MATH 5

ON YOUR OWNA. Arrange the following set of fractions from least to greatest. Write your answers in your notebook.1) 3 , 1 , 2 2) 7 , 3 , 1 , 1 693 8423B. Order from greatest to least. Write your answers in your notebook.1) 1 , 3 , 7 2) 1 , 6 , 1 , 9 3) 2 , 3 , 5 , 1 258 4 8 3 10 3472 4

ESTIMATION OF FRACTIONS GRADE V ESTIMATION OF FRACTIONS 1Objective: Estimate fractions as close to 0, 2 or 1REVIEWRound off the numbers in Column A. Look for the answers in Column B. AB1) 27 902) 21 303) 43 204) 12 405) 94 10 1

STUDY AND LEARNEstimating fractions is not entirely new to you.a. Look at the number line below. 1 1 0 2 01 23 4 5 6 7 7 77 7 7 7 7Which fractions are close to 0, 1 or 1? 2 1 and 2 are close to 0. The numerators 1 and 2 are very small compared to the 77denominator. 3 and 4 are close to 1 . The numerator 3 is about half of 7. 4 is more than half77 2but not nearly equal to 7. 5 and 6 are close to 1. Their numerator and denominator are nearly equal. 5 77and 6 are nearly equal to 7.b. Let’s try another example. 102 101 23 45 6 7 8 9 9 99 9 9 9 9 9 9 Which fractions are close to 0? Why?1 , 2 and 3 are close to 0. The numerators 1, 2 and 3 are very small compared99 9to the denominator 9. 2

 Which fractions are close to 1 ? Why? 24 , 5 and 6 are close to 1 . The numerator 4 is about half the denominator 9.99 9 2The numerators 5 and 6 are more than half but not nearly equal to thedenominator 9. Which fractions are close to 1? Why? 7 and 8 are close to 1. The numerators 7 and 8 are nearly equal to the 99 denominator.c. Let’s try estimating without using a number line. 2 is close to 1 because 2 is nearly equal to 3. 3 3 is close to 0. The numerator 3 is very small compared to the denominator 10. 10 5 is close to 1 . Why? 82TRY THESEUsing the number line tell which fractions are close to 0, 1 or 1. 201 21 2 5 5 55 5 51. ____ is close to 0. The numerator ____ is very small compared to the denominator 5.2. ____ , ____ are close to 1 . The numerators ____ and ____ are about half the 2 denominator.3. ____ is close to 1. The numerator ____ is nearly equal to the denominator. 3

WRAP UPA fraction is close to:  0 when the numerator is very small compared to the denominator.  1 when the denominator 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 answers in your notebook.01 23 45 6 6 66 6 6 61. What fractions are close to 0?2. What fractions are close to 1 ? 23. What fractions are close to 1? 4

B. Choose the letter of the correct answer. Write your answer in your notebook.1. Which fraction is close to 0?a. 1 b. 6 c. 5 10 8 72. ____ is close to 1 . 2a. 5 b. 1 c. 5 6 593. 7 , 8 and 9 are close to 1. Which else is close to 1? 8 9 10a. 2 b. 5 c. 2 7 75 5

ADDITION OF TWO TOGRFAODUERVSIMILAR FRACTIONSADDITION OF TWO TO FOUR SIMILAR FRACTIONS Objective: Add two to four similar fractionsREVIEWGive an estimate for the given fractions using the models. Write about 0, about 1 , or 2about 1.1) 3 2) 1 8 63) 4 4) 2 5 125) 1 3 STUDY AND LEARN Nora painted 1 of a large rectangle blue, 2 yellow and 1 green. What part of the 5 55rectangle did she end up painting?What are the fractions mentioned in the problem? ( 1 , 2 and 1 ) 55 5 1

Are these fractions similar or dissimilar? (They are similar fractions.)Let’s picture the problem. B ye ye gr L ll ll ee Uo o n E ww1 + 2 +15 55 4 5Nora painted 4 of the large rectangle. 5Here’s another way of solving the problem. Let’s add 1 , 2 and 1 . 55 5 Here’s how: Add the numerators.1+2 +1 1+2+1=4555 Use the same denominator. Reduce the answer to its lowest terms if needed.1 + 2 + 1 = 1 21  4555 55Did you find it easy? Well, here are other examples for you to study.a. 4 + 2 + 1 = 4  2  1 = 7 999 9 9b. 2 + 5 + 3 = 2  5  3 = 10 11 11 11 11 11c. 1 + 5 + 2 + 4 = 1 5  2  4 = 12 or 2 18 18 18 18 18 18 3 2

Remember, express your answer in the lowest terms if necessary.TRY THESEA. Add. Choose the letter of the correct answer.1) 1 + 3 + 2 + 1 a) 6 b) 7 c) 8 12 12 12 12 12 12 122) 2 + 3 a) 5 b) 4 c) 3 66 6 6 63) 2 + 4 + 1 a) 5 b) 6 c) 7 999 9 9 94) 14 + 5 + 8 a) 14 b) 15 c) 16 17 17 17 17 17 175) 2 + 7 + 2 + 1 a) 4 b) 13 c) 14 21 21 21 21 7 21 21B. Read and solve.1. What is the sum of 1 , 2 and 2 ? 66 62. What is 1 more than 2 ? 443. 1 when added to 6 is ____. 16 16WRAP UPIn adding similar fractions, just add the numerators and usethe same denominator. 3

ON YOUR OWNA. Find the sum. Write your answers in your notebook.1) 1  2 2) 15  6  10 55 100 100 1003) 1  2  3 4) 2  2  1  8 15 15 15 20 20 20 205) 2  7  9 19 19 19B. Read and solve. Write your answers in your notebook.1) 1 more than 4 is ____. 882) What is the total of 1 , 2 and 4 ? 99 93) 4 plus 2 equals ____. 17 174) 2 when added to 3 and 1 is ____. 7 775) What is the sum of 1 , 3 and 5 ? 11 11 11 4

VISUALIZATION OF ADDITGIROANDEOVF DISSIMILAR FRACTIONSVISUALIZATION OF ADDITION OF DISSIMILAR FRACTIONS Objective: Visualize addition of dissimilar fractionsREVIEWDo you still remember how to add similar fractions?Let’s see. Try to find the sum of the following. Remember to express your answersin their lowest terms if possible.1. 4 2. 1 1 93 2 11 9 11 4 9 3 11 113. 5 1 4. 4 7 7 15 6 1 15 155. 2 5 7 3 18 18 18 18 STUDY AND LEARN Study the problem below.Study the problem below. Nita used 1 meter of red ribbon and another 1 meter of yellow ribbon for her 23 project. Find the total length of ribbon that she used. 1

What is the total length of the ribbon? How are we going to get the total length of the ribbon? What are we going to add? ( 1 and 1 ) 23 What can you say about their denominators? They have different denominators. What kind of fractions are 1 and 1 ? They are dissimilar fractions. 23 Since 1 and 1 are dissimilar fractions, let’s change them to similar 23fractions to make adding easier. Let’s add 1 and 3 using models. 24 1+2 1 3What is the least common denominator of 2 and 3? (6)1 11 1 =36 66 2611 1=266 36 1 +1=3 +2 =511 111 2366666 666 The figures above show how the fractions are represented using the leastcommon denominator 6.The rectangles are divided into six equal parts. Dark lines divide therectangles to show the dissimilar fractions 1 and 1 . 23The broken lines show how these dissimilar fractions are converted intosimilar fractions. 2

By merely counting you’ll know that 3 is equal to 1 and 2 is equal to 1 . 6 26 3So 2 + 3 = 5 or 1 + 1 = 5 666 2 3 6 What’s the answer to the problem? 5 meter 6 Were you able to follow?Let’s have another example.Example:Let’s add 3 and 5 . 48 + LCD of 4 and 8 is 83548 +=3=6 548 8 11 or 1 3 88TRY THESENow that you were able to visualize addition of dissimilar fractions, try to answer theexercises below.A. Find the sum of the following using the models below. 2 1. 3 2. 5 4 3 + 3+ 4 8 3 2 4 4 3

3. 4. + 1+ 5 2 8B. Find the sum of the following using illustrations?1. 1  2  2. 3  2  3. 6  1  63 10 5 844. 4  1  5. 7  1  92 10 5WRAP UPWe can add dissimilar fractions using illustrations or models.  In adding dissimilar fractions, change first the dissimilar fractions into similar fractions, then add. ON YOUR OWNLet’s see how much you have learned. Answer the exercises below:In your notebook, illustrate and color the bars to show the sum of the fractions. 1. 1 2 + 11 552. 1 1 1 555 4

+ 1 23. 1 3 + 11 664. 1 2 + 11 335. 1 1 1 4 4 4 + 11 88 5

ADDITION OF DIGSRSAIDMEIVLAR FRACTIONS ADDITION OF DISSIMILAR FRACTIONS Objective: Add dissimilar fractionsREVIEWFind the least common denominator (LCD) of the following sets of fractions. 11 151) , 2) , 35 78 64 1213) , 4) , , 12 9 348 21 3 4315) , , 6) , , 5 8 10 742 STUDY AND LEARNExample 1: 11 Sarah bought kilogram of lanzones and kilogram of grapes for her 24 grandmother. How many kilograms of fruits did she buy in all? What shall we do to solve the problem? We shall add. 11 What are we going to add? ( and ) 24 11 What kind of fractions are and ? (They are dissimilar fraction.) 24 Do you know how to add dissimilar fractions? 1

Look closely as we solve the problem, by means of some illustrations.Change to 1 1similar fractions 2+ 4 2+ 1 44Add the 2+ 1= 3numerators and 44 4use the samedenominators. 33The sum is . Therefore, Sarah bought kilogram of fruits in all. 44Let us solve the same problem using the method of computation.STEP 1 Find the least common denominator (LCD).STEP 2 1 = 24 1 = 44 Find fractions equal to the given fractions. 122 x= 224 11 = 44STEP 3 Add the numerators and use the common denominator. Reduce to lowest terms if possible. 2

12 24 ++ 11 44 3 4 3Likewise, the answer is . 4Let’s have another example.Example 2:3 3 5 15 15 = x= 459 45 9 5 45 27 45 3 3 9 27 33 3 11+= + x= = 5 45 5 9 45 45 15 11 3The sum is . 15 TRY THESEA. Solve and write the correct answers in your notebook. 2 1 8 10 11 1) + = ( , , ) 3 4 12 12 12 211 3 1 5 2) + + = (1 ,1 ,1 ) 5 2 4 20 20 20 351 3 2 1 3) + + = (2 ,2 ,2 ) 4 6 2 12 12 12 5 2 1 122 4) + + = (1 ,1 ,1 ) 10 3 6 3 6 3 3

123 5 6 15) + + = (1 ,1 ,1 ) 6 3 8 24 24 24 WRAP UP In adding dissimilar fractions, follow these steps: Step 1: Find the LCD of the given fractions. Step 2: Change the fractions into similar fractions. Step 3: Add the similar fractions. Always express the answer in lowest terms.ON YOUR OWNFind the sum and express it in its lowest terms, if necessary. Write your answers inyour notebook. 32 131) + = 2) + = 11 3 45 313 4133) + + = 4) + + = 584 934 2135) + + = 536 4

ADDITION OF DISSIMILAR FRACTIONS AND WHOLE NUMBERS GRADE V ADDITION OF DISSIMILAR FRACTIONS AND WHOLE NUMBERS Objective: Add dissimilar fractions and whole numbersREVIEWAdd and reduce the sum to lowest terms. 32 21 611) + = 2) + = 3) + = 11 3 94 15 3 43 414) + = 5) + 74 96STUDY AND LEARN 1 Mang Joaquin painted the fence for 2 hours, the window panes for of an hour 2 1and the door for of an hour. How many hours did Mang Joaquin spend painting? 4Let’s try to picture the problem.++ = 11 32+ + = 2 24 4 1

3Mang Joaquin spent 2 hours painting. 4Let us solve the same problem by computation.Study the steps carefully. 1st 2nd 3rdAlign the fractions and the Change the fractions to Add the fractions then thewhole numbers separately similar fractions whole numbers 2 2 2 1 1→ 2 2 24 2 + 1→ 1 4 1 44 1+ + 4 4 3 2 4 3The sum is 2 . 4Here are other examples for you to study.1) 3 3 2) 5 5 + 4→ 24 2→ 2 5 30 15 15 1→ 5 3 6 30 + 1→ 15 5 29 51 3 5 =5 30 15 33) 3 3 4→ 12 7 21 + 2→ 14 3 21 26 5 3 =4 21 21 2

TRY THESEA. Write the missing similar fractions then add. Reduce your answers to lowest terms.a. 8 b. 6 3→ 4→ 4 9 + 1→ + 2→ 6 3c. 2 d. 1  3→ 4 7 2→ 5 + 1→ 2 +9e. 8 2→ 3 + 1→ 8 WRAP UPIn adding dissimilar fractions and whole numbers:Step 1: Align the whole numbers and the fractions separatelyStep 2: Change the dissimilar fractions to similar fractionsStep 3: Add the similar fractions then the whole numbersStep 4: Reduce the answer to its lowest terms when needed 3

ON YOUR OWNAdd. Reduce your answer to its lowest terms. Write your answers in your notebook.1) 4 2) 3 3) 2 2 7 2 7 9 7 3 2 1 + + + 4 3 44) 6 5) 7 1 1 4 6 3 2 + + 5 3 4

ADDITION OF WHOLE NUGRMABDEERVS AND MIXED NUMBERSADDITION OF WHOLE NUMBERS AND MIXED NUMBERS Objective: Add whole numbers and mixed numbersREVIEWA. Give the LCD of the following pairs of dissimilar fractions. 46 29 411) and 2) and 3) and 57 3 11 73B. Find the sum. Reduce to lowest terms when needed. 12 33 111) + 2) + 3) + 35 74 45 STUDY AND LEARN 1 Freddie sold 5 kilograms of avocados while Rose sold 3 kilograms. How 2many kilograms of avocadoes did the two sell together?What are we trying to find? The total number of kilograms of avocados sold. 1What is the mathematical sentence? 5 + 3 = N 2 1

Let’s solve the problem. 1  Bring down the fraction.+ 5  Add the whole numbers.  Reduce to lowest terms if 2 +3 . needed. 1 8 2Here are other examples. Study carefully.a. 5 1 2 b. 3 1 6+3 2 9 +4 1 6 2 10 31 9 9 =9 62Do you still remember how to add dissimilar fractions? Recall that we have tochange dissimilar fractions to similar fractions before summing them up. Lookat the example below. 4→ 4 3 1 → +2 +2 2 6 2 1 → 2 2 3 6 5 8 6TRY THESEA. Find the sum. Reduce to lowest terms if needed.1) 4 2) 7 3 2 +2 +2 6 3 2

3) 2 4 1 4) 1 +4 9 2 +7B. Compute. Simplify if possible. 1 2) 8 51) 3 1 3) 1 2 5 6 3 5 1 4 4 4 4 3 +7 +2 +3 7C. Add the length of the sides of the figure below. Reduce the answer to lowest terms. 2 cm 1 4 cm 2 7 cm 4 5 WRAP UP In adding whole numbers and mixed numbers, change the dissimilar fractions to similar fractions first. Add the fractions and then the whole numbers. Reduce the sum to its lowest terms. 3

ON YOUR OWNFind the sum. Simplify your answer. Write your answers in your notebook.1) 4 6 1 2 2) 2 3) 8 +2 11 8 7 +5 3 4 4 +2 1 5) 34) 7 1 7 5 2 5 +6 4 +2 7 4

ADDITION OF MIXED NUMBGERRASDEAVND DISSIMILAR FRACTIONSADDITION OF MIXED NUMBERS AND DISSIMILAR FRACTIONS Objective: Add mixed numbers and dissimilar fractionsREVIEWChange the following to similar fractions. 5 1 11) = 2) = 3) = 9 4 9 2 2 3 = = = 3 5 4 5 34) = 5) = 8 7 5 6 = = 7 21 STUDY AND LEARNStudy the map below. 1

How far is the school from Annie’s house? What process should be used to get theanswer? AdditionLet’s add 1 1 and 5 step by step. Look at the steps closely. 26STEP 1 Change the fractional part to similar fractions by using the least common denominator (LCD). 13 The LCD of 2 1 =1 and 6 is 6. 26 55 += 66STEP 2 Add the similar fractions and bring down the whole number. 3 1 6 5 + 6 8 1 (The answer contains an improper fraction.) 6STEP 3 8 Change the improper fraction ( ) to a mixed number. 6 Add this to the whole number. 82 Reduce the fraction to its =1 lowest form. 66 22 1 1 + 1 = 2 or 2 66 3Let’s have another example.Take a look at the map again.Example:If Annie is at the church and wants to go to the park, how far will she travel?What would be our number sentence? 121 + =N 43 2

Let’s solve. (Step 1) 13 What is the LCD of 4 1 =1 and 3? 4 12 (Step 2) Does the answer contain an 28 improper fraction? += 3 12 Is there a need to reduce the answer to its lowest term? 11 1 12We don’t need to go to step 3 since the fractional part in the answer is a properfraction and is already in its simplest form. 1 2 11 11So, 1 + = 1 . Annie will have to travel 1 km from the church to the park. 4 3 12 12 TRY THESEAdd. Look for the answer in the boxes in the next page. Match each letter to theanswer by writing the letter on top of the correct answer. 12 13 41 12 412 3 3 1 6 4 8 63 57 39 72 A C D E F 21 91 63 43 318 1 5 2 7 94 11 2 95 65 84 I L N O R 3

5 5 4 5 4 1 17 5 7 332 33 76 7 8 12 3 6 8 15 8 15 14 36 9 22 35 WRAP UP In adding a mixed number and a dissimilar fraction:  Change the fractional parts to similar fractions.  Add the similar fractions, then the whole numbers.  If the fraction in the sum is an improper fraction, change it to a mixed number. Add the whole numbers then reduce to lowest terms, if necessary. ON YOUR OWNAdd. Reduce the sum to its lowest term if necessary. Write your answers in yournotebook. 11 311) 4 + = 4) 2 + = 38 73 21 122) 2 + = 5) 5 + = 52 25 413) 1 + = 93 4

ADDITION OGFRMADIXEEVD NUMBERS ADDITON OF MIXED NUMBERS Objective: Add mixed numbersReviewFind the sum. Choose the correct answer in column B.Column A Column B 21 391) 1 + a. 4 35 40 33 12) 4 + b. 4 58 3 13 133) 6 + c. 1 47 15 51 34) 3 + d. 3 62 20 23 195) 2 + e. 6 54 28 Study and LearnYou have already learned how to add a mixed number and simple fractions with differentdenominators. This time you will learn how to add mixed numbers.Let’s read the story problem below.Cindy helps her mother sell different kinds of nuts on Saturdays. Last Saturday, theywere able to sell: 1

3 812 kilograms of peanuts 8 kilograms of cashew nuts 4 10 1 14 kilograms of pili nuts 3 kilograms of almonds 2 5What does Cindy do on a Saturday?How will you describe the kind of girl Cindy is?What things do you do that make you similar to Cindy?How many kilos of peanuts and pili nuts were Cindy and her mother able to sell?What is the correct number sentence? 3112 + 4 = N 42Let’s solve this step by step.STEP 1 Change the fractional parts to similar 33 fractions using the Least Common 12 = 12 Denominator (LCD) 44 12 + 4 =+ 4 24STEP 2 Add the fractions, then the whole numbers. 3 12 4 2 +4 4 5 16 4STEP 3 Change the improper fraction in the answer 51 to mixed form. =1 Add this to the whole number. Reduce the answer to its lowest term if 44 necessary. 11 16 + 1 = 17 44 31 1So, 12 + 4 = 17 42 4 2

1Therefore, Cindy and her mother were able to sell 17 kilograms of peanuts and pili 4nuts.Were you able to follow the steps?This time, let’s try to find out how many kilograms of nuts they were able to sell lastSaturday.Since we already have the number of kilograms of peanuts and pili nuts just add this tothe number of kilograms of almonds and cashew nuts sold. What would be our numbersentence this time? 1 + 8 1 =N17 8 +3 4 10 5Let’s solve. STEP 1 15 The LCD of 4, 5 and 10 is 20. 17 = 17 STEP 2The answercontains an 4 20improper fraction. 8 16 STEP 3 8 =8 10 20 14 + 3 =3 5 20 25 28 20 25 5 =1 20 20 28 + 5 51 1 = 29 = 29 20 20 4 3

Try TheseA. Add the mixed forms that are in the same shape. Simplify your answer. 1 1 52 1 2 3 1 6 4 8 5 2 3 3 3 4 2 3 4 6 1 3 4 4 2 7 3 81 3 7 16 5 3 Wrap Up In adding mixed forms:  Change the fractional parts to similar fractions.  Add the fractions, then the whole numbers.  If the fractional part of the answer is an improper fraction, change it to a proper fraction and add this to the whole number.  Reduce the answer to its lowest terms if necessary. 4

On Your OwnAdd the mixed forms in each of the following. Write your answers in your notebook. 13 1) 4 + 2 54 251 2) 10 + 2 + 3 364 41 3) 3 + 2 11 2 14 4) 8 + 2 5 15 6 41 5) 5 + 2 + 4 25 5 4 5

6

ESTIMATION OGFRSAUDME VOF FRACTIONSESTIMATION OF SUM OF FRACTIONS Objective: Estimate the sum of fractionsREVIEWMatch the chest with the correct key.To do that, answer the problems under each treasure chest and look for the key withthe correct answer.1) 110 What is the estimated sum of 125 and 268?2) Estimate the sum of 78 and 31. 903) 400 The estimated sum of 25 and 57 is _____. 1

STUDY AND LEARNRead the problem below. 7Miguel and Mike each bought a whole pizza pie. Miguel ate of his pizza pie. 8 4Mike ate of his. They shared the rest with their classmates. About how much of 6pizza was eaten?What did Miguel and Mike do with the rest of the pizza? (They gave it to theirclassmates.) What kind of persons are they?Are you willing to do what they did?Fraction circles are helpful when you are estimating the value of fractions. It is 1easier to decide whether the fractions are close to 0, or 1. 2 7 4 8 6In the problem above, we are asked to estimate the sum.74 +867 The numerator is nearly equal to the 78 denominator. is close to 1. 84 The numerator is about half the 416 denominator. is close to . 62 2

11So 1 + = 1 22 1About 1 pizza was eaten. 2Let us try another example. 92What is the estimated sum of + ? 10 3 9 is close to 1. Why?102 is close to 1. Why?392 1+1=2 +10 392 + is close to 2.10 3TRY THESEEstimate the sum. → → + 1. 5 5 is close to ____. → → + 88 11 + is close to ____. 10 102. 4 4 is close to ____. 5 5 24 24 + is close to ____. 25 25 3

WRAP UPIn estimating the sum of fractions, first determine whether each 1fraction is closest to 0, or 1. Then add the estimates. 2ON YOUR OWNEstimate each sum. Write your answers in your notebook. 14 31 111) 2 + 5 + + 2) 58 3) 84 43 23 + +4) 54 5) 54 4

WORD PROBLEMS INVOLGVRIANDGE AVDDITION OF FRACTIONSWORD PROBLEMS INVOLVING ADDITION OF FRACTIONS Objective: Solve word problems involving addition of similar and dissimilar fractions without and with regroupingREVIEWAdd the fractions found on the same line. Simplify your answer if necessary. 1 3 3 5) 2 10 1 4) 6 1 8 5 1 5 5 6 12 6 2) 4 1 5 7 3) 51) 1

STUDY AND LEARN 1Norie spent 2 hours helping her mother do 5 2the household chores and 3 hours doing her 5homework. How many hours did she spend inall for these activities?Let’s follow the steps below to answer the problem.STEP 1 Read and understand the problem.  What is asked in the problem? The number of hours Norie spent helping her mother and doing her homework.  What are the given facts? 1 2 hours - time spent in helping her mother do household 5 chores. 2 3 hours - time spent doing her homework. 5STEP 2 Plan.  What shall we do to solve the problem? We shall add.  What is the number sentence? 12 2 + 3 =N 55STEP 3 Solve. 12 The fractional parts 2 + 3 =N are similar 55 fractions. 1 2 5 2 +3 5 3 5 5 2

3Norie spent 5 hours helping her mother do household chores and doing her homework. 5Let’s have another word problem to solve. 2 Norie spent 1 hours doing her 3 3homework in Math and hours in English. 4How much time did she spend doing herhomework in the two subjects?Let’s solve for the answer.STEP 1 Understand the problem.  What is asked in the problem? The amount of time Norie spent doing her homework in the two subjects.STEP 2 Plan.  What process are we going to use to solve the problem? Addition  What is the number sentence? 23 1 + =N 34STEP 3 Solve. Let’s compute 1 2 + 3 = N. 34 28 The fractional parts are 1 =1 dissimilar fractions. Change them to similar 3 12 fractions first. 39 This can += still be 4 12simplified. 17 5 5 17 5 1 =1+1 = 2 1 = 2 12 12 12 12 12 3

5Norie spent 2 hours doing her homework in the two subjects. 12 TRY THESEA. Read the following story problem. Answer the questions that follow. 31 Kevin walked 1 km and jogged 2 km. How many kilometers did he walk 42 and jog altogether? 1. What is asked in the problem? a. The number of kilometers he jogged. b. The number of kilometers he walked. c. The number of kilometers he walked and jogged altogether. 2. What is the number sentence? 31 a. 1 + 2 = n 42 13 b. 2 - 1 = n 24 13 c. 2 x 1 = n 24 Mang Felipe picked 2 ripe papayas from the backyard. One papaya weighs 11 2 kilograms and the other weighs 2 kilograms. What is the total weight of the 2 42 papayas? 3. What shall we do to solve the problem? a. add b. subtract c. multiply 4. What is the answer? 4

1 1 3 a. 4 kg b. 4 kg c. 4 kg 4 2 4 35 1 Norma traveled km to school, km to the store and km home. How 4 12 2far did Norma travel?5. Norma traveled 35a. km and km 4 12 13b. km and km 24 35 1c. km, km and km 4 12 26. What process is involved in the problem? a. addition b. subtraction c. multiplication7. What is the answer? 1a. 1 km 3 2b. 1 km 3 3 1c. 3 kmB. Read the story problem and solve for the answer. 35 1. Alvin spent of his savings on Monday and on Tuesday. What fraction of 10 10 Alvin’s savings was spent on the two days? 11 2. Mother cooked 1 kilograms of beef for nilaga and 2 kilograms of chicken for 32 afritada. How many kilograms of meat did she cook in all? 31 3. Aling Maria bought 2 meters of cloth for 2 blouses and 5 meters for 2 pants. 42 How many meters of cloth did she buy in all? 5

WRAP UPIn solving problems involving fractions, follow these steps:Step 1: Understand the problem.Step 2: Make a plan.Step 3: Solve and look back.Step 4: Review your answer ON YOUR OWNChoose the letter of the correct answer. Write your solutions and answers in yournotebook. 411. A recipe calls for 1 cups of milk and 4 cups of chicken broth. How many cups of 53 liquid are called for in the recipe? 17 2a. 6 b. 6 15 15 17 2c. 5 d. 5 15 52. Mang Anselmo has a vegetable farm. One-third of his farm is planted with tomatoes 1 and 4 is planted with eggplants. What part of the vegetable garden is planted with tomatoes and eggplants? 1 5a. b. 12 12 7 11c. d. 12 12 6

13. Aling Miring harvested vegetables in her backyard. She harvested 2 kilograms of 2 3 patola, 1 kilograms of okra and 3 kilograms of eggplant. How many kilograms of 5 vegetable did she harvest in all? 1 1a. 5 kg b. 6 kg 10 10 1 1c. 7 kg d. 8 kg 10 10 524. Yeye ate 8 of the pizza while Ella ate 8 of it. How much did they eat altogether? 76a. b. 88 31c. d. 88 115. Manuel weighs 28 kilograms while Ruben and Jose weigh 26 kilograms and 25 3 29 kilograms, respectively. What is the total weight of the 3 boys? 4 7 7a. 84 kg b. 83 kg 12 12 9 5c. 84 kg d. 83 kg 20 12 7

SUBTRACTION OF WWWHHITOOHLLOEEUNNGTRUURAMMDEBBEGEEVRRROSSUFFPRRINOOGMM MIXED NUMBERSSUBTRACTION OF MIXED NUMBERS WITHOUT REGROUPINGObjective: Subtract whole numbers from mixed forms without regroupingREVIEWFind the sum. Reduce to lowest terms if needed. 1 1 3 31) 3 2) 10 3) 5 4) 13 5 8 4 8 3 2 1 2 +4 +8 +6 + 10 5 8 2 5 STUDY AND LEARN 1 Tony walked for 4 hours and ran for 2 hours. How much longer did he walk than 2run? 1What are the given facts? 4 hours spent walking and 2 hours spent running 2What is asked in the problem? The amount of time Tony spent walking more than runningWhat operation is needed to solve the problem? subtraction 1What is the number sentence? 4 - 2 = N 2What is the answer to the problem?How do you subtract a whole number from a mixed form? 1

1 4 Subtract whole numbers first. 2-2 Affix fraction to the difference. 1 2 2 1So Tony spent 2 hours walking more than running. 2Look at the answer to the problem. What can you say about it?Is it easy to subtract whole numbers from mixed forms? Describe the process.Let’s have another example: 1 Ric bought 15 kilograms of rice. On his way home, he met an old man begging 2alms. He gave 2 kilograms of rice to the beggar. How many kilograms of rice were left?So: 115 2-2 113 kg of rice left 2 1How did we get 13 2TRY THESEFind the difference. 3 2 5 2 31) 8 2) 10 3) 13 4) 9 5) 14 5 4 8 6 9 -4 -7 -6 -5 -7 2 5 3 3 16) 15 7) 5 8) 16 9) 20 10) 15 5 9 4 6 2 -7 -4 -8 - 15 -9 2