? Try to answer the exercises below by yourself.TRY THESEA. Solve the following:1. What is the sum of 2.712 and 3.254?2. What is 13.254 less 11.132?3. What is 6.271 increased by 2.004?4. What is 2.043 added to 12.302?5. How much more is 24.272 than 11.121?B. Find the sum or difference.1) 34.253 2) 123.268 3) 36.257 + 63.721 - 112.153 - 23.214 4. 2.4626 5. 23.4275 1.2130 15.2104 3.3121 + 30.3120 3

WRAP UPIn adding/subtracting mixed decimals follow these steps: Step 1: Arrange the mixed decimals in columns and align the decimal points. Use zero as place holder if necessary. Step 2: Add/subtract as whole numbers. Regroup if necessary. Step 3: Align the decimal point in the sum with the decimal points of the addends/minuend and subtrahend.ON YOUR OWNSolve the following. Write your solutions and answers in your notebook.1. What is 2.727 more than 13.201?2. Find the sum of 2.61, 3.227 and 4.030?3. Twelve and three hundred twenty-five thousandths less 10.214?4. Subtract 2.272 from 43.2855. What number should we add to 6.472 to get 9.685?6) 2.4785 7) 12.772 8. 43.23 2.1103 - 10.321 + 26.21 + 4.0100 9. 2.642 10) 12.731 + 1.234 21.051 + 31.013 4

ADDITION AND SUBTRAGCRATDIOE NV OF MIXED DECIMALSADDITION AND SUBWTRITAHCTRIEOGNROOFUMPIINXGED DECIMALS WITH REGROUPING Objective: Add and subtract mixed decimals without and with regrouping REVIEW Add or subtract. 00.4.493 00..7783 00..8866 + +00.4.422 --00..2211 ++00..1133 00..4488 --00..3322 0.566 00..7733 00..8866++00.32 -00.4.411 ++00..1133 00..6699 00.7.766 00..5511--00..2277 ++00.1.133 ++00..4433 1

STUDY AND LEARN Jeo and his mother went to Brgy. San Jose. Jeo’s friends wanted to know how farthe town proper was from Brgy. San Jose. One of his friends showed a map. Brgy. 4.57 km Town 5.06 km Brgy. Proper Trinidad Tagum 3.84 km 4.138 km 6.5 km Brgy. MalvarBrgy. San JoseLet’s talk about the word problem. Brgy. San IsidroExample 1: How far is Brgy. San Jose from the town proper? What are the facts needed to answer this question? 6.5 km from Brgy. San Jose to Brgy. Tagum 4.57 km from Brgy. Tagum to the town proper What operation shall we use? Addition Let’s solve. 1 6.50 km + 4.57km 11.07 kmThe distance between Brgy. San Jose to the town proper is 11.07 km.Let’s have another example. How far is Brgy. Tagum from Brgy. San Isidro if you will pass through the townproper?What is the number sentence?4.27 km + 5.06 km + 4.138 km = N 2

Let’s solve. 1  add zero  add zero 4.270 5.060+ 4.138 13.468The answer is 13.468 km.Brgy. Tagum is 13.468 km away from Brgy. San Isidro.Here’s another problem.Example 2:Which is farther from the town proper, Brgy. Trinidad or Brgy. Malvar? By how much?What operation are we going to use to solve the problem?Let’s subtract the mixed decimals. Take note of the steps as we solve:1. Write the numbers in column. Align the decimal points. Place zero to the empty decimal places. 5.06 - 3.842. Subtract the hundredths. Regroup if necessary. 5.06 - 3.84 23. Subtract the tenths. Regroup if necessary. 4 10 5.06 - 3.84 .22 3

4. Subtract the ones. Place the decimal point directly below the decimal points of the minuend and subtrahend. 4 5.06 - 3.84 1.22Brgy. Malvar is 1.22 km farther from the town proper than Brgy. Trinidad.Below are other examples for you to study.a. 36.7 – 25.964 = n 9 5 6 1010 36.700  add zeros to empty decimal places - 25.964 10.736b. 169.46 – 72.347 = n 5 169.460  add zeros to empty decimal places - 72.347 97.113TRY THESEA. Solve the following. Write your answers in your notebook.1. Find the sum of 2.712 and 3.64.2. What is 13.254 less 1.56?3. What is 6.271 increased by 2.032?4. What is 2.043 more than 12.382?5. What is the difference between 24.272 and 11.321?B. Find the sum or difference. Write your answers in your notebook.1) 34.253 2) 123.268 3) 36.25 .+ 14.29 - 14.207 - 12.3244) 2.462 5) 3.427 13.03 . 2.32 . + 21.27 . + 13.26 . 4

WRAP UPIn adding/subtracting decimal numbers, follow these steps:Step 1: Align the decimal points of the decimal number in one column.Step 2: Add/subtract as whole numbers, regroup if necessary.Step 3: Place decimal point in line with the decimal pointsON YOUR OWNSolve the following. Write your solutions and answers in your notebook.1) What is 2.727 more than 13.09?2) Find the sum of 2.61, 3.227 and 4.262.3) 12.325 less 4.274) Subtract 2.272 from 3.285) What number do we add to 6.472 to get 14.285?6) 2.478 7) 12.472 8) 43.23 + 1.23 - 5.28 - 21.07 2.429) 2.478 10) 12.472 + 1.23 - 5.28 2.42 5

PROBLEM SOLVINGGIRNAVDOELVVING ADDITION OR PROBLEMSUSBOTLRVAICNTGIOINNVOOFLDVEINCGIMAADLDSITION OR SUBTRACTION OF DECIMALSObjective: Solve word problems involving either addition or subtraction of decimalsREVIEWAdd or subtract the numbers at the outer circle to / from the number at the center. 2) +5.62 1) 5) 3) -7.27 -0.63 -1.25 12.5 4) +3.45 STUDY AND LEARNMiguel saved 25.65 from his weekly allowance. Andres saved 32.75. How muchmoney did they save altogether? 1

Let’s solve the problem.First, read and understand the problem.  What is asked for? the amount of money they saved together  What are the given facts? 25.65 Miguel’s savings and 32.75 Andres’ savingsSecond, plan how you will solve the problem.  What is the process to be used?( addition )  What is the number sentence? 25.65 + 32.75 = nThird, solve. 25.65 + 32.75 = n 1 25.65+ 32.75 58.40Miguel and Andres saved 58.40.Let’s have another problem. Miguel and Andres saved 58.40. They bought a bunch of flowers that cost50.50 for their mother’s birthday. How much money was left to the two boys?1. Read and understand the problem.  What is asked? the amount of money left to the 2 boys  What are given? They had 58.40 from their savings. The flowers cost 50.502. Plan how you will solve the problem.  What is the process to be used? subtraction  What is the number sentence? 58.40 - 50.50 = n3. Solve and look back. To check: 1 7 14 50.50 + 7.90 58.40 58.40 - 50.50 7.90 2

The two boys had 7.90 left with them.TRY THESEWrite the number sentence and solve.1. Marifel spent 15.75 for a sandwich and 7.50 for a glass of juice during recess. How much did she spend in all?Number sentence: _____________Answer: _____________2. The sides of a triangle have the following measurement 15.2 cm, 12.45 cm and 16.25 cm. What is its perimeter?Number sentence: _____________Answer: _____________3. Marissa bought a papaya for 25.50. How much change will she receive from a 50-bill?Number sentence: _____________Answer: _____________WRAP UPIn solving word problems, follow these steps:Step 1: Read and understand the problem.Step 2: Plan how you will solve the problem.Step 3: Solve and look back. 3

ON YOUR OWNRead and solve the following word problems. Write your solutions and answers in yournotebook.1. Mr. Aguilar drove 12.4 km going to Pampanga. From there he drove 35.8 km going to Tarlac. How many kilometers did he drive in all?2. Roel is 1.27 meters tall. Marvin is 1.51 meters tall. What is the difference in their height?3. There is 3.75 kilograms of flour in the jar. Me-anne baked cupcakes and used 1.5 kilograms of flour. How many kilograms of flour were left?4. Sarah purchased two books one costs 124.50 and the other 135.75. How much did she pay for the books?5. Mary Anne bought two water containers of different sizes. One of the containers can hold 7.5 liters of water while the other can hold 10.5 liters. How many liters of water in all can the two containers hold? 4

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TWO-STEP WORD PROBLGERMASDEINVVOLVING ADDITION ANDTWO-STEP WOSRUDBTPRRAOCBTLIEOMNSOIFNVDOELCVIMINAGLSADDITION AND SUBTRACTION OF DECIMALSObjective: Solve two-step word problems involving addition and subtraction of decimals including problems that involve moneyREVIEWStudy the table then answer the questions that follow. TOY SALE 1) Anne bought one large toy and one small toy. How much did she spend?Large …………… 99.75Medium-sized…. 65.50 2) Mercedes bought 2 small toys and aSmall…………… 24.75 large toy. How much did she pay? 3) Norie bought a toy of each size. How much did she pay for the 3 toys? STUDY AND LEARNExample 1: Ann attended a Book Fair and bought 3 books. The books were marked 149.75, 88.50 and 129.30. She gave a 500-bill for her payment. How much was her change? 1

What did Ann buy?Do you enjoy buying books? Why?In what ways are books helpful?Let’s now solve the problem following the steps below.1. Understand the problem.  What is asked for? Change for the 500-bill she gave for her payment  What facts are given? 149.75, 88.50, 129.30, 500-bill  What is the hidden question? The total cost of book bought by Ann2. Plan on how to solve the problem. What are the processes involved? Addition and subtraction What shall we add? Add the costs of the 3 books What shall we subtract? Subtract the total cost of the 3 books from the 500.3. Solve and look back. For the change received: For the amount of the 3 books: 121 4 9 9 9 10 149.75 500.00 88.50 - 367.55 + 129.30 367.55 132.45Ann received a change of 132.45. 2

Let’s try solving another word problem.Example 2: Father bought 15.5 liters of gasoline for his car. He consumed 3.5 liters onMonday and 4.75 liters on Tuesday. How many liters of gasoline were left?Let’s analyze and solve the problem.1) What is asked?The amount of gasoline left2) What are the given facts?15.5 liters, 3.5 liters and 4.75 liters3) What is the hidden question?The amount of gasoline consumed in 2 days.4) What shall we do to solve the problem? Add the amount of gasoline consumed in 2 days, then subtract this from 15.5 liters of gasoline.Here’s the solution:For the amount of gasoline consumed To find the amount of gasoline left:in 2 days 15.50 1 - 8.25 3.50 7.25 + 4.75 liters 8.25 liters7.25 liters of gasoline were left. 3

TRY THESEHere are some more word problems. Try to solve them.1) The perimeter of a triangle is 53.9 cm. If 2 sides measure 20.5 cm and 15.2 cm, what will be the length of the third side?2) Joanne spent 3.5 hours studying her lessons. She spent 1.25 hours studying Science, 0.75 hour was devoted to English and the rest for Math. How much time did she spend studying Math?3) Aling Annie has 300 in her purse. She went to the market and spent 47.50 for vegetables, 125 for chicken and 55.50 for fruits. How much money did she have left?4) Mang Fred harvested 3 baskets of guavas with the following weights: 26.2 kg, 34.7 kg, and 31.5 kg. If he sold 55.75 kg in all, how many kilograms of guavas did he have left? WRAP UP In solving two-step word problems, follow the steps below: Step 1: Understand the problem – take note of the hidden question. Step 2: Plan how you will solve it. Step 3: Solve and look back. Step 4: Check your answer. 4

ON YOUR OWNRead and solve the following word problems. Write your solutions and answers in yournotebook.1) Michaela prepared 12.5 liters of buko juice. She was able to sell 6.25 liters in the morning and 4.5 liters in the afternoon. How many liters of buko juice was left at the end of the day?2) Claudine bought some materials needed for her project. She bought glue for 31.50, a pair of scissors for 25.75, a red cartolina for 6.75 and pieces of art paper for 12.50. If she gave the saleslady a 100-bill, how much change did she receive?3) A blouse pattern requires 1.25 meters of cloth and a pair of pants requires 1.5 meters. If the dressmaker has 5 meters of cloth available, how many meters of cloth will be left?4) Mercedes joined a dance presentation for the “Buwan ng Wika.” She bought a kimona which costs 79.75 and a floral skirt for 95.25 for her costume. If mother gave her 200 for her costume, how much change did she return to her mother? 5

MULTIPLICATION OF DECGIRMAADELSV BY ANOTHER DECIMALSMULTIPLICATIOTNHORFODUEGCHIMHUANLSDRBEYDATNHOSTHER DECIMALS THROUGH HUNDREDTHS Objective: Multiply decimals by decimals through the hundredths place REVIEWFind the product of the following. 1) 24 2) 45 3) 57 x3 x6 x5 4) 32 5) 64 6) 71 x 43 x 38 x 26 STUDY AND LEARNExample 1: Arnold had a rectangular garden. What is its area if the length is 0.85 m and the width is 0.4 m? To find the area of the rectangular garden, we multiply 0.85 by 0.4. 1

To solve for 0.85 x 0.4, follow the steps below.1. Multiply the numbers as you 0.85 would multiply whole numbers. x 0.4 Regroup if necessary. 0.3402. Count the number of decimal 0.85  2 decimal places places in the factors. x 0.4  1 decimal place 0.340  3 decimal places in all3. Place the decimal point in the 0.85 product according to the number of decimal places in the x 0.4 factors. 0.340  3 decimal places in allHere are other examples for you to study.Example 2: 0.29  2 decimal places x 0.6  1 decimal place 0.174  3 decimal places in allExample 3: 0.37  2 decimal places x 0.42  2 decimal places 74  4 decimal places in all 148 . 0.1554Example 4: 0.16  2 decimal places x 0.21  2 decimal places 16  4 decimal places in all 32 . 0.0336Use zero as placeholder whenever necessary. 2

TRY THESEFind the product in each case.0.25 x 0.5 0.64 x 0.8 0.32 x 0.40.27 x 0.16 0.85 x 0.34 0.62 x 0.27 0.25 0.69 0.72 x 0.31 x 0.43 x 0.13 WRAP UPTo multiply a decimal by another decimal through the hundredthsplace, follow these steps: Step 1: Multiply in the same way as you would multiply whole numbers. Regroup if necessary. Step 2: Count the decimal places in the factors. Step 3: Place the decimal point in the product according to the number of decimal places in the factors. 3

ON YOUR OWNFind the product. Write your equality sign and the solutions and answers in yournotebook.1) 0.06 x 0.72 = 2) 0.85 x 0.3 = 3) 0.37 x 0.40 = 4) 0.63 x 0.42 = 5) 0.53 x 0.15 = 6) 0.79 x 0.067) 0.55 x 0.238) 0.63 x 0.219) 0.87 x 0.7510) 0.19 x 0.73 4

MULTIPLICATION OF MIXEDGRDAEDCEIVMALS BY WHOLE NUMBERS MULTIPLICATION OF MIXED DECIMALS BY WHOLE NUMBERSObjective: Multiply mixed decimals in the tenths and hundredths place by whole numbers REVIEW Find the product. 1) 0.37 x 0.4 2) 0.4 x 0.39 3) 0.36 x 0.22 4) 0.14 x 0.9 5) 0.89 x 0.4STUDY AND LEARNLook at this square.What is its perimeter? 3.5 cmHow can you find the perimeter?How many sides does a square have? 4What can you say about its sides? They are all equal. 1

Because there are 4 equal sides and each measures 3.5 cm, we can compute this as4 x 3.5 = n. Here’s how this is done. Multiply as with whole numbers. Regroup if necessary. 3.5 x4 140 Count the number of decimal places in the factors. 3.5 x4 140 Place the decimal point in the product. The decimal place in the product is equal to the total number of decimal places in the factors. 3.5  1 decimal place x4 14.0  1 decimal placeHere are other examples for you to study to understand our lesson better. Study themcarefully. a. 4.32  2 decimal places x2 8.64  2 decimal places b. 6.2  1 decimal place x6 37.2  1 decimal place c. 3.47  2 decimal places x 21 347 694 . 72.87  2 decimal placesMultiplying decimals by whole numbers is easy as long as you know how to multiplywhole numbers! 2

TRY THESEA. Multiply. Choose your answer from the choices given inside the parenthesis.1) 4 x 7.28 = (a. 29.12 b. 291.2 c. 2.912)2) 7 x 3.14 = (a. 20.98 b. 21.98 c. 22.98)3) 3 x 6.25 = (a. 18.25 b. 18.5 c. 18.75)4) 2 x 12.55 = (a. 25.1 b. 25.12 c. 25.13)5) 6 x 5.75 = (a. 34.5 b. 3.45 c. 0.345)B. Find the product in each of the following: 1) 4.29 2) 12.47 3) 8.4 x 12 x3 x 14 4) 26.43 5) 10.78 x5 x 13C. Solve.1) What is 3.65 multiplied by 12?2) What is the product of 4 and 8.79?3) What is 24.5 times 6?WRAP UPIn multiplying decimal numbers by whole numbers follow these steps:Step 1: Multiply as with whole numbersStep 2: Count the decimal places in the factorsStep 3: Place the decimal point in the product. The total number of decimal places in the product must be equal to the number of decimal places in the factors. 3

ON YOUR OWNA. Find the product. Write your solutions and answers in your notebook.1) 22.35 2) 13.39 3) 9.27 x7 x4 x 14 4) 10.25 5) 3.65 x5 x8B. Solve for the answer. Write your answers in your notebook.1) What is 2.64 multiplied by 4?2) What is the product of 3.25 and 24?3) What is 16.79 times 5? 4

MULTIPLICATIOGNROADFEMVIXED DECIMALS MULTIPLICATION OF MIXED DECIMALSObjective: Multiply mixed decimals by mixed decimals with tenths and hundredths placesREVIEWMatch with the correct product. Write the letter of the correct answer.1) 62.4 x 3 a. 41.452) 1.47 x 13 b. 25.623) 8.29 x 5 c. 187.24) 4.27 x 6 d. 89.265) 22.25 x 4 e. 89 f. 19.11 STUDY AND LEARNExample 1: Roselle jogs around the village every morning. She spends a total of 8.75 hours a week jogging. How many hours does she spend jogging in 1.4 weeks? Do you also jog every morning? Why is it a good practice to jog everyday? Aside from jogging, what other activities will keep our body fit and healthy? 1

Let’s talk about the story problem. How many hours does Roselle spend jogging in a week? 8.75 hours What are we supposed to find? the number of hours she spends in jogging in 1.4 weeks? What shall we do to solve for this? We shall multiply.Let’s multiply 8.75 by 1.4 following the steps below. Multiply as you would multiply whole numbers. 32 8.75 x 1.4 3500 875 . 12250Count the number of decimal places in the factors. 8.75 2 decimal places x 1.4 1 decimal place 3500 875 .12250Place the decimal point in the product. The number of decimalplaces in the product is the same as the number of decimal placesin the factors. 32  3 decimal places 8.75 x 1.4 3500 875 .12.250 1Roselle spends 12.25 or 12 hours jogging in 1.4 weeks. 42

Here are other examples for you to study.Example 2: 1  2 decimal places 31  1 decimal places 3.73  3 decimal places x 2.5 1865 746 . 9.325Example 3: 1  2 decimal places  2 decimal places 31  4 decimal places 6.43 x 3.27 1 4501 1 1286 . 1929 . 21.0261TRY THESEA. Insert decimal points in the appropriate places to give the correct product. 1) 2.97 x 4.8 = 1 4 2 5 6 2) 6.48 x 2.24 = 1 4 5 1 5 2 3) 30.62 x 1.3 = 3 9 8 0 6 4) 16.03 x 4.22 = 6 7 6 4 6 6 5) 27.17 x 5.14 = 1 3 9 6 5 3 8B. Solve the following. Choose your answer from the box. Write the letter of the correct answer.1) product of 2.5 and 3.45 A. 3.76 B. 50.6942) 18.72 times 2.93) 2.35 x 1.6 C. 8.6254) 24.56 multiplied by 3.55) product of 3.57 x 14.2 D. 85.96 E. 54.288 3

WRAP UP When multiplying mixed decimals, multiply as youwould multiply whole numbers. The number of decimal placesin the product is the same as the total number of decimals inthe factors.ON YOUR OWNFind the products. Write your solutions and answers in your notebook.1) 81.24 x 3.62 = 4) 32.06 5) 126.352) 9.38 x 1.23 = x 3.49 x 1.323) 16.4 x 3.63 = 4

MULTIPLICATION OF DEGCRIAMDAELVNUMBERS BY 10 AND 100MULTIPLICATION OF DECIMAL NUMBERS BY 10 AND 100 Objective: Multiply decimals by 10 and 100 REVIEW Multiply as fast as you can. 1) 26 x 10 2) 245 x 100 3) 365 x 10 4) 483 x 100 5) 121 x 100STUDY AND LEARNLook at the table below. A B0.12 x 10 = 1.2 0.12 x 100 = 120.45 x 10 = 4.5 0.45 x 100 = 450.61 x 10 = 6.1 0.61 x 100 = 610.74 x 10 = 7.4 0.74 x 100 = 74Study the multiplication sentences in Column A.Each of the decimal numbers were multiplied by 10.Look at their products. What do you notice?How many places were the decimal point moved?Were the decimal point moved to the left or to the right?Look at Column B this time.One hundred (100) is the common factor in the multiplication sentences.What do you notice with the products?How many decimal places were the decimal point moved? 1

What do you observe…a. when a decimal is multiplied by 10?b. when a decimal is multiplied by 100?Here are some more examples. Observe closely the movement of the decimal point.1.45 x 10 = 14.5  move 1 decimal place to the right76.43 x 10 = 764.3  move 1 decimal place to the right6.42 x 100 = 642  move 2 decimal places to the right42.78 x 100 = 4278  move 2 decimal places to the rightVery easy! We just move the decimal point 1 or 2 places to the right when wemultiply decimals by 10 or 100, respectively.TRY THESEA. Find the product.1) 4.25 x 10 5) 7.9 x 102) 16.72 x 100 6) 8.35 x 1003) 45.27 x 10 7) 1.25 x 104) 33.45 x 100 8) 0.47 x 100B. Write 10 or 100 in the box to make the multiplication sentence correct.1) 2.46 x ___ = 24.6 6) 4.27 x ___ = 4272) 23.72 x ___ = 2372 7) 10.25 x ___ = 102.53) 42.73 x ___ = 427.3 8) 3.04 x ___ = 3044) 62.29 x ___ = 622.9 9) 40.02 x ___ = 400.25) 0.23 x ___ = 2.3 10) 3.63 x ___ = 36.3 2

WRAP UP When multiplying decimals by 10 or 100 simply move the decimal point 1 or 2 places, respectively, to the right. ON YOUR OWNA. Multiply. Write your answers in your notebook. 1) 2.69 x 10 2) 3.33 x 100 3) 14.38 x 100 4) 2.27 x 10 5) 102.34 x 10B. Write 10 or 100 on the blank. Write your answers in your notebook. 1) 6.85 x ___ = 68.5 2) 2.3 x ___ = 23 3) 14.27 x ___ = 1427 4) 3.99 x ___ = 399 5) 16.41 x ___ = 164.1 3

MULTIPLICATION OF DECIMALS MENTALLY MULTIPLICABTYIO0.N1,GO0R.F0A1DDAEENCVDIM0A.0L01S MENTALLY BY 0.1, 0.01 AND 0.001 Objective: Multiply decimals by 0.1, 0.01 and 0.001 mentally REVIEWA. Insert the decimal point in the products to make the number sentences correct. 1) 3.72 x 10 = 372 2) 61.217 x 100 = 6121 3) 18.177 x 100 = 18177 4) 25.64 x 10 = 2564 5) 7.214 x 100 = 7214B. Multiply. 1) 8.93 x 10 =  2) 4.72 x 10 =  3) 17.25 x 100 =  4) 42.7 x 100 =  5) 86.41 x 10 =  1

STUDY AND LEARNDo you know that we can easily multiply decimals by 0.1, 0.01 and 0.001 in a very, veryeasy way? Study the examples below. 0.1 x 21.4 = 2.14 0.01 x 21.4 = 0.214 0.001 x 21.4 = 0.0214Compare the multiplicands and the products.In what direction is the decimal point in the product moved? to the leftWhen 21.4 is multiplied to 0.1, how many decimal places was the decimal point in theproduct moved? ( one )When it is multiplied by 0.01? 0.001? ( two, three )What pattern do you observe? Since any number multiplied by 1 is equal to the number, just count thedecimal places in 0.1, 0.01 and 0.001 and move the decimal point of the other factorto the left by the appropriate number of decimal places.What do we put in the product if the decimal places are not enough? zeroBelow are other examples for you to study.0.1 x 14.52 = 14.52 = 1.4520.01 x 314.35 = 314.35 = 3.14350.001 x 49.73 = . 4973 = 0.04973Look at the last example, we used zero (0) as place holder. 2

TRY THESELet’s see if you can answer the following:A. Write the missing number.1) 12.79 x ___ = 1.2792) 151.82 x ___ = 15.1823) 426.34 x .001 = ___4) 289.01 x .01 = ___5) 603.45 x ___ = 6.0345B. Multiply. Complete the table below. 0.1 0.01 0.0011) 14.352) 156.323) 412.454) 123.735) 249.02 WRAP UP In multiplying decimals by 0.1, 0.01 and 0.001 move the decimalpoint of the other factor to the left by the number of decimal places in 0.1,0.01 and 0.001, respectively. 3

ON YOUR OWNMultiply the following mentally. Write your answers in your notebook.1) 43.35 x 0.1 6) 26.72 x 0.0012) 62.14 x 0.01 7) 89.99 x 0.013) 14.35 x 0.001 8) 143.15 x 0.14) 314.78 x 0.1 9) 365.01 x 0.0015) 543.96 x 0.01 10) 337.14 x 0.01 4

WORD PROBLEMS INVOLVINGGRAMDUE LVTIPLICATION OF DECIMALS WORD PROBLEMS INVOLVING MULTIPLICATION OF DECIMALS Objective: Solve word problems involving multiplication of decimals REVIEW Find the product in each of the following: 3.05 x 0.45 1

STUDY AND LEARN The weight of man on the moon is only 0.167 of his weight on Earth. If Nelly weighs 35.75 kg. on Earth, what will be her weight on the moon?Let’s solve the problem following the steps below:1. Read and understand the problem.  What is asked for in the problem? the weight of Nelly on the moon  What are the given facts? 0.167 of man’s weight on earth as the weight of man on the moon and 35.75 kg. Nelly’s weight on earth2. Plan  How are we going to solve for the answer? We have to find 0.167 of 35.75 kg.  What would be our number sentence? 0.167 x 35.75 = n3. Solve and look back.0.167 x 35.75 = n 35.75  2 decimal placesx 0.167  3 decimal places 25025  5 decimal places 21450 3575 .5.97025Look at our answer. Does 5.97025 make sense?So, 0.167 x 35.75 = 5.97025Nelly weighs 5.97025 kg on the moon. 2

TRY THESEA. Read the story problems. Answer the questions that follow. Marina uses 0.5 m of cloth to make a throw pillow case. How many meters of cloth does she need to make 16 throw pillow cases? 1. What is the number sentence? 2. What is the answer? A meter of lace costs 36.50. Marifel needs 8.5 meters for her table cloth. How much will she spend for the lace? 3. What is the number sentence? 4. What is the answer?B. Read and solve. Manuel bought 15 notebooks at 12.75 each. How much did he pay for the notebooks? Freddie works in a shoe factory in Marikina. He earns an average wage of 450.00 a day. How much will he earn in 5.5 day? WRAP UP In solving word problems involving multiplication of decimals, remember these: Step 1: Read and understand the problem. Step 2: Make a plan. Step 3: Solve and look back. 3

ON YOUR OWNSolve these word problems. Write your solutions and answers in your notebook.1. Jimmy measures the length of the blackboard using his hand span and finds that it is 27 hand spans long. If his hand span is 17.25 cm, how long is the blackboard?2. Rebecca bought 8 cans of evaporated milk for 32.75 each. How much did she pay for all the milk?3. Julia sells mangoes in the market. She earns 2.75 for every mangoes she sells. If she was able to sell 65 mangoes, how much will she earn?4. A rectangular lot measures 12.75 m by 20.36 m. What is its area?5. Michelle prepared 3.5 liters of orange juice a day. How many liters of orange juice will be made if she prepares the same amount of juice for 5 days? 4

DIVISIONGROAFDDE EVCIMALS DIVISION OF DECIMALSObjective: Divide decimals by decimals through hundredths.REVIEW1) 3 13.5 3) 12 6.24 5) 17 4.422) 8 60.8 4) 6 11.22 6) 14 1.764 1