MATH 6

WRAP UPA fraction is close to: 0 when the numerator is very small compared to the denominator. 1 when the numerator is about half the denominator. 2 1 when the numerator and the denominator are nearly equal. ON YOUR OWNA. Look at the number line. Write the correct answer in your notebook. 1 02 1 01 23 4 5 6 7 7 77 7 7 7 7 1. What fractions are close to 0? 2. What fractions are close to 1 ? 2 3. What fractions are close to 1? 4

B. Choose the letter of the correct answer.1. Which fraction is close to 0?a. 1 b. 6 c. 5 10 8 72. ____ is close to 1 . c. 5 2 9a. 5 b. 1 653. 7 , 8 and 9 are close to 1. Which else is close to 1? 8 9 10 a. 2 b. 5 c. 2 7 75 5

GRADE VI COMPARING FRACTIONS Objective: Compare fractions using the cross product method REVIEW Subtracting makes a number smaller. Adding makes a number bigger. Write whether the answers to these problems will be bigger or smaller. 1. I had Php500. I gave my sister Php100. The amount I have now is… 2. Rey had Php50.00. I gave him Php20.00. The amount he has now is… 3. There were 20 candies in a box. I ate 3. The number of candies left is… 4. Cielo had 10 hair clips. Her friend gave her 5 more. The number of hair clips she has is… 5. There were 30 cakes. 10 Were sold. The number of cakes left is…Let’s follow theSsTt UDY AND LEARN Read the problem below. Laura and Ruby bought one buko pie each. Laura ate 2 of her pie while Ruby 3 ate 2 of her pie. Who ate more? 4 1

To find out the answer to the problem, we need to compare the fractions. We can do thatby changing them first to similar fractions. We can easily compare them by using ashortcut called getting their cross products.Study how comparing of unlike fractions is done. Take note of the steps that you shouldfollow. 2 and 2 34Let’s get first their common denominator to make them similar fractions. We can easilyget their common denominator by multiplying 3 and 4, 3 x 4 = 12. So 12 is their commondenominator.Then, let’s get their new numerators.2 and 2 2x4 and 2x3 8 and 634 3x4 4x3 12 122= 8 2= 63 12 4 12We can see that 2 > 2 because 8 > 6 . So Laura ate more.34 12 12As another example, let us compare 7 and 3 . 85 7 = 35 and 3 = 24 8 40 5 40 So 7 > 3 85Notice that the numerator of each fraction is multiplied by the denominator of the other.In the cross product method, which is the shortcut, the products are the numerators of thesimilar fractions; the denominators are not shown. Let us compare 7 and 3 by the 85shortcut. 35 24 73 85 2

35 is bigger than 24 so 7 > 3 . 85Let us try more examples. 54 24 3 , 54 is greater than 24.6 and 3 , 6 > 3 since 6 98 98 9 8 27 143 and 2 , 3 > 2 since 3 2 , 27 is greater than 14.7 97 9 7 9 14 152 and 3 , 2 < 3 since 2 3 , 14 is smaller than 15.5 75 7 5 7 24 244 and 3 , 4 = 3 since 4 3 , 24 is equal to 24.8 68 6 8 6TRY THESEUse the cross product method to compare the pair of fractions. Write =, >, < inyour answer sheet.1) 2 and 3 2) 5 and 8 36 893) 6 and 10 4) 4 and 8 7 16 8 12 3

WRAP UPTo compare two fractions using the cross product method: a. Multiply the numerator of each fraction by the denominator of the other b. Compare the products1) What is the area of a r2) Gigi ON YOUR OWNCompare the pair of fractions below. In your answer sheet, write =, >, or <. 1) 3 and 4 2) 2 and 4 3) 1 and 3 9 12 7 14 8 24 4) 2 and 10 5) 3 and 1 6) 2 and 4 3 15 42 36 7) 1 and 2 8) 5 and 3 9) 5 and 3 83 64 74 10) 3 and 5 58 4

GRADE VISUBTRACTION OF DISSIMILAR FRACTIONS IN SIMPLE FORMSObjective: Subtract dissimilar fractions in simple forms.REVIEWDo you want to find the MESSAGE? Write the letter of the correct answer in the boxcorresponding to the number. Write the message in your notebook.1) 5  4  n 6) 2  3  8  n 86 8 5 202) 3  2  n 7) 4  3  2  n 65 6 15 53) 4  3  n 8) 1  3  5  n 96 2 7 144) 5  4  n 9) 1  2  4  n 12 36 3965) 12  3  n 10) 9  2  3  n 16 4 16 4 8A. 9 L. 1 1 10 4E. 1 1 M. 17 2 18I. 1 7 P. 1 4 24 15F. 1 2 U. 1 2 7 9H. 19 L. 1 7 36 16MESSAGE: (Refer to the picture for the message) 1 2 3 4 5 6 7 8 9 10Is the message true for you? How? 1

Recall the steps in adding dissimilar fractions in simple form. Enumerate the stepsone by one.STUDY AND LEARNYou have learned how to add dissimilar fractions. This time, you will learn how tosubtract dissimilar fractions in simple forms. Observe where adding and subtractingdissimilar fractions are alike.Read this problem. Mother had 3 meter of red ribbon. She used 2 meter to tie her daughter’s 43hair. How many meter of ribbon was left? How long was the ribbon at before using? How long was used for the daughter’s hair? What will you do to find out the remaining length of ribbon?Explore this: What kind of fractions are these? 3 - 2 =n Do you think you can subtract them at once? Why? 43Let’s show 3 and 2 on the number line. 430 12 3 44 44 4 4 0 1 23 3 3 330 1 2 3 4 5 6 7 8 9 10 11 1212 12 12 12 12 12 12 12 12 12 12 12 12 2

In the number line, which fraction is equivalent to 3 ? 9 4 12Which is equivalent to 2 ? 8 3 12If 3 = 9 and 2 = 8 , what do you call now 9 and 8 ?4 12 3 12 12 12Why are 9 and 8 similar fractions? 12 123= 9 Since 12 is the least common multiple (LCM) of 3 and 4,4 12 12 is used as LCD or least common denominator of 3 and 22= 83 12 43Can we now subtract 8 from 9 ? Why? 12 12So: 3= 9 4 12 -2= 8 3 12 1 The difference is 1 meter. Is this fraction in its the lowest term? 12 12Let’s have another example:Subtract 4 from 6 . 57The difference is 2 . Is this in the lowest term already? 35Work on these examples as fast as you can.Example 1: Example 2: 9 3 =10 4 4  ___  9___ - ___ = ____ - 3  ___ 15 ___ 3

TRY THESEWrite the difference in the . Reduce the answers to lowest terms if necessary.52 9463 12 912 5225 83 WRAP UPIn adding dissimilar fractions in simple forms,  find the least common denominator (LCD)  change the fractions to similar fractions  find the difference between the numerators and write the common denominator  reduce the answer to lowest terms when necessary 4

ON YOUR OWN“UP and DOWN the HILL.” Find the difference. Follow the arrow. 31 43 7 7 53 8 12 65 11  11 83 12 18 15 101 7 (5  1) 32 25 64 85 5 ( 3  9 ) (1  1)8 10 10 15 2 3 5

GRADE VISUBTRACTION OF DISSIMILAR FRACTIONS IN MIXED FORMS WITHOUT REGROUPING Objective: Subtract dissimilar fractions in mixed forms without regrouping.REVIEWSubtract, then look for your answer inside the box. Each time the answer appears,write the corresponding letter in the blank. Reduce answers to lowest terms.A. 3  2 I. 6  8 T. (14  1)  1 46 7 14 15 2 5B. 7  3 N. 11  2 U. (5  1)  1 84 15 6 63 4D. 4  3 O. 3  7 5 10 4 12G. 5  1 R. (8  2)  1 64 96 3H. 9  9 S. (18  3 )  2 10 25 20 10 5____ ____ ____ ____ ____ ____ ____ ____ ____ 1 2 2 7 27 7 5 2 1 8 9 7 12 50 30 12 5 2___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ 22111 7 22111 7 5 2 4 5 30 9 7 6 4 5Are you really this kind of student?Enumerate again the rules in subtracting dissimilar fractions in simple forms. 1

STUDY AND LEARNThis time, you will be subtracting mixed forms having different denominators.Read the problem below: After the party, there were still 3 5 pieces of pizza left. The members of the 8family ate 1 1 pieces. How much pizza was left? 4Study the following: 1 or 2 48 35 11  2 3 84 8Without using the diagram, can you subtract 3 5 and 1 1 at once? 84Study this: How do you change 5 and 1 to similar 35  35 84 88 fractions?- 11  - 12 After changing to similar fractions, can you find the difference between the 48 numerators? 23 8 2

Do this example:Subtract 1 2 from 4 3 . 74 43  4 12  7 10 6  8- 2  4 5What is your answer?Is it in its lowest term? TRY THESEFill up each box with the correct difference. Subtract the fractions in Column A fromthe fractions in the other columns. Write the answers in your notebook.A. Column A Column B Column C Column D Column E  6 7 5 4 7 9 10 2 8 5 10 3 2 2 6 1234 31 4 5678 43 7 9 10 11 12 3

WRAP UPIn subtracting dissimilar fractions in mixed forms without regrouping:  find the least common denominator (LCD)  change the fractions to similar fractions  find the difference between the numerators and write the common denominator  subtract the whole numbers  express the answer in lowest terms if necessaryON YOUR OWNIt’s now time for you to find out whether you have mastered this skill.Complete Column C. Column B Column C Subtrahend Difference Column A Minuend 51 1. 12 2 9 2 3 2. 8 5 4 5 6 3. 9 1 32 5 2 4. 15 3 10 1 4 5 5. 12 3 82 3 4 4

GRADE VISUBTRACTION OF DISSIMILAR FRACTIONS IN MIXED FORMS WITH REGROUPING Objective: Subtract dissimilar fractions in mixed forms.REVIEWA. Subtract as fast as you can. Rename the minuend first then subtract. Number 1 is done for you.1) 8 7 9 2) 6  3) 12  -5 9 9 -5 -3 -3 -6 -6 9 88 10 104) 11  5) 10  6) 9  -3-6 -6 -4 -4 -3 12 12 77 5 5 Can you do the above exercises mentally? If you can, you call yourself “SPEEDY BOY” or “SPEEDY GIRL!”B. Recall the steps on how to subtract dissimilar fractions in mixed forms. Then, do the following activity. Here’s the map of 5 barangays and their distances from one another.Brgy. Masagana  8 1 km Brgy. Mapayapa 2  2 4 5 km6 2 km  Brgy. Maunlad 3Brgy.  3 4Mapagkawanggawa 1 9 km 3 9 km  Brgy. Maunawain 1

Answer the following questions:1. How much farther is the distance from Brgy. Masagana to Brgy. Mapayapa than the distance from Brgy. Mapayapa to Brgy. Maunlad? _________2. Which has a greater distance, Brgy. Maunawain to Brgy. Maunlad or Brgy. Kawanggawa to Brgy. Maunawain? __________ By how many km? __________STUDY AND LEARNDo you want to learn how to subtract dissimilar fractions with regrouping in theminuend?Look at the map of the 5 barangays again.Example 1 - How much farther is the distance from Brgy. Masagana to Brgy. Mapayapa than the distance from Brgy. Mapagkawang-gawa to Brgy. Masagana?STEP 1 Let’s subtract 6 2 from 8 1 . Find the least common 32 multiple of 2 and 3. change the fractions to similar 81 → 83 fractions. 26 - 62 →- 64 36Note that 3 < 4 , so you cannot subtract at once. 66STEP 2 Regroup the minuend.81 → 83 → 76 + 3 → 79 2 6 66 6- 62 →- 64 →- 64 36 6STEP 3 Find the difference between the numerators and write the common denominator. Then find the difference of the whole numbers.Is 1 5 in its lowest term? 6 2

The answer is 1 5 km farther. 6Let us try to do another example.Example 2:91 - 35 =n 289 1 → 9 4 → 8 8+ 4 → 8 1228 88 8- 35 → 35 →- 35 88 8 57 8Is your answer 5 7 ? Is this in lowest term? 8Solve another one.What is the difference between 12 3 and 6 2 ? 8312 3 → 12 9 → ____ → ____ → ____ 8 24- 6 2 → 6 16 → 6 16 3 24 24What can you say about the day’s lesson?TRY THESEFind the difference. Write the letter on the blank space that corresponds to your answer.6 14 6 14 4 19 5 13 4 19 6 5 ! 45 45 36 20 36 9 S. 11 5A. 9 2 12 5 3

- 33 - 68 4 9E. 72 Y. 12 6 7 7 - 3 25 - 87 28 9O. 12 1 Z. 12 6 9 7 - 54 - 52 5 4 WRAP UP In subtracting dissimilar fractions in mixed forms with regrouping,  Find the LCD of the given denominators.  Change the fractions to similar fractions.  Regroup 1 from the whole number in the minuend and change it into a fraction. Add this to the fraction part.  Find the difference between the numerators write the given denominator. Then find the difference the whole numbers.  Reduce the answer to its lowest term, if necessary. 4

ON YOUR OWNSubtract. Reduce answers to lowest terms if necessary.1) 4 1 4) 10 1 5 9 - 23 - 52 4 32) 12 1 5) 15 4 4 9 - 85 - 67 8 83) 9 3 8 - 24 5 5

GRADE VI WORD PROBLEMS INVOLVING SUBTRACTION OF DISSIMILAR FRACTIONSObjective: Solve one-step word problems involving subtraction of dissimilar fractions.REVIEWRefresh your skill in analyzing word problems. Read each problem carefully and writethe letter of the correct answer in your notebook.A. Father’s car is filled with 16 3 liters of gasoline. He used 8 2 liters. How much 48 gasoline is left?1. Do you have enough information to solve the problem?a. Yes b. No c. Maybe d. I don’t know.2. What is asked for in the problem?a. the total number of liters of gasoline used by fatherb. the total number of liters of gasoline put it in the tankc. the cost of gasoline per liters.d. the amount of gasoline left after using the car3. What operation can be used to solve the problem?a. addition c. multiplicationb. subtraction d. division4. Which number sentence can be used to solve the problem?a. 16 3 + 8 2 = n c. 16 3 - 8 2 = n 48 48b. 16 3 + n = 8 2 d. N - 8 2 = 16 3 48 84 1

B. The Cruz family has a family outing. They will travel a distance of 32 2 kilometers 3 to reach the resort. If they have driven 21 1 kilometers, how far do they still have to 4 travel?1. What do you need to find?a. the total distance the family will travelb. the number of kilometers the family has traveledc. the number of kilometers left still to be traveledd. the number of kilometers from the residence to the resort2. Which will help you solve the problem?a. 32 2 + 21 1 = n c. 21 1 + 32 2 = n 34 43b. 32 2 - 21 1 = n d. 21 1 - 32 2 = n 34 43C. On their way back home, the family bought 7 pieces of buko pie. While traveling, they ate 3 5 pieces. How many pieces of buko pie were left? 61. What data are given in the problem?a. the number of pieces of buko pie bought and the number of boxes eatenb. the number of pieces left after eating and the number of boxes eatenc. the number of pieces bought and the number of boxes left after eatingd. A, B and C2. Which number sentence can be used to solve the problem?a. 7 + 3 5 = n c. 3 5 + 7 = n 6 6b. 7 - 3 5 = n d. 3 5 - 7 = n 6 6Were you able to answer the problems correctly? 2

STUDY AND LEARNYou have had the chance to analyze some problems. This time you will be solvingproblems using subtraction of dissimilar fractions. Follow the four-step approach sothat you can solve the problems easily.Problem No. 1 An athlete can run a kilometer in 6 9 minutes. If he runs the first half 10kilometers in 3 2 minutes, how long will it take him to run the second half? 5STEP 1 – Read to understand.  How long does it take the athlete to finish 1 kilometer run?  How long does it take him to finish the first half kilometer?  What is asked for in the problem?STEP 2 – Plan what to do.  What operation will you use to find the length of time to finish the second half?STEP 3 – Do the computations. Length of time to finish the second half = 6 9 - 3 2 10 5 Recall the steps in subtracting dissimilar fractions in mixed forms. Can you subtract now? 6 9  _____ 10 - 3 2  - _____ 5 _____STEP 4 – Check if your answer is reasonable. Go over the computations carefully. Is your answer 3 1 kilometers? 2 If you get the same answer, VERY GOOD! 3

If you didn’t get the answer right, do the steps once more. If you are ready, you can proceed to the next problem.Problem No. 2 Mrs. Cruz bought 5 1 kilos of chicken. She cooked 3 2 kilos for adobo. The 43rest was cooked for afritada. How many kilos of chicken was cooked for afritada?Perform the different steps in your notebook.STEP 1 – Read to understand the problem.  How many kilos of chicken did Mother buy?  How many kilos of the chicken were cooked for adobo?  What do you need to find?STEP 2 – Plan what to do.  In the above problem, what operation is needed to solve the problem?STEP 3 – Do the computations.  Write the number sentence needed to solve the problem, then solve for the answer.STEP 4 – Check if your answer is reasonable.  Go over the computation if needed.Is your answer 1 7 kilos? Check it again. 12 4

TRY THESEFor your practice, solve the three (3) problems given in the “Review.”This time, write only the number sentence for each problem, then solve for the correctanswer. Show your answers to your teacher for checking. WRAP UP Again, here is the four-step approach in solving word problems:  Read to understand the problem.  Plan what to do.  Do the computations.  Check if your answer is reasonable. ON YOUR OWNRead each problem carefully. Solve for the correct answer. You can write thesolution in your notebook.1. A piece of wire 5 3 m long is cut from a piece 11 1 m long. What is the length of 42 the remaining piece?2. The total length of one roll of red ribbon is 30 6 meters. If 15 3 meters were cut 85 from the roll, how many meters were left? 5

3. The scoutmaster drove to the campsite in 12 1 hours. If he drove 6 3 hours in the 24 morning, how many hours did he drive in the afternoon?4. Mrs. Cruz earned 10 2 vacation days. She already spent 6 2 days. How many 83 vacation days are still left?5. Mang Ramon owns 6 hectares of land. He planted 4 4 hectares with coconuts 10 and the rest with banana plants. What part of the land was planted with bananas? 6

GRADE VI SIMPLIFYING FRACTIONSObjective: Simplify fractions by cancellation method before multiplying REVIEWMatch the pair of numbers in Column A with theirgreatest common factor in Column B.Column A Column B1) 24, 64 a) 42) 72, 81 b) 103) 32, 36 c) 74) 50, 80 d) 35) 56, 63 e) 9 f) 8 STUDY AND LEARNMultiplication of fractions is easier if you know how to simplify the task. This lessonwill teach you how to simplify factors before multiplying. Later on you’ll realize thatindeed multiplication of fractions is an easy job.Study how it is done in the examples on the next pages. 1

Example 1:What is the area of the rectangle below? 2m 4 6m 8You’ve learned that to find the area of a rectangle, you have to multiply the length bythe width, so: 6 x 2 =n 84 6 x 2 can be simplified by cancellation. 84Look at the numerator of the multiplicand and denominator of the multiplier.6x284What is their greatest common factor? Divide 4 and 6 by 2.3 Divide the numbers mentally, then write the6x2 quotients above or below the cancelled numerals.84 2Look at the denominator of the multiplicand and numerator of the multiplier. What istheir greatest common factor?31 Divide the numbers mentally, then write the6/ x 2/ quotients above or below the cancelled numerals.8/ 4/42So 6 x 2 after cancellation is 3 x 1 .84 423 x 1 = 3 The area of the rectangle above is 3 square meter.4 28 8Which product is easier to find? 6 x 2 or 3 x 1 84 42 2

Example 2:Let’s have another example. 12 12 is the greatest common factor of 12 and 36. Divide 36 by 12, we get 3 and divide also 12 by 12 and we get 1.12 x 3015 36 15 is the greatest common factor of 15 and 30 so divide 13 15 by 15, we get 1 and divide also 30 by 15 and we get 2.12 x 30 after cancellation is 1 x 2 .15 36 13So 1 x 2 = 2 13 3That’s very easy! Try the next exercises. You may go back to the previous pages ifyou forget the process. . 4) 24 x 60  _____ TRY THESE 30 48Simplify the fractions. 5) 18 x 108  _____1) 21 x 18  _____ 27 126 24 272) 9 x 36  _____ 18 453) 63 x 8  _____ 72 9 3

WRAP UPTo simplify fractions before multiplying: Divide the numerator of the multiplicand and the denominator of the multiplier by their greatest common factor. Do the same with the denominator of the multiplicand and numerator of the multiplier.ON YOUR OWNSimplify the factors before multiplying.1) 15 x 81 4) 27 x 63 27 45 54 722) 23 x 52 5) 16 x 45 26 69 18 243) 54 x 70 60 162 4

GRADE VI ONE-STEP WORD PROBLEMS INVOLVING MULTIPLICATION OF FRACTIONSObjective: Solve one-step word problems involving multiplication of fractions.REVIEWRecall your steps in multiplying:  a fraction by another fraction  a fraction by a whole number  a mixed number by another mixed numberMultiply the fraction under the given column by the given fraction. Write your answerin the output column.A. 2 multiplied by B. 3 48 multiplied byInput Output Input Output 12 3 56 63 39 12 44 8857 1

STUDY AND LEARNLet us now go through some problems involving the multiplication of fractions.Have you gone to the airport? What have you seen there?Example 1: One-half of the runway area of an airport is being renovated. The runway area is 3 of the whole airport. What part 4 of the whole airport is being renovated?  Read and understand the problem. a. What part of the whole airport is the runway area? b. What part of the runway is being renovated? c. What do you need to find?  Plan what to do. a. Using a diagram, you can find what part of the airport is being renovated.The part shaded with bolder lines is 1 of 3 which is 3 of the whole 24 8airport.b. Instead of a diagram, you can use multiplication. Do the computation.1 of 3 → 1 x 3 = 3 of the airport2 4 248  Check the answer if it’s reasonable. Review your computation.Example 2. 2

An airline was able to accommodate 4 of the 45 passengers on standby. 5How many people were able to board the flight? Read and understand the problem.a. How many passengers were on standby?b. What part of the chance passengers was able to board the place?c. What do you need to find in the problem? Plan what to do Using the diagram, show how many people boarded the plane. Shade 4 of 45. 5 How many is 4 of 45? 5 You can do the shorter way of solving the problem. Find 4 of 45. 5 Do the computation 94 of 45 → 4 x 45 → 4 x 45 = 36 or 36 passengers.55 51 1 1 Check if your answer is right.Let’s move on to another problem.Example 3: The airplane consumes 62 2 liters of gasoline in one trip. How much gasoline 3is consumed in 5 trips?1. How many liters of gasoline is consumed for one trip?2. What will you find in the problem?3. This time you can now find: 3

62 2 x 5 = amount of gasoline consumed 3 4. Multiply: 62 2 x 5 = ___ x ___ = ____ 3 5. The answer is ____. TRY THESEAre you now ready to solve the following problems?Read each problem carefully. Find the correct answer.1) An airplane has 4 tanks of gasoline. Each tank is 2 full. How much gasoline 3 does the airplane have?2) A truck was 7 filled with grocery items for delivery. The driver delivered 2 of 83 this to SM Supermarket. What part of the truckload of grocery items was delivered?3) A certain mixture is made using 1 bag of gravel for every 1 1 bag of sand. How 3 many bags are needed for 5 1 bags of gravel? 2 4

WRAP UP In solving problems involving multiplication of fractions:  Read and understand the problem - find what are given and asked for in the problem  Plan what to do - Use a diagram to visualize the problem if needed - Determine what operation to use  Do the computation - Use cancellation when necessary  Check the answer if it’s reasonable. - Be sure to simplify the answer ON YOUR OWNHave you mastered the skill? Do these problems and find out! Solve then answer inyour notebook.1. A handler spends 3 of an hour checking baggages for each flight. How much 4 time is spent for 15 flights?2. Two-thirds of the wall will be painted yellow. The worker has already finished 3 8 of it. What part of the whole wall was already painted with yellow?3. Daniel finished mopping the floor of a conference hall in 2 1 hours. How much 2 time will be spent mopping 1 1 floors? 2Copy any two problems using multiplication of fractions then solve them. 5

GRADE VI TWO TO THREE-STEP WORD PROBLEMS INVOLVING FRACTIONSObjective: Solve 2- to 3-step word problems involving fractions.REVIEWA. Perform the indicated operations.1) 5 – ( 3  1) =  3) 25 – ( 5 1 x 2 1 ) =  42 222) 6 3 - (1 4 11) =  4) 20 – ( 2 x 20) =  4 58 5B. Read each problem carefully. Analyze what each problem is all about and solve for the correct answer.1. Andrew read 1 of the book on Monday, 1 of the book on Tuesday and 1 of 84 2the book on Wednesday. What part of the whole book did he read duringthese 3 days?a. What is asked in the problem?b. What operation will you use?c. Solution:2. In a science experiment, Plant A grew 2 cm more than Plant B. If Plant B 3 grew 7 cm, how much did Plant A grow? 8a. What do you need to find in the problem?b. What operation will you use?c. Solution: 1

STUDY AND LEARNYou are already exposed to solving one-step word problems involving any of thefundamental operations in fractions.This time, get ready to solve 2 to 3 step word problems.The same steps are used just like solving 2- to 3-step problems of whole numbers.Try to analyze the first problem.Example 1: Mother bought 8 1 kilos of beef. She cooked 2 3 kilos for beef steak, 243 5 kilos for beef stew and the rest was stored in the refrigerator. How 8many kilos of beef were kept in the refrigerator?a. How many kilos of beef did Mother buy?b. How many kilos did she cook for beef steak? for beef stew?c. What do you need to find in the problem? You need to find how many kilos of beef were put in the refrigerator. Plan what to doa. Before you find how much beef was left, what are you going to find first?Find first the hidden question.In the problem, the hidden question is: How many kilos of beef were cooked for beef stew and beef steak?What operation will you use?Solution: 2 3 + 3 5 = number of kilos cooked 48b. After finding the total number of kilos cooked, subtract it from the number of kilos Mother bought. 2

Solution: 8 1 - ( 2 3  3 5) = amount left to refrigerate 2 48 Do the computations a. 2 3 + 3 5 = 2 6 + 3 5 = 511 or 6 3 48 88 8 8 b. 8 1 - 6 3 = 8 4 - 6 3 = 2 1 28 88 8 The answer is: 2 1 kilos of beef to be put in the refrigerator. 8 Check if your answer is correct.Let’s have another one. Mrs. Cruz bought 3 kilo of potatoes at Php60 a kilo and 2 kilo of 43 tomatoes at Php45 a kilo. If she gave the seller Php100, how much was herchange? What is asked in the problem? Before you can solve the problem, you need to find the answer to the hidden questions first.- How much is 3 kilo of potatoes? 4- How much is 2 kilo of tomatoes? 3- What is the total amount Mrs. Cruz spent?This problem involves multiplication of fractions, as well as addition andsubtraction of whole numbers involving money. Do all the computations. 2 of Php45 = Php30 Find: 3 3 of Php60 = Php45 4 Amount spent = Php45 + Php30 = Php75 Change = Php100 - Php75 = Php25 Check your answer. Is your answer reasonable?If not, review your computations. 3

Do you like to solve another one?Here’s another problem. Mrs. Elmo gave 1 of the cake she baked to her daughter. The 4remaining portion was divided equally among her 6 co-teachers. What partof the whole cake did each teacher get? What is asked in the problem? What is the hidden question in this problem? - How will you find the remaining portion of the cake? - What operation will you use? - After looking for the remaining portion, what process will you use to find the part of the whole cake each teacher got? - Will you use subtraction and division in this problem? Find:1- 1 = 4 - 1 = 3 remaining portion 4 44 43  6 = ___ x ___ = ___ part of the cake each teacher got.4 Did you get 1 ? 8 Check if your answer is correct. TRY THESEThis time, try to solve the following problems.1. Adela bought 8 1 kilos of oranges. She gave 2 2 kilos to her brother and 3 1 4 32 kilos to her sister. How many kilos of oranges were left with her? Solution: 4

2. Liza harvested 320 mangoes. She gave 3 of them to her friends and relatives. 8 How many mangoes were left to be sold? Solution:3. A painter can finish painting a house in 5 1 days. He uses 4 1 litres of paint a 22 day. How much paint will be left from 30 L of paint? Solution: WRAP UP In solving 2- to 3-step word problems involving fractions,  Read and understand the problem very well. - identify the given data - find what is asked for in the problem - look for the hidden question(s)  Plan what to do. - What operation will you use first to answer the hidden question? - What will you do to find the final answer?  Do all the computations. Follow the steps in adding, subtracting, multiplying or dividing fractions and whole numbers.  Check if your answer is reasonable. 5

ON YOUR OWNLet’s evaluate your skill!A. Choose the letter of the correct answer.1) Rosa used eggplants for her menu. 3 kg for inihaw, 1 kg for 42 pinakbet and 1 kg for fish sinigang. How many kilos of eggplants 8 were left from the 2 kilograms of eggplants that she bought?a) 1 3 kg c) 5 kg 8 8b) 1 5 kg d) 3 kg 8 82) Mang Jose’s chickens can consume 2 5 kilos of feeds in one day. After one 10 week, how many kilos of feeds will be left from 28 3 kg? 4a. 17 1 b. 12 1 c. 11 3 d. 11 1 2 4 4 43) Mother bought 40 ponkan oranges. She gave 2 of the fruits to her daughter, 5 1 of them were already eaten and the rest were placed in a tray. How many 2 ponkans were put in the tray?a. 5 b. 4 c. 3 d. 2B. Read and solve.1) There are 48 guavas in the basket. Romy took 1 of the guavas and Jaime took 1 63 of the guavas. How many guavas remained in the basket?2) Rowena put 1 of his stamp collection in one book and 1 of it in another book. 32 He had 9 stamps left. How many stamps did she have altogether?3) Mr. dela Rosa withdrew Php12 000 to pay for the school needs of his children. One-fourth was spent for school supplies and another 2 was spent for uniforms. 3 How much money was left? 6

GRADE VI DIVISION OF A FRACTION BY A WHOLE NUMBERObjective: Divide a fraction by a whole number.REVIEWA. Do the following exercises mentally. Write the product in the .1 of 1 3 x2 3x 245 65 733 of 1 3 of 442 85B. What number will you place in the  to give a product of 1? Number 1 has been done for you.1) 1 x 4  1 4) 5 x  = 1 41 5) 6 x  = 12) 3 x  = 1 43) 4 x  = 1 6 STUDY AND LEARNYou have already mastered the skills of adding, subtracting and multiplying fractions.This time, you will learn how to divide fractions by a whole number.Look at the two examples. 1

Example 1: A. One-half of the circular cake is shared among 3 children. What fraction of the cake will each child get?1  3  _____2 1 of the cake 21 3 126 Each child gets 1 6  From the model, you see that each child gets 1 of the cake. 6  You will also see that each child should get 1 of 1 of the cake. 32 1 of 1 → 1 x 1 = 1 3 2 32 6  Another way to find what part each child gets: 1 3 1 x 1  1 2 2 36 Which is the dividend? Which is the divisor? To get 1 , multiply the dividend by the reciprocal or multiplicative inverse of the 6 divisor. (Reciprocal is multiplying a given fraction by its multiplicative inverse to have a product of 1.) So the reciprocal of 3 is 1 . 3Example 2:B. Find the value of 3  6 . 5 3  6 =13 x 1 = 1 5 5 6 2 10 2

Is your answer 1 ? 10C. What is 9  3 ? 119  3 1 9 x 1= 1 11 11 3 11 1 TRY THESEComplete each of the following division sentences.1. A string 4 m long is cut into 6 pieces. How long is each piece? 54  6  x = or52. A 4 kg watermelon is cut into 2 equal parts. How heavy is each piece? 74  2  x = or73. Divide 2 by 8. 32 8 x = or34. Divide 6 by 9. 7 6  9  x = or 75. Divide 4 by 8. 5 3

4  8  x = or 5 WRAP UP In dividing a fraction by a whole number:  multiply the fraction (the dividend) by the reciprocal of the whole number (divisor). Reduce answers to lowest terms when necessary. The reciprocal is the multiplicative inverse of a number. The product of a number and its reciprocal is 1. ON YOUR OWNDivide. Simplify your answer.1) 2  4 72) 3 12 43) 2  8 34) 9  3 105) A plank of wood 3 m long is cut into 4 equal pieces. Find the length of each 5 piece. 4

GRADE VI DIVISION OF A FRACTION BY A FRACTIONObjective: Divide a fraction by another fraction. REVIEWRecall the rule in dividing a fraction by a whole number. Pick a bag from this“PABITIN” and solve it. 9 8 103 3 2 4 3 6 4 74 5 12 8 12  2 2 5 1 6 14 6 2 1

STUDY AND LEARNIn the PABITIN exercise, a whole number was used as a divisor. In the next lesson,you will divide a fraction by another fraction.Example 1 - Read this problem. A nursery owner had 2 sack of onion bulbs. He planted 3 them in plots with 1 of the bulbs in each plot. How many plots 6 did he use? 2  1  number of plots to be used 36 Using the diagram, the owner used 4 plots. 11 111 1 66 666 6232  1  4 plots36Note that 2  1  2 x 6  12 or 4 plots 3 6 31 36 is the reciprocal of 116Example 2 - Divide 4 by 2 . 53 Change4  2  4 x 3 = 12 or 1 2 or 1 15 3 5 2 10 3 10 5 2

Example 3 - Find the quotient. 3  5 ? 48353 x = or _____48 4 TRY THESEDivide. Simplify your answers.1) 3  1 4 122) 2  5 583) 5  5 12 94) Mother had 3 of a pack of cereals left. She placed 1 of the pack in each bowl. 55 How many bowls did mother use?5) A farmer had 3 bag of fertilizer. He put 1 bag in each garden plot. How many 48 garden plots were given fertilizers? WRAP UPIn dividing a fraction by another fraction  multiply the dividend by the reciprocal of the divisor.If the final answer is an improper fraction, change it to a wholenumber or mixed number. 3

ON YOUR OWNDivide. Write the letter that corresponds to the correct answer in the box. Makesure your answer is in its simplest form.A. 3  1 S. 12  1 62 15 4I. 4  2 T. 15  2 73 18 6M. 4  3 V. 20  5 54 30 6N. 6  1 95Question:What helps build body resistance and regulate body processes?4 6 21 1 1 1 6 31 3157 2 15 7 35 4

GRADE VI DIVISION OF MIXED NUMBERSObjective: Divide a mixed number by another mixed number. REVIEWA. FRACTION TREE Change all the mixed numbers to improper fractions and all improper fractions to mixed numbers.20 1015 15 891 4 57 2 8 1