MATH 5

TRY THESE1) Number sentence: Php 15.75 + 7.50 = N Answer: Php 23.252) Number sentence: 15.2 + 12.45 + 16.25 = N Answer: 43.93) Number sentence: 50 – 25.50 = N Answer: 24.50ON YOUR OWN1) 48.2 kilometers2) 0.24 meters3) 2.25 kilograms4) 260.255) 18 litersKey to Correction2-STEP WORD PROBLEMS INVOLVING ADDITION AND SUBTRACTION OFDECIMALSREVIEW1) 124.502) 149.253) 190.00TRY THESE 50

1) 18.2 cm2) 1.5 hours3) 724) 36.65 kilogramsON YOUR OWN1) 1.75 liters of buko juice2) 23.503) 2.25 meters of cloth4) 25.005) 27.1%Key to CorrectionMULTIPLICATION OF DECIMALS BY ANOTHER DECIMALS THROUGHHUNDREDTHSREVIEW1) 722) 2703) 2854) 1 3765) 2 4326) 1 846 51

TRY THESE B C 0.512 0.128 A 0.2890 0.1674 0.125 0.2967 0.0936 0.0432 0.0775ON YOUR OWN1) 0.04322) 0.2553) 0.1484) 0.26465) 0.07956) 0.04747) 0.12658) 0.13239) 0.652510) 0.1387Key to CorrectionMULTIPLICATION OF MIXED DECIMALS BY WHOLE NUMBERSREVIEW1) 0.1482) 0.1563) 0.07924) 0.1265) 0.356TRY THESE 52

A B C1) a 1) 51.48 1) 43.82) b 2) 37.41 2) 35.163) c 3) 117.6 3) 1474) a 4) 132.155) a 5) 140.14ON YOUR OWN B 1) 10.56A 2) 781) 156.45 3) 83.952) 53.563) 129.784) 51.255) 29.2Key to CorrectionMULTIPLICATION OF MIXED DECIMALSREVIEW TRY THESE B. A. 1) C1) c 1) 14.256 2) E2) f 2) 14.5152 3) A3) a 3) 39.806 4) D4) b 4) 67.6466 5) B5) e 5) 139.6538ON YOUR OWN 53

1) 294.08882) 11.53743) 59.5324) 111.88945) 166.782Key to CorrectionMULTIPLICATION OF DECIMALS BY 10 AND 100REVIEW1) 2602) 24 5003) 3 6504) 48 3005) 12 100TRY THESE B 1) 10A1) 42.5 54

2) 1 672 2) 1003) 452.7 3) 104) 3 345 4) 105) 79 5) 106) 835 6) 1007) 12.5 7) 108) 47 8) 100 9) 10ON YOUR OWN 10) 10A B1) 26.9 1) 102) 333 2) 103) 1 438 3) 1004) 22.7 4) 1005) 1023.4 5) 10Key to CorrectionMULTIPLICATION OF DECIMALS MENTALLY BY 0.1, 0.01 AND 0.001REVIEWA. B.1) 37.2 1) 89.32) 6121.7 2) 47.23) 1817.7 3) 17254) 256.4 4) 42705) 721.4 5) 864.1TRY THESEA.1) 0.12) 0.13) 0.426344) 2.8901 55

5) 0.01 0.1 0.01 0.001 1.435 0.1435 0.01435B. 15.632 1.5632 0.15632 41.245 4.1245 0.412451) 14.35 12.373 1.2373 0.123732) 156.32 24.902 2.4902 0.249023) 412.454) 123.735) 249.02ON YOUR OWN1) 4.3352) 0.62143) 0.014354) 31.4785) 5.43966) 0.026727) 0.89998) 14.3159) 0.3650110) 3.3714Key to CorrectionWORD PROBLEMS INVOLVING MULTIPLICATION OF DECIMALSREVIEW1) 1.38882) 0.2523) 1.80044) 9.03065) 154.35TRY THESE1) 16 x 0.5 = n2) 8 metres of cloth3) 8.5 x 36.50 = n4) 310.255) 191.25 56

6) 1295.25ON YOUR OWN1) 465.75 cm2) 262.003) 178.754) 259.59 sq. m5) 17.5 litersKey to Correction ON YOUR OWNDIVISION OF DECIMALS 1) 681 2) 428REVIEW 3) 2 4) 6321. 4.5 5) 652. 7.63. 0.52 574. 1.875. 0.266. 0.126TRY THESEA.1) 4.71 15.0722) 0.6 215.4

3) 1.8 1.17184) 0.025 0.975B.1) 6882) 363) 3034) 9Key to CorrectionDIVISION OF DECIMALSREVIEWA.1) 15.282812) 0.77763) 1.2835B.1) 1.05 cm2) 3253) 0.125 cm4) 0.25 cmTRY THESE1) 0.44 58

2) 13.473) 3.6674) 2.665) 5.2ON YOUR OWN1) 23.42) 1.2353) 6.254) 7.775) 26.4Key to CorrectionDIVISION OF DECIMALSREVIEW1. 352. 503. 7.64. 1355. 4.6TRY THESE1. a. 0.336 liters, 8 b. 0.336  8 = N c. 0.042 liter2. a. 598.5  342 = N b. the average weight of each freight c. 1.75 kilos 59

3. a. 6  0.65 = N b. 94. a. 7.5 km., 3 days b. average distance c. divide d. 2.5 km.ON YOUR OWN1. a. The number of objects that container can hold b. 20.4 kilograms and 1.2 kilograms c. 20.4  1.2 = 172. a. 13.8  1.15 = N b. 1.15 m, 13.8 m c. 13.8  1.15 = 12 d. 12 x 1.15 = 13.83. a. The number of times Ben will fill the dipper b. 4.5  0.75 = N c. 4.5  0.75 = 6Key to CorrectionPERCENTREVIEWTRY THESE Fraction Ratio 73 73:100 Percent 100 73% 60

21% 21 21:100 10:100 or 1:10 10% 100 10 or 1 89:100 89% 100 10 5:100 or 1:20 5% 89ON YOUR OWN 100A. 5 or 11) 51 100 20 100 TRY THESE2) 30 or 3 1. 0.87 2. a. 0.03 100 10 b. 0.1153) 43 c. 0.01 d. 0.715 100B.1) 35:1002) 26:100 or 13:503) 73.5:100Key to CorrectionPERCENT AND DECIMALREVIEW 15 15% = or 15:100 100 5 5% = or 5:100 100 75 75% = or 75:100 100 90 90% = or 90:100 100ON YOUR OWN 61

0.05 0.78 0.125 0.03 0.2785% 0.85Key to CorrectionCIRCLEREVIEW1) e2) b3) a4) d5) cTRY THESE1) XB, XC, XD, XE, XF, XG, XH2) 8 62

3) HD, GC, EA4) 45) YesON YOUR OWN1) OT,OR,OS2) RT3) 3 cmKey to CorrectionCIRCUMFERENCE OF A CIRCLEREVIEW1) 99 cm2) 196 cm3) 122 cm4) 340 cm5) 75 cmTRY THESE1) 31.4 m2) 9.42 m 63

3) 47.1 cm4) 56.52 cm5) 78.5 cmON YOUR OWN1) 53.38 cm2) 40.82 cm3) 38.622 cm4) 26.69 cm5) 14.13 cmKey to CorrectionWORD PROBLEMS INVOLVING CIRCUMFERENCEREVIEW1) 53.38 cm2) 81.64 cm3) 94.2 cm4) 18.84 cm5) 21.98 mTRY THESE1) 32.97 meters2) 30 cm 64

ON YOUR OWN1) 47.1 cm2) 62.8 cm3) 157 cmKey to CorrectionREVIEW1. diameter2. radius3. diameterTRY THESE1) 200.96 sq. cm2) 153.86 sq. m3) 452.16 sq. m4) 113.04 sq. m5) 226.865 sq. cmON YOUR OWN 65

1) 78.5 sq. m2) 379.94 sq. m3) 530.66 sq. dm4) 63.585 sq. m5) 415.265 sq. cmKey to CorrectionAREA OF A TRAPEZOIDREVIEW1) 40 sq. cm2) 24 sq. cmTRY THESE1) 56 sq. cm2) 70 sq. cmON YOUR OWN1) 56 sq. cm2) 55 sq. m3) 54 sq. m4) 60 sq. cm 66

Key to CorrectionVOLUME OF A RECTANGULAR PRISMREVIEW1) 60 sq. cm2) 120 sq. cm3) 30 sq. m4) 84 sq. cm5) 36 sq. mTRY THESE1) 240 m32) 300 dm33) 896 cm34) 189 m35) 960 cm3ON YOUR OWN 67

A.1) 525 cm32) 576 m33) 1000 dm34) 147 m35) 243 m3B.1) 252 cm32) 1800 cm3Key to CorrectionPARTS OF A THERMOMETER/READING A THERMOMETERREVIEW1) cold2) hot3) hot4) cold5) hot6) coldTRY THESE1) 81 C2) 57 C3) 40 C4) 89 C5) 54 C6) -5 C 68

ON YOUR OWN1) 80 C2) 80 C3) 5 C4) 40 C5) 100 C6) 0 CKey to CorrectionWORD PROBLEMS INVOLVING BODY/WEATHER TEMPERATUREREVIEW1) 39 C2) 10 C3) 37 C4) 39 CTRY THESE1) 7.8 C2) 7 CON YOUR OWN1) 40 C2) 4 C3) Mt. Makiling, 2 C4) 10 C 69

Key to CorrectionLINE GRAPHREVIEW1) basketball2) tennis3) 304) volleyball5) badminton and swimmingTRY THESE1) Tuesday and Thursday2) Monday3) Friday4) 40 kaings5) 10 kaingsON YOUR OWN1) 15.002) 2nd and 5th week 70

3) 3rd week4) 4th week5) 20.00 71

MISOSA MODULESMATHEMATICS V LIST OF TITLES TITLE OF MODULE NO. OF PAGES1. Prime and Composite Numbers 72. Prime Factors of a Number 43. Least Common Multiples 44. Changing Dissimilar Fractions to Similar Fractions 65. Equal Fractions 56. Fractions in Lowest Terms 67. Fractions in Higher Terms 48. Ordering Dissimilar Fractions 59. Estimation of Fractions 610. Addition of 2 to 4 Fractions 611. Visualization of Addition of Dissimilar Fractions 1012. Addition of Dissimilar Fractions 513. Addition of Dissimilar Fractions and Whole Numbers 514. Addition of Whole Numbers and Mixed Forms 515. Addition of Mixed Forms and Dissimilar Fractions 516. Addition of Mixed Forms 617. Estimation of Sum of Fraction 518. Word Problems Involving Addition of Fractions 819. Subtraction of Whole Numbers from Mixed Forms without 5 Regrouping 520. Subtraction of Fractions from Whole Numbers 521. Subtraction of Fractions from Mixed Numbers without Regrouping 622. Subtraction of Mixed Numbers from Whole Numbers 723. Subtraction of Mixed Numbers without Regrouping 624. Subtraction of Mixed Numbers with Regrouping 625. One-Step Word Problems Involving Subtraction of Fractions 626. Two-Step Word Problems Involving Addition and Subtraction of 6 Fractions 627. Visualization of Multiplication of Fractions 528. Multiplication of Fractions by another Fraction 529. Multiplication of Fractions by Whole Numbers 730. Multiplication of Mixed Numbers and Fractions 631. One-Step Word Problems Involving Multiplication of Fractions 732. Two-Step Word Problems Involving Multiplication of Fractions 533. Visualization of Ratio 534. Expressing Ratio 735. Ratio in its Simplest Form 536. Proportion37. Renaming Fractions in Decimal Form 1

TITLE OF MODULE NO. OF PAGES38. Rounding Decimals 539. Addition and Subtraction of Decimals Up to Hundredths Place 640. Addition and Subtraction of Decimals Through Thousandths without 5 Regrouping 641. Addition and Subtraction of Decimals Through Thousandths with 6 Regrouping 642. Addition and Subtraction of Mixed Decimals without regrouping 543. Addition and Subtraction of Mixed Decimals with Regrouping 644. Problem Solving Involving Addition or Subtraction of Decimals45. Two-Step Word Problems Involving Addition and Subtraction of 5 5 Decimals 546. Multiplication of Decimals by Decimals Through Hundredths 447. Multiplication of Mixed Decimals by Whole Numbers 548. Multiplication of Mixed Decimals 549. Multiplication of Decimals by 10 and 100 650. Multiplication of Decimals Mentally by 0.1, 0.01, and 0.001 551. Word Problems Involving Multiplication of Decimals 552. Division of Decimals 553. Division of Decimals by Whole Numbers 554. Word Problems Involving Division of Decimals 655. Percent, Fractions and Ratios 556. Percent and Decimals 557. Parts of a Circle 458. Circumference of a Circle 559. Word Problems Involving Circumference 560. Area of a Circle 661. Area of a Trapezoid 562. Volume of Rectangular Prisms 663. Parts of a Thermometer64. Word Problems Involving Body/Air Temperature65. Line Graphs 2

PRIME AND COGMRAPDOESVITE NUMBERS PRIME AND COMPOSITE NUMBERObjective: Give the factors of a number Differentiate prime and composite numbersREVIEW Find the hidden message. Find the product of the numbers in the first column. Matcheach letter on the second column to the answer in the boxes below. Write the letter in thebox above each answer.2x9 A 8x5 E 4x7 G 6x9 O 4x6 R 9x7 T 7x7 U 8x6 YHidden Message: ! 48 54 49 18 24 40 28 24 40 18 63 STUDY AND LEARN Alex has 7 balls. He wanted to place the balls in boxes such that each boxcontains an equal number of balls. He tried to place them in the following manner. 1 box of 7 7 boxes of 1 1

How many different arrangements was he able to make? (2)The ways of arranging the balls illustrate the factors of 7.To get the factors of 7, we think of the following mathematical sentences.1x7=77x1=7Therefore, the factors of 7 are 1 and 7.Seven is a prime number. It has only 2 factors – one and itself.Five and 11 are other examples of prime numbers.What are the factors of 5? 1 and 5What are the factors of 11? 1 and 11Can you name the prime numbers between 12 and 20?Alex bought 5 more balls.How many balls has he now? 12 ballsHow many arrangements can he now make?Let’s help him.1 box of 122 boxes of 63 boxes of 44 boxes of 36 boxes of 212 boxes of 1 2

Into how many ways were we able to arrange the 12 balls? (6 different ways)Can you name the factors of 12? (1, 2, 3, 4, 6 and 12)How many factors has 12? 6 factorsTwelve is a composite number. It has more than 2 factors.Let’s have another example.Let’s try to get the factors of 18.To get its factors, we think of:1 x 18 = 18 18 x 1 = 182 x 9 = 18 9 x 2 = 183 x 6 = 18 6 x 3 = 18What are the factors of 18? 1, 2, 3, 6, 9 and 18Is 18 a prime or composite number? compositeWhy is 18 a composite number? It has more than 2 factors.Can you think of other composite numbers?Name some.How are prime numbers different from composite numbers?TRY THESEA. List down the factors of the given number on the petals. Then tell if the given number is prime or composite. Number 1 has been done for you.1) 2) 13 14 15 5 15composite 3

3) 4) 24 375) 6) 36 23B. Look at the numbers inside the jar. Cross out all the prime numbers and box all the composite numbers. 21 17 48 19 27 42 31 24 38 12 50 4

WRAP UP A number has a set of factors. A prime number has exactly 2 factors, 1 and itself. A composite number has more than 2 factors. It has factors other than 1 and itself.ON YOUR OWNWrite prime or composite. Write your answers in your notebook.1) 45 __________ 6) 30 __________2) 26 __________ 7) 35 __________3) 32 __________ 8) 81 __________4) 10 __________ 9) 71 __________5) 47 __________ 10) 23 __________ 5

PRIME FACTGORRADSEOVF A NUMBER PRIME FACTORS OF A NUMBER Objective: Find the prime factors of a number REVIEWDo you know how to work out a maze? It’s easy, just follow the path of 11 primenumbers from the start to the finish. start 232235 257375 9 8 11 13 15 7 8 6 6 17 19 3 4 10 15 4 23 29 24 21 18 5 7 31 finish STUDY AND LEARNObserve how the prime factors of 36 are obtained. 36 3618 2 4 99x2 2 x2 3x 3 The prime factorization of 36 is 2 x 2 x 3 x 3.3 x3The prime factorization of 36 is 3 x 3 x 2 x 2. 1

We followed the following procedures:a. Find two factors whose product is 36. These are the first two branches of the factor tree.b. Find the factors whose products are 4 and 9. These are the next four branches of the tree. The last factors are already prime factors.Try another number. 72 What are the factors of 72? (9 x 8) Are 9 and 8 prime numbers? 9 8 (No. They are composite numbers.) What are the factors of 9? (3 and 3) 3342 What are the factors of 8? (2 and 4) 2 2 Are the factors of 9 prime factors? (Yes) How about 8? 4 is a composite number What are the factors of 4? 2 and 2 What is the prime factorization of 72? 72 = 3 x 3 x 2 x 2 x 2TRY THESEComplete the factor tree.1) 48 2) 63 3) 546  9 62 2 4 33    2

WRAP UP To find the prime factors of a number:  Using the factor tree method, find any two factors of the number.  If one of the factors is a composite number, find any two factors of that number.  Continue factoring until all the factors are prime numbers.  You may start with any two factors but the final row should contain only prime numbers. ON YOUR OWNFind the prime factors of the following numbers. Write your answers in yournotebook.1. 30 6. 292. 42 7. 313. 81 8. 134. 100 9. 175. 27 10. 23 3

LEAST COMGMRAODNE VMULTIPLES LEAST COMMON MULTIPLESObjective: Find the least common multiple of a set of numbers.REVIEWLook at the two flowers. Write the numbers in a box if the number printed on thepetal is a multiple of 2; in a triangle, if a multiple of 3; and in a circle if a multiple of5. 14 659 21 2 55 25 1654 35 27 8 3Multiples of 2 Multiples of 3 Multiples of 5 1

STUDY AND LEARNThe skill of finding the least common multiple is needed when you add or subtractdissimilar fractions. Thus, it is important to learn this skill.Look at the set of numbers below and their multiples.3 – 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36…6 – 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, …9 – 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, …3, 6, 9, 12, 15, 18, 21, 24, 27, 30 are multiples of 3. What are the multiples of 6? 9?Look at the multiples of the three numbers. Which multiples are common? (18 and36)If we continue to list down the multiples of these numbers, will it be possible thatthey’ll have other common multiples? YesSince 18 is the first common multiple, we call 18 the least common multiple of 3, 6,and 9.Try another set of numbers:4 - 8, 12, 16, 20, 245 - 10, 15, 20, 25, 3010 - 20, 30, 40, 50, 60What is the least common multiple of 4, 5 and 10? (20) TRY THESEDo what is asked.1. a. List the multiples of 2. b. List the multiples of 3. c. List the multiples of 4. d. What is the least common multiple of 2, 3 and 4? 2

2. What are the multiples of 5? What are the multiples of 6? What are the multiples of 10? What is the least common multiple of 5, 6, and 10? WRAP UP The least common multiple (LCM) of two or more numbers is the smallest non-zero number that is common multiple to all of them.ON YOUR OWNGive the least common multiples of each set of numbers. Write your answers in yournotebook.1) 2 2) 3 3) 5 7) 6 5 6 4 3 10 4 10 2 LCM ____ LCM ____ LCM ____ LCM ____4) 3 5) 2 6) 8 8) 8 4 6 10 2 9 9 5 4 LCM ____ LCM ____ LCM____ LCM ____ 3

CHANGING DISSIMILAR FRACTIONS TO SIMILAR FRACTIONS GRADE VCHANGING DISSIMILAR FRACTIONS TO SIMILAR FRACTIONS FROM 100 001 THROUGH MILLIONS/BILLIONS Objective: Change dissimilar fractions to similar fractionsREVIEWLook at the pair of fractions in each box. Write D if they are dissimilar and S if theyare similar fractions.1) 1 , 3 2) 5 , 3 3) 5 , 7 4) 2 , 5 5) 3 , 5 6) 5 , 6 44 78 88 5 10 47 97 STUDY AND LEARNLook at the fraction bars. Do they have the same length? 4 10 3 5 4 and 3 are dissimilar fractions. Their denominators are not the same.10 5Let’s make 4 and 3 similar fractions. Look at the second fraction bar. Broken lines 10 5were drawn to show how 3 can be changed to fraction whose denominator is 10. By 5 1

counting the shaded area you will get 6 . 4 and 6 . They are now similar 10 10 10fractions. They have the same denominators.Let’s try another example.Example 1: 1 2 3 41 and 3 are dissimilar fractions because they have different denominators.24How can we change 1 and 3 to similar fractions? 24Look at the fraction bar with broken lines. If we count the shaded parts you’ll have2 . So 3 and 2 have the same denominators now. They are similar fractions.4 44Let’s change 4 and 3 , 1 and 3 into similar fractions without using illustrations. 10 5 2 4Drawing fraction bars will consume a lot of your time. The process of changingdissimilar fractions into similar fractions without the use of fraction bars is actuallyvery simple. You’ll find it easier and faster.4,310 5Look at the denominators. 10 is a multiple of 5. The least common multiple of 10and 5 is 10.What will you multiply to 4 to retain its denominator? What will you multiply to 3 10 5to change its denominator to 10?4 x1= 4 3x2= 610 1 10 5 2 10 2

4 and 6 have the same denominators. They are now similar fractions.10 10How about 1 and 3 . The least common multiple of the denominators is 4. 241 x2 =22243 x1=34142 and 3 are similar fractions. They have the same denominators which is 4.44Now, let’s try fractions whose least common multiple is not one of the denominators.STEP 1 1,2 → List down the multiples of the denominators in 34 increasing order. Find their least common multiple. 3, 6, 9, 12 4, 8, 12, 16 The least common multiple of 3 and 4 is 12.STEP 2 1 x 4 = 4 → Multiply 1 by 4 since 12 is the 4th multiple of 3 4 12 34 3.STEP 3 2 x 3 = 6 → Multiply 2 by 3 since 12 is the 3rd multiple of 4 3 12 43 4.So 1 , 2 when changed to similar fractions are 4 and 6 . 3 4 12 12 3

TRY THESEChange the following dissimilar fractions to similar fractions. In the first two items,study the illustrations.1) 1 4 3 62) 23) 2 , 2 → , 4 5 3 15 15 94) 6 , 2 → 6 , 4 12 845) 6 , 2 → , 7 3 21 4

WRAP UP  To change dissimilar fractions to similar fractions, first find their least common denominator.  The least common denominator (LCD) of dissimilar fractions is the least common multiple (LCM) of their denominators.  Use the LCD to write similar fractions. ON YOUR OWNChange the following to similar fractions. Write your answers in your notebook.1) 2 , 1 342) 1 , 5 5 153) 3 , 1 724) 4 , 2 365) 7 , 2 84 5

FRACTIONS GINRALDOEWV EST TERMS FRACTIONS IN LOWEST TERMS Objective: Change fractions to lowest termsREVIEWMatch the numbers in Column A with the greatest common factor of the two numbersfound in Column B.AB1) 24 and 20 a. 82) 30 and 36 b. 43) 45 and 50 c. 74) 21 and 35 d. 55) 16 and 40 e. 6 STUDY AND LEARNStudy the problem below. Sleep is an important part of a good fitness plan. Therese Marie sleeps 8 hoursor 8 in a day. 24What other fractions are equivalent to 8 ? 24 1

8Look at the strips of paper that show the equivalent fractions of . 24 8 24 4 12 2 6 1 3Among the fractions presented in the fraction strips, what is the lowest term orsimplest form of 8 ? 24 The simplest form of 8 is 1 . 24 3So, Therese Marie sleeps 1 of the day. 3You can find the simplest form of a fraction by dividing the numerator and thedenominator by the greatest common factor (GCF). 88   1 24    8 3 1Why is considered to be in simplest form? The numerator is 1 and both the 3numerator and denominator have no common factor except one.Let’s try other examples: 2

Example 1: 3  3  3  1 15 15  3 5 44  2  2 6 62 3TRY THESEUse the illustrations to complete the following: 3)1) 2) 2 82 242 6WRAP UP  A fraction is in its simplest form or lowest terms when the numerator and denominator have no common factor other than 1.  You can find the simplest form of a fraction by dividing the numerator and the denominator by their greatest common factor. 3

ON YOUR OWNWrite each fraction in its simplest form. Write your answers in your notebook.1) 8 2) 12 3) 10 4) 6 5) 14 18 36 24 10 166) 5 7) 8 8) 13 9) 18 10) 25 30 26 26 36 100 4

FRACTIONSGIRNAHDEIGVHER TERMS FRACTIONS IN HIGHER TERMS Objective: Change fractions to higher terms REVIEWUse your pencil and paper to solve the following. Write your answers in lowest terms.1. An employee spends 8 hours a day working in the office. What fraction of a day is this? Hint: How many hours are there in a day?2. An audio compact disc has 16 songs. Four of them are Original Pilipino Music (OPM). What part of the total number of songs is OPM?STUDY AND LEARNFractions are also renamed in their higher terms. Here’s how.2x2=4 2 x3=6 2 x 5 = 1032 6 339 3 5 15To get 4 , what did we multiply with 2 ? ( 2 ) 6 32To get 6 , what did we multiply with 2 ? ( 3 ) 9 33To get 10 , what did we multiply with 2 ? 15 3 1

Let’s try other examples.Example: a. 6 x 3 = 18 7 3 21 b. What are we going to multiply with 3 to get 18 ? 4 24 c. Are 6 and 18 equal? Why? Which is the fraction in higher terms? 7 21 TRY THESEMultiply continuously by 2 to produce five fractions of higher terms equivalent to 2 23 2 3 2

WRAP UP To change fractions to higher terms, multiply the numerator and the denominator by the same non-zero digit or fractions equal to one. ON YOUR OWNMultiply 3 by 2 , 3 , 4 , 5 , 6 , 7 to produce fractions in higher terms. Write the 4 234567answers on the outer circle. 3 4 3

ORDERING DISGSRIAMDIELVAR FRACTIONS ORDERING DISSIMILAR FRACTIONS Objective: Order dissimilar fractions written in different forms from least to greatest and vice versa REVIEWArrange the following fractions from least to greatest. Write your answer on a piece ofpaper.1) 657 ,, 16 16 162) 2 , 1 , 3 3333) 5 , 8 , 4 7774) 8 , 5 , 3 9995) 2 , 3 , 1 666 STUDY AND LEARNLook closely at the fraction bars below. 3 4 3 8 5 6Which is the longest shaded part? ( 5 ) 6 1

Which is longer between 3 and 3 ? ( 3 ) 4 84Let us arrange the fractions from least to greatest or vice versa by merely looking at thefraction bars.3, 3, 5 (least to greatest)846 (greatest to least)5, 3, 3648You can use the LCD to order fractions. Let’s use the same set of fractions.Order 3 , 3 and 5 from least to greatest. 48 6Find the LCD by listing the multiples of 4, 8, 12, 16, 20, 24the denominator. 8, 16, 24 6, 12, 18, 24Use the denominator 24 to find 3  3  x  6  18 Why did we multiplyequivalent fractions. 4 4  x  6 24 33 x 3 9 36 8 8 x 3 24 by ? 24 is the 46 6th multiple of 4. 5  5 x 4  20 6 6 x 4 24How about the next two fractions? Can you now give the reasons why we multiply themby 3 and 4 , respectively? 34Order the equivalent fractions by their 9  18  20numerators. 24 24 24So, from least to greatest the fractions are: 3 , 3 , 5 . 846From greatest to least the fractions are 5 , 3 , 3 . 648 2

TRY THESEOrder from least to greatest then greatest to least.3, 2, 5, 143621. List the multiples of the denominators. 2, ___, ___, ___, ___, ___, ___ Encircle the least common multiple. 4, ___, ___, ___, ___, ___, ___ 3, ___, ___, ___, ___, ___, ___ 6, ___, ___, ___, ___, ___, ___2. Use the LCD to find equivalent 1x = fractions. 2 3x = 4 2x = 3 5x = 63. Order the equivalent fractions by their ___, ___, ___, ___ numerators.WRAP UPTo arrange dissimilar fractions:  Find the Least Common Denominator (LCD) for a set of fractions.  Use the LCD to find equivalent fractions.  Order the equivalent fractions by looking at their numerator. 3