MATH 5

WRAP UPIn subtracting a whole number from a mixed number:  Bring down the fractional part.  Find the difference of the whole numbers.ON YOUR OWNA. Find the difference. Reduce the answers to its lowest terms if possible. Write your answers in your notebook. 3 1 21. 17 2. 10 3. 9 8 4 8 - 14 -5 -5B. Solve. Write your solutions and answers in your notebook. 1 1. Riza bought 4 kilograms of fish. When she removed the scales, gills and 4 intestines, the weight was just 4 kilograms. How many kilograms was the waste?2. Father spends 3 hours working in his garden every Saturday. From Monday to 5 Friday, he works a total of 10 hours in his garden. How much longer does 6 father work in his garden from Monday to Friday than on Saturday? 3

SUBTRACTION OF FRACTGIROANDES VFROM WHOLE NUMBERSSUBTRACTION OF FRACTIONS FROM WHOLE NUMBERS Objective: Subtract fractions from whole numbersREVIEWFind the difference. Express the answer in lowest terms, if necessary. 3 1 9 1 31) 15 2) 9 3) 21 4) 18 5) 16 8 3 12 4 9 -4 -5 - 10 -9 -4 STUDY AND LEARNExample 1: Read the problem. 2 Rizal had 2 cartons of orange juice. He drank of the 2 cartons for breakfast. 8 How much orange juice is left? Let us solve the problem. 2 2 - 8 2 We cannot subtract from 2 immediately. 8 1

Step 1 – Write 2 as mixed number, whose fractional part has the samedenominator as the subtrahend. 88 2 = 1 + = 1 , 8 is used as the denominator since the denominator of the 88 2 given subtrahend ( ) is 8. 8 8 2 1 8 = N . Perform theStep 2 – Set up the new number sentence, 8 operation 2= 8 1 8 2 2 -= - 8 8 6 1 8Step 3 – Reduce the answer to its lowest terms if needed. 2 8 2 1 -= 8 8 2 - 8 63 1 or 1 84Example 2:Let’s have another example. Brix can run around a 400-metre track oval in 5 minutes. If he runs the first 100 9meters of the oval in minute, how long does it take him to run the remaining 300 10meters? What is asked in the problem? What are the given facts? What is operation to be used? What is the number sentence? Can you follow the steps in subtracting fractions from a whole number? If yes, then, show your solutions to the problem. If not, then fill in the following box with the correct answers. Step 1 – Express whole number as a mixed number. 2

10 10 5 = 4 + 10 = 5=4+ =4 10 10Step 2 – Write the new number sentence, then subtract. 5= 4 9 9 -= - 10 10Step 3 – Reduce the answer to lowest terms if needed. Is there a need to reduce the answer to its lowest term? _____The final answer is _____.TRY THESEFind the difference. Reduce the answers to lowest terms if needed.1) 9 2) 10 3) 15 4) 5 5) 8 3 5 9 4 5 - - - - - 5 9 12 6 86) 9 7) 3 8) 15 9) 5 10) 9 1 1 3 2 5 - - - - - 5 2 8 6 9 WRAP UPIn subtracting a fraction from a whole number:  Convert the whole number into a mixed number whose fractional part has denominators identical to the fraction in the subtrahend.  Find the difference.  Reduce the answer to its lowest term if possible. 3

ON YOUR OWNA. Find the difference. Reduce the answers to lowest terms if possible. Write your answers in your notebook.1) 2 2) 7 3) 15 3 5 9 - - - 8 9 10B. Solve. Write your solutions and answers in your notebook. 9 1. Eugene spent 3 hours in doing his homework. He rested for hour. How 15 many minutes did he spend actually working on his homework? 5 2. Mother bought 1 large pizza for the afternoon snacks. Her children ate of 8 the pizza. What portion of the pizza was left? 4

SUBTRACTION OF FRACGTRIAODNESVFROM MIXED NUMBERSSUBTRACTION OF FRACTIONS FROM MIXED NUMBERS WITHOUT REGROUPING WITHOUT REGROUPING Objective: Subtract fractions from mixed numbers without regroupingREVIEWSubtract. Simplify the answers if necessary.1) 15 2) 2 3) 21 4) 50 5. 45 3 5 9 5 3 - - - - - 9 9 12 15 18 STUDY AND LEARN 51 Toni Rose has 2 meters of lace. She used meter for her blouse. How 95many meters of lace were left? What is asked in the problem? What are the given facts? What is the number sentence? How do you subtract fractions from mixed forms? Let’s see how this is done. 5 15 2 We cannot subtract from immediately because the fractions 9 59 1 are dissimilar. Let’s change dissimilar fractions to similar - 5 fractions.Step 1 – 51 Find the LCD of and . 95 51 The LCD of and is 45. 95 1

Step 2 – 15 Find the fractions that are equivalent to and by using the 59 14 LCD of and which is 45. 59 5 25 (45  9 x 5 = 25) = 9 45 19 (45  5 x 1 = 9) = 5 45Step 3 – Subtract. 5 252= 2 9 45 1 9-= - 5 45 16 2 m of lace were left 45 Step 4 – Simplify or reduce the answers to lowest terms if necessary.Let’s have another example.Example: 13 Cris bought 1 gallons of paint. He used to paint a small portion of their 28fence. How much paint was left? 131. The LCD of and is 8. 28 142. 1 = 1 28 33 -= 88 1 1 gallons of paint were left 8 2

TRY THESEMatch Column A with the correct answers found in Column B. Write your answers inyour notebook. Column A Column B 23 91. 7 - = N a. 3 35 20 51 72. 4 - = N b. 4 64 12 11 73. 7 - = N c. 4 23 20 32 14. 4 - = N d. 7 58 15 13 15. 4 - = N e. 7 54 6 WRAP UPTo subtract fractions from mixed forms with unlikedenominators:Step 1: Find the LCD of the fractions.Step 2: Find the equivalent fractions.Step 3: Subtract.Step 4: Reduce answers to lowest terms if needed. 3

ON YOUR OWNSubtract and simplify. Write your answers in your notebook. 5 3 5 3 21. 5 2. 6 3. 6 4. 5 5. 3 8 4 4 5 3 1 2 3 2 2 - - - - - 3 4 4 4 8 4

SUBTRACTION OF MIXED NGURMABDEERVS FROM WHOLE NUMBERSSUBTRACTION OF MIXED NUMBERS FROM WHOLE NUMBERS Objective: Subtract a mixed number from a whole numberReviewLet’s see how fast you can do this exercise.Choose the correct answers from the box below. 2 4 5 3 51) 3 2) 9 3) 3 4) 5 5) 7 3 5 6 4 9 1 1 3 1 1 - - - - - 2 4 5 2 3 7 2 1 1 1 9a. 3 b. 7 c. 3 d. 7 e. 5 f. 9 30 9 6 3 4 20 Study and LearnExample 1: Read this problem. 1 Richard plays the piano for 3 hours each day. He has played for 2 hours. How 4 much longer will he play?  What are the given facts?  What is asked for in the problem?  What is the number sentence?  Which is the minuend?  Which is the subtrahend? 1

1We cannot subtract 2 from 3 immediately. 4We have to follow some steps to do this as a mixed number whose fractional part has thesame denominator as the subtrahend.Step 1 – Write the whole number. 34 Rename 3 as 2 so that the denominators 1 4 -2 are the same. 4 4 3 = 2 + 1; and 1 = since the denominator 4 of the subtrahend is 4. 44 Thus, 3 = 2 + 1 = 2 + = 2 44Step 2 – Subtract. 4 3= 2 1 -2 = 4 4 1 -2 4 3 4Let’s have another example.Example 2: Therese was told by her mother to unpack the 5 boxes of books and put them in the 1bookshelf. She unpacked 2 of the boxes. How many boxes are still to be unpacked? 5 The number sentence is _____. 55 5 can expressed as a mixed number: 5 = 4 + = 4 . 55 15 Can you now subtract 2 from 4 ? 55 If yes, then, show your solution. If you were Therese, would you obey your mother? Why? What kind of a child is Therese? Do you think her mother will be proud of her? Why? 2

Try TheseA. Let’s play. The problems are on each step of the ladder. Each step has a corresponding point if you can give the correct answer. If not, the points in that step will be subtracted from your total score. 50 points 40 points 30 points 20 points10 points ScoreB. Subtract and simplify your answers. 4 2 25 - 18 = N 21 - 5 = N 5 4 40 points 50 points 2 3 16 - 10 = N 9- 3 =N 8 5 20 points 30 points 1 Score5- 4 =N 410 pointsWhat’s your total score?Can you give the steps in subtracting a mixed fraction from a whole number? 3

Wrap Up Steps in subtracting a mixed fraction from a whole number Step 1: Rename the whole number as a fraction by getting 1 from the whole number and changing it into a fraction equivalent to 1. Step 2: Subtract the fractions. Step 3: Reduce answers to lowest terms if needed. On Your OwnSolve and simplify. Write your solutions and answers in your notebook. 31. Freddie worked 14 hours on the first week and 9 hours the next week. How many 4 more hours did Freddie work on the first week than on the second week? 12. Beng had a ribbon 5 meters long. She used 3 meters to make award badges. How 5 many meters of ribbon were left? 33. At a track meet, Paula Joy jumped 8 feet. Robinee Mae jumped 6 feet. How much 4 farther than Robinee Mae did Paula Joy jump? 14. Shay Michaela cut a 4 meter piece of ribbon from a piece 7 meters long. How long 2 is the remaining piece? 15. Jan Alexis works 40 hours a week as a cashier in a gym. He has worked 28 hours 8 already. How many more hours will he work? 4

SUBTRACTIONGORAFDME IVXED NUMBERSSUBTRACTION OF WMIITXHEODUNTUMREBGERROS UWPIITNHGOUT REGROUPINGObjective: Subtract a mixed number from another mixed number without regroupingREVIEWDo you still remember how to subtract a mixed fraction from a whole number?Answer the following. Show your solutions.1) 18 2) 42 3) 12 4) 16 5) 21 - 93 - 38 5 - 75 - 10 3 - 18 4 4 9 8 9 5 STUDY AND LEARNRead and analyze problems a and b.a. Father harvested 25 3 kilograms of mangoes. He sold 15 1 kilograms. How many 44 kilograms of mangoes were left?b. Leo rides his bicycle 5 3 km. Francis rides his bicycle 4 1 km. How much farther 10 3 did Leo ride his bicycle than Francis? What is the difference between the two problems? Which problem do you think is easy to solve? Why? Which problem do you think is difficult to solve? Why? 1

Let’s solve the problems.Problem A The number sentence is:25 3 - 15 1 = N 44What can you say about the fractions in Problem A?(The fractional parts are similar fractions.)Is there a need to change the fractions?How do you subtract similar fractions? Subtract the numerators then write its answerover the common denominator. 25 3 4- 15 1 410 2 or 10 1 42Problem B The number sentence is:5 3 - 41 =N 10 3 What can you say about the fractions in Problem B? Can we subtract 1 from 3 immediately? Why? 3 10 What shall we do with the fractions? Change them to similar fractions. How do we change dissimilar fractions to similar fractions?Step 1 – Rename the fractions as equivalent fractions with the least common denominator (LCD). 5 1 = 5 10 The LCD of 1 and 3 is 30. 3 30 3 10-43 =49 (30  3 x 1 = 10) 10 30 (30  10 x 3 = 9) 2

Step 2 – Subtract. 5 1 = 5 10 3 30 -43 =49 10 30 11 30Step 3 – Reduce the answer to its lowest term if needed. Is there a need to reduce 1 1 to its lowest term? Why? 10Let’s have more examples.Example 1: One goat weighs 36 7 kilograms. The smaller one weighs 17 5 kilograms. 88 How much lighter is the smaller goat than the other goat? What is the number sentence in Problem A? Can we subtract 17 5 from 36 7 immediately? Why? 88 So: 36 7 8 - 17 5 8 49 2 or 49 1 84Example 2: Ted is feeding the chickens in his uncle’s farm. When he started, there were 8 3 4buckets of chicken feed. When he finished feeding the chickens, 1 3 buckets of feed 6were left. How much feed was used? What is the answer to Problem B? 3

We want to know how much chicken feed Ted used. We know that he startedwith 8 3 buckets of feed and he has 1 3 buckets left. To find the amount used, we must 46subtract the amount left from the original amount. Can we subtract 1 3 from 8 3 64immediately? Why? What is the LCD of 3 and 3 ? 64 83 = 8 9 4 12 - 13 = 1 6 6 12 7 3 or 7 1 12 4 TRY THESESubtract and simplify. 4

WRAP UPIn subtracting mixed fractions where the fractions are similar:  subtract the whole numbers  subtract the numerators  reduce the answers to lowest terms if neededIn subtracting mixed fractions where the fractions are dissimilar:  rename the fractions as equivalent fractions with the least common denominator (LCD)  subtract  reduce the answers to lowest terms if neededON YOUR OWNSubtract and simplify. Write your solutions and answers in your notebook.1) 5 3 2) 8 2 3) 7 2 4) 9 3 5) 15 2 5 3 3 5 3 31 21 35 31 84 3 2 8 2 86) 15 6 7) 8 4 8) 20 5 9) 18 3 10) 10 3 8 5 6 4 9 94 42 15 3 91 64 8 5 6 4 9 5

SUBTRACTION OF MIXEDGRNAUDME BVERS WITH REGROUPING SUBTRACTION OF MIXED NUMBERS WITH REGROUPINGObjective: Subtract a mixed number from another mixed number with regrouping REVIEWLet’s see how fast you can solve this. Just remember the steps in subtracting fractionsfrom mixed numbers with regrouping. Choose the correct answers below. 1) 11 4 7 2 - 72) 6 7 6) 9 3 8 8 -4 -1 8 83) 16 2 4) 15 8 5) 8 8 9 6 9 -1 -5 -5 9 6 9A B CD E F11 2 9 1 8 1 6 3 15 1 16 174 38 29 1

STUDY AND LEARN What is the difference when 6 5 is subtracted from 21 7 ? 8 12Let’s analyze the problem.What is asked in the problem? The difference when 6 5 is subtracted from 821 7 12What are the given facts? 6 5 , 21 7 8 12What is the number sentence? 21 7 - 6 5 = N 12 8Let’s solve the problem. 21 7 12 - 65 8STEP 1 – Change the fractional parts to similar fractions. The least common denominator of 7 and 5 is 24. 12 8 21 7 = 2114 (24  12) x 7 = 14 12 24 (24  8) x 5 = 15 - 6 5 = 6 15 8 24STEP 2 – The subtrahend has a larger fraction than the minuend, so take 1 fromthe whole number part of the minuend and change it to fraction using thecommon denominator. 21 7 = 2114 21 – 1 = 20 + 24 = 20 38 12 24 24 24 - 6 5  6 15 8 24 2

STEP 3 – Add the fraction equal to one and the fraction in the minuend. 20 14  24  20 38 24 24 24STEP 4 – Subtract. 20 38 24 - 6 15 24 14 23 24The final answer is 14 23 . 24Reduce the answer to its lowest term when necessary.Let’s have another example.Example:Find the difference of 9 3  5 2 . 53The LCD of 3 and 2 is 15. 53Solution: 9 3  9 9  815  9  8 24 5 15 15 15 15- 5 2  510 3 15 8 24 15- 510 15 3 14 15 3

TRY THESEA. Solve for the difference. 2) 8 2  3 3  N 3) 11 3  5 2  N 1) 16 3  2 2  N 54 93 53 4) 20 3  9 4  N 5) 10 3  8 1  N 56 92B. Subtract.1) 9 1 2) 5 2 8 5 - 33 - 31 4 23) 16 1 4) 15 1 4 3 - 75 - 73 8 55) 4 2 - 1 5 = N 68 WRAP UPIn subtracting a mixed fraction from another mixed fractionwith unlike denominators:  Rename the fractions and make them similar fractions.  Subtract and reduce the answers to lowest terms when necessary. 4

ON YOUR OWNMatch Column A with the correct answer in Column B. Write your answers in yournotebook.A B1) 19 1 12 3 a) 1 7 25 82) 4 3  2 1 b) 113 82 183) 5 2  3 4 c) 3 5 45 124) 6 2  4 3 d) 6 9 96 105) 6 1  2 3 e) 1 7 64 10 5

ONE-STEP WORDGPRRAODBE LVEMS INVOLVINGONE-STEP WORSUDBPTRROABCLTEIMOSNIONFVFORLAVCINTGIOSNUSBTRACTION OF FRACTIONS Objective: Analyze word problems Solve word problems involving subtraction of fractions REVIEW Choose the correct answer below. Write the letter of the correct answer on your notebook.41- 22  N 83- 52  N 12 3 - 7 1  N 13 3 - 10 2  N 92 - 56  N 34 43 63 53 38A. 311 L. 5 1 O. 3 1 P. 1 5 Y. 214 12 6 12 6 15 If you get the correct answer, you will also know the man behind problemsolving. This man is renowned as a brilliant teacher. His most famous work “How toSolve It” published in 16 languages, explains problem solving. His name is George. 1

STUDY AND LEARNDo you know the magic words in solving word problems?Read the word problem below, then refer to the diagram showing the steps in problemsolving. This rice dispenser can hold 49 3 kilograms of rice 4 when full. Rita put 42 1 kilograms of rice in the dispenser. 2 How many more kilograms of rice are needed to fill the rice dispenser?Let’s analyze the problem.a. See/Know/Understand 1. What is asked in the problem? The number of kilograms of rice needed to fill the rice dispenser. 2. What are the given facts? 49 3 kilograms of rice the dispenser can hold 4 42 1 kilograms of rice – the amount of rice placed in the rice dispenser 2 3. What operation should be used? Subtraction 4. What is/are the hidden questions? None 2

b. PlanWhat is the number sentence? 49 3 - 1 =N 4 42 2c. DoSolve. 3 = 49 3 49 44 12 - 42 = 42 24 71 4d. Check We can check our solution to see if it fits the facts of the problem. To check, add the difference and the subtrahend to get the minuend. 71 4 + 42 2 4 49 3 4 We were able to get the minuend (the total number of kilograms of rice the dispenser can hold). Therefore our answer is correct.Let’s have another example.Example: Richelle spent 3 3 hours in the gym one Saturday and 3 1 hours the next 82Saturday. How much longer did she spend in the gym on the second Saturday?Answer the following questions:a. What is required in the problem?b. What are the given facts?c. What operation is to be used?d. What is the number sentence?e. What is the answer?f. Is your answer reasonable? Check your answer. 3

TRY THESESolve the following problems. Follow the steps in solving word problems. 1. Connie weighs 45 1 kilograms. When Connie and Dolly Ann step on the scale 2 together, the scale shows 125 3 kilograms. What is the weight of Dolly Ann? 4 2. Patty has a roll of ribbon 8 3 meters long. She used 5 1 meters of the ribbon for 43 decoration. How long is the remaining ribbon? 3. Tina bought 1 5 kilograms of cheese from the deli. Her friends ate 3 of it. How 64 much was left?WRAP UP See/know/ What is asked for? understand What are the facts?Steps in Plan solving Do What operation is to be word used?problems What is/are the hidden question? What is the number sentence? Solve Check Review your answer and see if reasonable. 4

ON YOUR OWNRead, analyze and solve. Write your solutions and answers in your notebook.1. Eden planted vegetables in a 3 1 square meter plot in his garden. One 3 square 24 meters are planted with carrots and the rest is planted with vegetables. What part of the plot is planted with other vegetables?2. Ric and Rod use 9 of a liter of white paint for their project in Industrial Arts. So far 16 today, they have used 1 of a liter. How much is paint is left for completion of their 4 project? 5

TWO-STEP WORDGPRRADOEBVLEMS INVOLVINGTWO-SATDEDPITWIOONRDANPDROSBULBETMRASCINTVIOONLVOIFNFGRAADCDTIITOINOSN AND SUBTRACTION OF FRACTIONSObjective: Solve two-step word problems involving addition and subtraction of fractionsREVIEWPerform the indicated operations.1) 2  5 2) 6  2 3) 2 2  5 1 33 88 334) 3 2  2 1 5) 5 7  2 2 33 84 STUDY AND LEARN Mandy filled his car’s tank with 15 2 liters of gasoline. He used his car for 2 3days. He consumed 6 1 liters on Monday and another 3 3 liters on Friday. How many 24liters of gasoline were left in Mandy’s tank?Let’s analyze the problem.a. What are the given facts? (15 2 ,6 1 ,3 3 ) 324b. What is asked for in the problem? The number of liters of gasoline left.c. What is/are the hidden questions? ( The total number of liters of gasoline used on Monday and Friday. ) 1

d. What operation/operations is/are needed to solve the problem?( addition and subtraction )e. What is the appropriate number sentence?15 2 - (6 1  3 3)  N 3 24f. Show your solution15 2 - (6 1  3 3)  N Answer to the hidden question 3 2415 3 - 10 1 = 5 2 or 5 1 4 44 2There were 5 1 liters of gasoline left 2TRY THESERead the problems then answer the questions that follow:1) Ronald and Kits have to practice riding bicycles 10 3 km two weeks altogether. 4 Ronald has covered a distance of 2 3 km while Kits has covered 4 1 km. How many 54 more kilometres do the two boys have to practice? a. What is asked for in the problem? b. What are the given facts? c. What is the hidden question? d. What operation/operations is/are to be used? e. What is the number sentence for the problem? f. What is the answer to the hidden question? g. What is the answer to the problem? 312. Father bought 8 hectares of land. He planted rubber trees on 3 hectares and 53 1 coconut trees on 2 hectares. How much land was left? 4 a. What is asked for in the problem? b. What are the given facts? c. What is the hidden question? d. What operation / operations is / are to be used? 2

e. What is the number sentence for the problem?f. What is the answer to the hidden question?g. What is the answer to the problem? WRAP UP Steps In Solving A Problem What are What is the the given hidden facts? question? 1 Know/ Understand What is asked What for in the operation is problem? to be used?Check if your 4 2 answer is Check Plan correct What is the Solve the number problem sentence of the 3 problem? Do Solve for the hidden question 3

ON YOUR OWNRead the problems carefully then answer the questions that follow. Write your answersin your notebook.1. Mother had 9 2 meters of cloth. She used 2 1 m for a dress, 1 1 m for pants and 5 4 32 6m for a blouse. How many meters of cloth were left?a. What is asked in the problem?b. What are the given facts?c. What is/are the hidden question?d. What operations are to be used?e. What is the number sentence for the problem?f. What is the answer to the hidden question?g. What is the answer?2. Cora bought 10 1 kilograms of pork for her daughter’s birthday. She used 23 3 kilograms for menudo, 1 1 kilograms for chopsuey, 2 1 kilograms for spaghetti42 3and the rest for lumpia and pork kaldereta. How many kilograms of pork were usedfor lumpia and kaldereta?a. What is asked in the problem?b. What are the given facts?c. What is/are the hidden questions?d. What operations are to be used?e. What is the number sentence for the problem?f. What is the answer to the hidden question?g. What is the answer? 4

VISUALIZATION OF MUGLRTAIPDLE IVCATION OF FRACTIONSVISUALIZATION OF MULTIPLICATION OF FRACTIONSObjective: Visualize multiplication of fractions 12 Translate expressions such as of into multiplication sentence 23REVIEWWrite the multiplication sentence for each illustration.1) 2) ____ x ____ = _____ ____ x ____ = _____3) 4) ____ x ____ = _____ ____ x ____ = _____5) ____ x ____ = _____ 1

STUDY AND LEARNNelia draws a big She then crosses out 1 of 3 3square and colors of the colored part. 4it yellow. 1 of 3 3 34 43 4The part with crosses is 1 of the part she colored yellow which is 3 of the big 34square.So, we say 1 of 3 is _____. 34The word “of” means to multiply and “is” means “equals.”We can write this as a mathematical sentence. 1 x 3 =N 34Let’s solve for the answer.1 x 3 = 1x3=3 Multiply the numerators.3 4 3 x 4 = 12 Multiply the denominators.So, 1 x 3 = 3 or 1 . Reduce to lowest terms. 3 4 12 4 2

Let’s have another example.Example:Find 3 of 1 . 52Let’s illustrate this. Study the process closely.1325 3 of 1 52The shaded part in the first illustration is 1 . 2The double shaded part in the second illustration is 3 of 1 . 52The mathematical sentence for this is: 3 x 1=N 52Let’s solve it. 3 x 1= 3 5 2 10Multiply the numerators then the denominators.The answer is 3 . 10Do we need to reduce this to its lowest terms? Why? 3

TRY THESEA. Do the activity below.1. Get 1 whole bond paper. 22. Color of it with blue. 33. Draw red lines on 1 of the colored parts. What portion of the colored part 4 has red lines on them?What fraction of the whole bond paper has red lines on it?1 of 2 is 1 x2 = =43 43B. Complete the table. Write your answer in your notebook. Number 1 is done for you. Illustration Number Sentence Answer 1x5 51) 1 of 5 38 24 382) 1 of 1 623) 4 of 1 524) 2 of 5 365) 1 of 2 45 4

WRAP UP To illustrate multiplication of fractions  shade part of the region representing the second fraction  double-shade the part representing the first fraction  the double-shaded parts is the numerator of the product and the total number of parts is the denominator The word “of” means to multiply and the word “is” means equals. ON YOUR OWNUse the pictures to show the product. Then, write the multiplication sentence on theblank. Reduce the answer to its lowest terms if possible. Write your answers in yournotebook.1) 2 of 3 is __________ 342) 1 of 5 is __________ 273) 1 of 2 is __________ 43 5

4) 3 of 7 is __________ 5 105) 2 of 3 is __________ 38 6

MULTIPLICATION OF FRAGCRTAIDOENVS BY ANOTHER FRACTIONMULTIPLICATION OF FRACTIONS BY ANOTHER FRACTION Objective: Multiply a fraction by another fractionREVIEWCopy the figure in your notebook.Change the fractions to their simplest forms. One has been done for you. 1. 2. 3. 14 6 15 2 16 12 20 6. 6 8 4. 9 9 32 45 5. STUDY AND LEARNExample 1: Michelle bought 3 kg of carrots for her pet rabbit. Her pet ate 1 of this. 43 How many kg of carrots did her pet eat? 1

To know the amount of carrots the rabbit ate, let us compute 1 of 3 . 34How do we write 1 of 3 in a number sentence? 1 x 3 = N 34 34Let’s solve this in two ways.First, let’s use an illustration to get the product, as we did in Module 27. 3 4 1 3 33 44 1x3= 3 =1 3 4 12 4 The double-shaded parts show the parts of the 3 kg of carrot eaten by the rabbit. 4 3 when reduced to its lowest terms is 1 .12 4So, Michelle’s pet ate 1 kg of carrots. 4Let’s solve 1 x 3 again, this time through computations. 34STEP 1 Multiply the numerators. 1 x3 =3STEP 2 Multiply the denominators. 34 1x3= 3 3 4 12STEP 3 Reduce the product to its lowest term. 3 31 12 3 4 2

Did we get the same answer? What method do you find easier?Let’s have another example.Example 2: Let’s multiply 3 by 1 . 83Study the solution below: 3 x 1 =N 83 3 3 = 1 24  3 8 3 31 24 3 8 So, 3 x 1 = 1 . 838Here are other examples for you to study.a) 1  2 = N b) 3  2 = N 63 751  2 = 2 = 2 2 = 1 3 2 =66  3 18 8 2 9 7 5 35 3

TRY THESEFind the products of the fractions in diagonally adjacent pairs of hexagons. Write youranswer on the appropriate circle. Reduce the products to lowest terms if necessary. 151342 263857 3 21 3 4 43385 WRAP UP In multiplying a fraction by another fraction, simply multiply the numerators then, multiply the denominators. Reduce the answers to lowest terms if necessary. 4

ON YOUR OWNMatch Column A with Column B. Write the letter of the correct answer. Write youranswers in your notebook.Column A Column B1) 4 x 2 a) 4 7 582) 3 x 2 b) 4 93 113) 5 x 2 c) 1 65 34) 8 x 1 d) 6 11 2 275) 5 x 4 e) 2 75 9 f) 1 5 5

MULTIPLICATION OF FRGARCATDIEOVNS BY WHOLE NUMBERSMULTIPLICATION OF FRACTIONS BY WHOLE NUMBERS Objective: Multiply fractions by whole numbersREVIEWMultiply. Reduce your answers to lowest terms.1) 4 x 1 2) 2 x 1 3) 4 x 2 82 35 57 4) 2 x 3 5) 7 x 3 95 94 STUDY AND LEARNRead the story problem carefully. Mother bought 12 apples. She asked Rizza to keep 2 of them in the 3refrigerator. How many apples did Rizza place in the refrigerator? How many apples did mother buy? Here are the 12 apples. Using the denominator of 2 , into how many small groups should Rizza divide 3the apples? threeHow many small groups of apples should be placed in the refrigerator? Two 1

How many apples are there in 2 small groups? 8 applesSo, 2 of 12 is 8. 3Rizza kept 8 apples in the refrigerator.Let’s try to solve the problem in another way, by computation.2 of 12 is the same as 2 x 12 = N.33 Solving this is easy because you already know how to multiply 2 fractions. 12can be written as 12 in fraction form. 1Look closely at the solution below.2 x 12 = 2 x 12 = 2 x 12 = 24 or 83 3131 3Did we arrive at the same answer?How did you find this lesson? Let’s solve some more problems. Study them.a. 16 mangoes b. 15 roses 3 are ripe 1 are red 4 3 How many are ripe? How many are red roses? 3 x 16 = N 1 x 15 = N 4 3 3 x 16 = 48 or 12 mangoes 1 x 15 = 15 or 5 red roses 41 4 31 3 2

TRY THESESolve the exercises below by yourself. Don’t forget to express your answers in lowestterms.A. Read and solve.1) 36 birds in the cage, 5 are love birds. 9 How many are love birds?2) 45 children in the party, 2 are girls. 3 How many are girls?3) 60 papayas, 2 are ripe. 5 How many are ripe?B. Multiply.1) 4 of 35 = N 2) 3 of 42 = N 3) 6 x 44 = N 5 7 11 WRAP UP In multiplying a whole number by a fraction, rename the wholenumber as a fraction, then multiply. Reduce the answer to lowest terms. 3

ON YOUR OWNFind the product. Write your solutions and answers in your notebook. 1) 10 pillow cases, 3 are yellow. 5 How many are yellow? 2) 120 profit, 1 is saved. 5 How much is saved? 3) 3 of 12 7 4) 2 x 13 5 5) 4 x 49 7 4

MULTIPLICATION OF MIXGREADDNE UVMBERS AND FRACTIONSMULTIPLICATION OF MIXED NUMBERS AND FRACTIONS Objective: Multiply a mixed number by a fractionREVIEWMultiply the following: 2) 7 x 54 3) 24 x 3 1) 4 x 39 9 8 13 5) 7 x 2 4) 10 x 5 8 8 STUDY AND LEARN Mang Emong harvested 3 1 crates of watermelons. He sold 2 of them. How 23many crates of watermelon were sold?To find out what is 2 of 3 1 , let’s follow the steps below. 32 1st Change the mixed number to improper fraction. 31  7 222nd Multiply. Use cancellation, if possible, before multiplying. 1 1

2 x 31 = 2 x 7 = 7 = 21 3 2323 3 1In canceling, make sure one numerator and one denominator aredivided by the same number.Mang Emong sold 2 1 crates of watermelons. 3Always remember to express your answer in its lowest terms if possible.Were you able to follow? Here are other examples for you to study.a. 2 of 1 2 3 372 x 12 = 2 x 9 = 63 7377 1b. 4 5 x 3 = n 64 129 x 3 = 29 or 3 5648 82 TRY THISFor greater mastery, try to answer the exercises below.A. Solve the following. Express your answers in lowest terms. 1) 2 1 multiplied by 3 35 2) Find the product of 5 and 3 5 12 9 3) What is 3 1 by 4 ? 27 4) 5 of 1 1 is ____. 82 5) 2 times 2 1 equals ____. 93 2

B. Write the missing number and multiply. Express the products in their lowest terms. 1) 3 1 x 7 = x 7 48 48 2) 7 1 x 3 = x 3 24 24 3) 5 x 2 1 = 5 x 6 363 4) 3 x 8 1 = 3 x 5 252 5) 2 3 x 1 = x 1 43 4 3 WRAP UP When we multiply mixed numbers by a fraction, change the mixed number first into improper fraction. Use cancellation before multiplying whenever possible, to simplify the task. Express the product in lowest terms, if necessary. 3