1PART I

Content and Practice Exercises

d = 8 m = 3.14c = ?

8 m

c = dc = 3.14 x 8c = 25.12 m

2MATHEMATICS

WHOLE NUMBERS

Points to remember:

In writing large numbers in words: separatethegivennumberbycommasstartingfromtheunits placeandgoingtotheleft,whenitcontains4ormorefigures, intoasmanygroupsorperiodsof3figureseachaspossible Inreadinglargenumbersreadeachgroupoffiguresseparately startingfromtheleftandgoingtotheright,applyingtheproper nametothecommaasitisreached. The first comma from the right is read and written thousand. The second comma from the right is read and written million. The third comma from the right is read and written billion.

Theabovenumberisread:Six hundred twenty-one billion, fourhundredsixty-eightmillion,threehundredfifty-nine thousand, seven hundred eighty-two.

A. Directions: Writethefollowinginwords.

1. 476 923 3. 5 000 000 000 2. 147 194 652 805 4. 241 849 000

B. Directions: Writeeachofthefollowinginfigures.

1. Sixthousand,eighthundredforty-three 2. Twomillion,sevenhundredtwenty-fivethousand,twohundred thirty-five 3. Sixbillion,fourhundredfiftymillion 4. Fourhundredsixmillion,ninehundredtwenty-threethousand, sixhundredeighty-five

6 2 1 4 6 8 3 5 9 7 8 2

Hundre

d B

illio

ns

Ten B

illio

ns

Bill

ions

Hundre

d M

illio

ns

Ten M

illio

ns

Mill

ions

Hun

dred

Tho

u-sa

nds

TenTh

ousand

sTh

ousand

sH

undre

ds

Tens

,

b b Reading and Writing Large

-

-

3COMMON FRACTIONS

Addition of Fractions and Mixed Numbers

Points to remember:

Whenaddingsimilarfractions,addthenumeratorsandwritethe sumoverthecommondenominator.Thenwritetheanswerinits simplestform. + =

Whenaddingdissimilarfractions,findtheirleastcommon denominatorsandchangethefractiontoequivalentfractions havingacommondenominator.Thenaddasshownbelow.

= =

or 1 = 1

Toaddmixednumbers,firstaddthefractions,thenaddthesum tothesumofthewholenumbers.

A. Directions: Add.

1. 6 5. 15 8 9

2. 6.

3. 5 7. + + = 2

4. 4 8. 8 7

B. Directions: Solvethefollowingproblems.

1. Rosemadea2-piecedressrequiring2metersforonepart and1metersfortheother.Howmuchmaterialdidsheuse? 2. Aliworksafterschool.Duringacertainweek,heworked hoursonMonday,2hoursonWednesday,and4hourson Friday.Howmanyhoursdidheworkaltogether? 3. Whatisthedistancearoundatriangleifitsthreesidesmeasure 6inches,4inches,and5inchesrespectively?

1238

,

-

bb

-

11216

15

25

35

2356

625825

23

12

58

712112

13512

1434

783

8 341

2

3 8

11 16

34

710

810710

1510

45

510

12

4 Points to remember:

Insubtractingfromawholenumber,takeoneandchangeittoa fraction,makingthenumeratoranddenominatorsimilar.

7 = 6 7=6sincethe1takenfrom7equals. 7 = 6

Ifthefractionintheminuendislesserthanthefractioninthe subtrahend,takeone(1)fromthewholenumberof theminuend andchangeittoafraction.Thenaddthistotheoriginalfraction and subtract. 9+=so, 8 - 4 - 4 4 = answer

One (1) borrowed from 9 is changed to . Add and .

6 +=so, 5 - 3 -3 2 Thefinalanswershouldbeexpressedinlowestterm.

A. Directions: Findthemissingnumbers:

1. 4 = 3 5. 1 = 2. 3 = 2 6. 7 = 6 3. 12 = 11 7. 6 = 5

4. 1 = 8. 1 =

B. Directions: Subtract.

1. -= 3. 8-2=

2. 14 4. 12 - 5 - 9

8

5

b bBorrowing in Subtraction of Fractions

,

-

-

2757

77

97

97574 7

33

33

33

2959

29

119

11959611

2

3

8

12

2

4

10

4

3

77

77

27

23

712

31014

13

23

3767

15

45

4878

12

5C. Solve.

1. TherunningtimeofatrainfromManilatoanotherpartof Luzonis 9hours.Anothertraintakes15hourstomakethesame trip.Howmuchfasteristhefirsttrain?

2. Amerchantsold7metersofclothtoacustomer.Ifitwascut fromaboltthatcontained18meters,howlongistheremaining clothinthebolt?

3. Ifonemechaniccanassembleamotorin6hours,whileanother mechaniccandothesamejobin10hours,howmuchmore quicklycanthefirstmechanicdothejob?

Points to remember:

Incomparingfractions: changethegivenfractionstofractionshavingacommon denominator taketheresultingfractionwiththelargernumeratorasthe largerfraction.

A. Directions: Writethelargerfraction. 1. and 5. and 2. and 6. and

3. and 7. and

4. and 8. and

B. Directions:Writethesmallerfraction.

1. and 5. and

2. and 6. and

3. and 7. and

4. and 8. and

Comparing Fractionsb b

-

,

-

34

24

57 2

7

295

9

14

13

12

116

716

25

1316

56

23

58

45

34

112

110

16

110

12

16

516

14

18

14

23

1116

18

110

25

38

58

712

13

15

6 C. Directions: Arrangefromthelargesttothesmallest.

1. ,,and 5. ,,and

2. ,,and 6. ,,and

3. ,,and 7. ,,and

4. ,,and 8. ,,and

Multiplication of Fractions and Mixed Numbers

Points to remember:

Inmultiplyingfractionsandmixednumbers: changeeachmixednumbertoanimproperfraction.Awhole numbermaybeexpressedinfractionsbywritingthewhole numberasthenumeratorandone(1)asthedenominator.

6 x = x = = 2

The numerator 6 and the denominator 8 are divided by the same number (2) being the greatest common multiplier, before multiplying the numerator and the denominator. This is called cancellation.Sincethefinal answer is a an improper fraction, it is changed to a mixed number in its lowest form.

Directions: Multiplyasindicated.

1. 3 x 6. 2 x

2. x 3 7. 5 x

3. 4 x 8. x 2 4. x 1 9. x 3 5. 1 x 1 10. 5 x 4

-

b b

,

-

12

15

13

58

23

35

34

916

712

58

35

34

14

12

16

12

25

310

1116

58

34

14

516

38

3

4

38

61

38

94

14

13

35

12

15

12

15

78

14

14

35

15

56

23

58

56

310

12

38

13

12

7Division of Fractions and Mixed Numbers

Points to remember:

Individingfractionsandmixednumbers:

changeeachmixednumbertoanimproperfractionandexpress eachwholenumberinfractionformbywritingthewholenumber asthenumeratorwithone(1)asthedenominator getthereciprocalorinvertthedivisorandreplacethedivision signwithamultiplicationsign multiplyasinmultiplicationoffractions,usingcancellation wherepossible.

2 = = x = or 3

Directions: Divideasindicated.

1. 2 5. 1

2. 1 6. 1

3. 4 7. 1

4. 2 8. 8

DECIMAL FRACTIONS

Reading and Writing Decimals

Points to remember:

Adecimalfractionisafractionwhosedenominatoris10, 100, 1000,etc.However,itdiffersfromacommonfractioninthat thedenominatorisnotwrittenbutisexpressedbyplacevalue. Inreadingadecimalfraction,readthenumbertotheright ofthedecimalpointasyouwouldawholenumberanduse thenamethatappliestothevalueofthelastfigure. Thevalueofeachplaceisthevalueofthenextplaceto theleft.Thefirstplacetotherightoftheunitsplaceexpresses tenths(.6=).Thedecimalpointisusedtoseparatethe fractionfromthewholenumber. Thesecondplacetotherightoftheunitsplaceexpresses hundredths(.06=),thethirdplaceexpresses thousandths(.006=),thefourthplaceexpressesten thousandths(.0006=),thefifthplaceexpresses

b b

,

-

b b

,

56

12

56

5 2

65

5 2

3010

35

58

34

78

12

23

13

514

23

71634

34

23

35

34

56

610

110

66

1000 610 000

8hundred-thousandths(.00006=),andthesixthplaceexpressesmillionths(.000006=)

Inreadingamixeddecimal,firstreadthewholenumberandthen thedecimalfraction.Usethewordandtoshowthepositionof thedecimalpoint.Sometimesthedecimalfractionmayhavea zerowrittenintheunitsplacejustprecedingthedecimalpoint.

Thus,thenumber427518203.964287isread:Four hundred twenty seven million, five hundred eighteen thousand, two hundred three and nine hundred sixty-four thousandths, two hundred eighty-seven millionths. Inwritingadecimalfraction,writethefiguresasyoudoa wholenumber,butinsertadecimalpointsothatthename ofthepartcorrespondstotheplacevalueofthelast figure.Prefixasmanyzerosasarerequiredbetweenthe decimalpointandthefirstfigurewhenitisnecessarytomake thenameofthepartandplacevalueofthelastfigure correspond. Inwritingamixeddecimal,writethewholenumber,inserta decimalpointforthewordand,thenwritethedecimalfraction.

Examples: a. Read .734 (sometimes written as 0.734) Answer: Seven hundred thirty-four thousandths b. Read 14.06 Answer: Fourteen and six hundredths. c. Write as a decimal: Nineteen ten-thousandths Answer: .0019

A. Directions: Writethefollowingaswordstatements:

1. .2 6. .076 2. .06 7. .289 3. .58 8. 14.708

4. 1.5 9. .0037

5. 3.73 10. .17925

-

Hundre

d M

illio

ns

Ten M

illio

ns

Mill

ions

Hun

dred

Tho

usan

dsTenTh

ousand

sTh

ousand

sH

undre

ds

Tens

Units

and

Tenths

Hun

dred

ths

Thou

sand

ths

Ten-Th

ousand

ths

Hun

dred

-Tho

usan

dths

Millionths

4 2 7 5 1 8 2 0 3 . 9 6 4 2 8 7

34

6100 000

61 000 000

9 B. Directions: Writeeachofthefollowingasadecimal number:

1. Sixandfourhundredths 2. Fiveandsixty-twohundredths 3. Sixty-ninethousandths 4. Seventy-threeandeighteenhundredths 5. Thirty-sixandtwohundredfifty-threethousandths 6. Fourhundredninety-fourtenthousandths 7. Threehundredthousandths 8. Nineteenandonehundredtwenty-twothousandths 9. Forty-twohundredthousandths 10. Fourhundredsevenandtwenty-fivehundredths

Addition of Decimals

Points to remember:

Writetheaddendsincolumnsothatthedecimalpointsare directlyundereachother.Zerosmaybeannexedtothe decimalfractionssothattheaddendsmayhavethesame numberofdecimalplaces. Placethedecimalpointinthesumdirectlyunderthedecimal pointsintheaddends. Whenadecimalanswerendsinoneormorezerostotheextreme rightofthedecimalpoint,thezerosmaybedroppedunlessitis necessarytoshowtheexactdegreeofmeasurement.

A. Directions: Add:

1. .752 + 4.53 + 6 2. 6.4 + .976 + 2.87

3. .17 + .38 + .53

4. 15.6 + .19 + 4.75 + .836 + 200

5. 3.3 + .07 + 6 + 2.63 + .174

6. P32.40+P4.80+P2.62+P.61+P.89

7. P3.42+P6.51+P12.54+P9.49+P8.68

8. .74 + 1.60 + .99 + 4.88 + .04

-

b b

,

-

10

Multiplication of Decimals

Points to remember:

Inmultiplyingdecimals: writethegivennumbersandmultiplyasinthemultiplicationof wholenumbers.Thedecimalpointinthemultiplierdoesnot necessarilyhavetobeunderthedecimalpointinthemultiplicand findthetotalnumberofdecimalplacesinthemultiplicandand multiplierandpointoffintheproduct,countingfromrightto left,asmanydecimalplacesasthereareinthemultiplicand andmultipliertogether prefixasmanyzerosasarenecessarywhentheproductcontains fewerfiguresthantherequirednumberofdecimalplaces.

Directions: Multiply.

1. .268 2. 3.1416 3. 8.504 x .924 x 6.25 x .015

4. 2.423 5. .179 6. 3.14 x 9.146 X .04 X .002

Points to remember:

Ifthedivisorisawholenumber: divideasindivisionofwholenumbers placethedecimalpointinthequotientdirectlyabovethe decimalpointinthedividend. 1.41 2/3 = 1.42 6)8.50

Ifthedivisorisadecimal: makethedivisorawholenumberbymovingitsdecimalpointto therightofthelastfigureindicatingitsnewpositionbyacaret(^) movethedecimalpointinthedividendtotherightasmanyplaces asyoumovedthedecimalpointinthedivisorandindicateits newpositionbyacaret(^) divideasinthedivisionofwholenumbersandplacethe decimalpointinthequotientdirectlyabovethecaret(^)in thedividend whenthedividendcontainsfewerdecimalplacesthanrequired, annexasmanyzerosasarenecessarytoadecimaldividendand adecimalpointandtherequiredzerostoadividendcontaininga wholenumber.

b b

,

-

,

b bDivision of Decimals

11

Divide28.5by.87andfindthequotienttothenearesttenth.

32.7 .87^ ) 28.50^0 26 1 2 40 1 74 660 609 51

A. Directions: Divide.

1. .4)7.6 4. .16)48.00

2. 7.5)456.2 5. 1.8)36

3. .6).0552 6. .3).84

Changing Common Fractions to Decimals

Points to remember:

Tochangeacommonfractiontoadecimal: dividethenumeratorbythedenominator

=5)2.0

or,ifthedecimalequivalentisknown,writethedecimaldirectly (reducethegivenfractiontolowesttermsfirst) or,ifthegivenfractionhasasitsdenominator10,100,1000,etc., dropthedenominatorandrewritethenumerator,placinga decimalpointintheproperlocation.

= 1.65

Tochangeamixednumbertoamixeddecimal: changethefractiontoadecimal annextothewholenumber.

Change1toadecimal:

= .87 or .875

1 = 1.87 or 1.875

NOTE: Since the remainder (51) is more than one-half of the divisor(87),1isaddedtothelastfig-ureofthequotient.

Answer: 32.8

-

.4

b b

,

16510 0

25

78

78

12

78

12

12

Directions: Expressthefollowingcommonfractionsormixednumbersto decimals.

1. 6. 9.

2. 7. 10.

3.

4. 8.

5.

Changing Decimals to Common Fractions

Points to remember:

Tochangeadecimaltoacommonfraction:

writethefraction,usingthefiguresofthedecimalasthenumerator

andapoweroften(10,1001000,etc.)correspondingtothe

placevalueofthelastfigureofthedecimalasthedenominator.

Thensimplifyandreducetolowestterms.

.05 = =

or,ifthecommonfractionequivalentisknown,writethecommon

fractiondirectly.

Tochangeamixeddecimaltoamixednumber:

changethedecimalfractiontoacommonfractionandreduceto

lowest terms

annexthisanswertothewholenumber.

5.875 = 5 = 5

Directions: Expressthefollowingdecimalsascommonfractionsormixed

numbers:

1. .3 6. 1.9

2. .25 7. 2.85

3. .04 8. 1.37

4. .60 9. .672

5. .66 10. .028

-

,

b b

-

91012

1478

56

89

2025

3712

100

125100

27100

5100

120

8751 000

78

12

23

13

Points to remember:

Changethepercenttoadecimalorcommonfraction. Multiplythegivennumberbythisdecimalorcommonfraction.

Find23%of64.

64 x .23 1 92 12 8 14.72

A. Directions:Findthefollowing:

1. 18%of46 6. 6%of24 2. 39%of6.75 7. 140%of295 3. .3%of160 8. 25%of75.24 4. 3%of200 9. 18%of4.7 5. 9%of50 10. 200%of75

B. Directions: Solve.

1. Ofthe20problemsgiven,Joancorrectlyanswered85%. Howmanyproblemsdidsheanswercorrectly? 2. Theenrolmentinacertainhighschoolis850.Iftheattendance forthemonthofMarchwas92%,howmanyabsenceswerethere duringthemonth?

Finding What Percent One Number is of Another

Points to remember:

Tofindwhatpercentonenumberisofanother: makeafraction,indicatingwhatfractionalpartonenumber isofanother changethefractiontoapercent,usingthepercentequivalentif itisknown;otherwisechangethefractionfirsttoa2-place decimalbydividingthenumeratorbythedenominator,the changethedecimaltoapercent.

27iswhatpercentof36? = = 75% .75 = 75% = 36) 27.00 25.2 1 80 1 80

Finding a Percent of a Numberb b

,

-

-

b b

,

2736

34

2736

14

A. Directions: Findthefollowing:

1. 4iswhatpercentof5? 2. Whatpercentof12is6? 3. 45is_____%of54? 4. Whatpercentof18is10? 5. 8is_____percentof4?

B. Directions: Solvethefollowingproblems.

1. Thereare18girlsand27boysinaclass.Whatpercentofthe classareboys? 2. Charlesanswered19questionscorrectlyandmissed6questions. Whatpercentofthequestionsdidheanswercorrectly? 3. Theschoolteamwon9gamesandlost6.Whatpercentofthe gamesdidtheteamlose?

Points to remember:

Tofindanumberwhenapercentofitisknown: changethepercenttoadecimalorcommonfraction dividethegivennumberrepresentingthegivenpercentof theunknownnumberbythisdecimalorcommonfraction followthealternatemethodshowninthesamplesolutions.

16%ofwhatnumberis48?

Method 1 16% = .16 300 . Divide48by.16 .16^)48.00^

Method 2

16%ofthenumber=48 1%ofthenumber=4816=3 100%ofthenumber=100x3=300 Therefore,thenumber=300

Check:16%of300=48 Answer:300

Directions: Findthemissingnumbers:

1. 12%ofwhatnumberis24? 2. 18is36%ofwhatnumber? 3. 25%ofwhatnumberis6? 4. 662/3%ofwhatnumberis14? 5. 6%ofwhatnumberis12? 6. 20is20%ofwhatnumber? 7. 100%ofwhatnumberis70?

-

-

,

Finding a Number When a Percent of it is Knownb b

-

A. Directions: Findthefollowing:

1. 4iswhatpercentof5? 2. Whatpercentof12is6? 3. 45is_____%of54? 4. Whatpercentof18is10? 5. 8is_____percentof4?

B. Directions: Solvethefollowingproblems.

1. Thereare18girlsand27boysinaclass.Whatpercentofthe classareboys? 2. Charlesanswered19questionscorrectlyandmissed6questions. Whatpercentofthequestionsdidheanswercorrectly? 3. Theschoolteamwon9gamesandlost6.Whatpercentofthe gamesdidtheteamlose?

Points to remember:

Tofindanumberwhenapercentofitisknown: changethepercenttoadecimalorcommonfraction dividethegivennumberrepresentingthegivenpercentof theunknownnumberbythisdecimalorcommonfraction followthealternatemethodshowninthesamplesolutions.

16%ofwhatnumberis48?

Method 1 16% = .16 300 . Divide48by.16 .16^)48.00^

Method 2

16%ofthenumber=48 1%ofthenumber=4816=3 100%ofthenumber=100x3=300 Therefore,thenumber=300

Check:16%of300=48 Answer:300

Directions: Findthemissingnumbers:

1. 12%ofwhatnumberis24? 2. 18is36%ofwhatnumber? 3. 25%ofwhatnumberis6? 4. 662/3%ofwhatnumberis14? 5. 6%ofwhatnumberis12? 6. 20is20%ofwhatnumber? 7. 100%ofwhatnumberis70?

15

Points to remember:

Thedistancearoundapolygoniscalledperimeter. Theperimeterofarectangleisequaltotwicethelengthadded totwicethewidth.

Formula:p=2L+2W

Findtheperimeterofarectangle26feetlongand17feetwide.

p=2l+2w p=2x26+2x17 p=52+34 p=86feet

Directions: Solve.

1. Whatistheperimeterofarectangleifitslengthis47cm and widthis21cm?

2. Howmanymetersoffencingarerequiredtoinclosearectangular garden 32 meters long and 13 meters wide?

3. Aliwishestomakeaframeforhisclasspicture.Thepicture measures50cmby24cm.Howmanycentimetersofmolding willheneed?

Points to remember:

Thedistancearoundacircleiscalledcircumference. Thepartsofthecirclearerelatedasfollows: a) Thediameteristwicetheradius.Formula:d=2r b) Theradiusisonehalfthediameter.Formula:r=d/2 c) Thecircumferenceofacircleisequaltopi( )timesthe diameter. Formula: c = dwhere=3oror3.14 Forgreateraccuracy,3.1416isused. Thecircumferenceofacircleisequalto2timespi( )timesthe radius. Formula: c = 2 r Thediameterofacircleisequaltothecircumference dividedbypi( ).Formula:d=c/

Findthecircumferenceofacirclewithadiameterof8meters.

26

17

d = 8 m = 3.14 c = ?

c = dc = 3.14 x 8c = 25.12 m

8 m

Perimeterb b,

-

Circumference of a Circleb b

,

12

17

227

16

Directions: Solve.

1. Howlongisthediameteriftheradiusis: a) 7m? b) 23cm? c) 6.5cm?

2. Howlongistheradiusifthediameteris:

a) 38m? b) 5cm? c) 8.9m?

3. Whatisthecircumferenceofacirclewhosediameteris60cm?

4. Findthecircumferenceofacirclehavingadiameterof:

a) 5cm b) 35m c) 260dm d) 49m e) 440cm

Points to remember:

Theareaofarectangleisequaltothelengthtimesthewidth. Formula: A = lw Theanswershouldbeexpressedinsquareunits(sqcm,sqdm,sqm)

Findtheareaofarectangle23cmlongand16cmwide.

Directions: Solve:

1. Whatistheareaofarectangleifitslengthis14mandwidthis9m?

2. Findtheareasofrectangleshavingthefollowingdimensions:

a) l=23m b) l=125cm w = 17 m w = 95 cm

23

16

A = lwA = 23 x 16A=368sqcm

-

,

-

b bMeasuring Area of a Rectangle

17

Points to remember:

Theareaofasquareisequaltothelengthofitssidetimesitselfor thesidesquared. Formula: A = s2

37 cm

s = 37 cmA= ?

A= s2

A=(37)2

A = 37 x 37A=1369sqcm

Directions: Solve. 1. Whatistheareaofasquarewhosesideis23meters?

2. Findtheareasofsquareswhosesidesmeasure:

a) 10m c) 42cm

b. .62dm d) 6080cm

Points to remember:

Theareaofaparallelogramisequaltothealtitudetimes thebase.

Formula: A = ab

Or,theareaisequaltothebasetimestheheight.

Findtheareaofaparallelogramwithanaltitudeof 25cmanda baseof32cm.

Directions: Solve.

1. Whatistheareaofaparallelogramifitsaltitudeis6mandits base is 8 m?

2. Findtheareaofalawnshapedlikeaparallelogramwithabaseof 18mandanaltitudeof15m.

a = 25 cmb = 32 cmA = ?

A = abA = 25 x 32A=800sqcm

,

-

Measuring Area of a Parallelogramb b

,

25 cm

32 cm

-

MeasuringAreaofaSquareb b

18

3. Findtheareasofparallelogramshavingthefollowingdimensions:

a) b) c)

Altitude -26m 75cm 8.3m Base -14m 98cm 4.7m

Points to remember:

Theareaofatriangleisequaltoone-halfthealtitudetimes thebase.

Formula: A = ab

Or,theareaisequaltoone-halfthebasetimestheheight.

Formula:A=bh

Findtheareaofatrianglewithanaltitudeof26dmandabaseof 17 dm.

Directions: Solve.

1. Whatistheareaofatriangleifitsaltitudeis10cmandthebaseis 8 cm?

2. Findtheareasoftriangleshavingthefollowingdimensions:

a) b) c)

Altitude 18 dm 13 cm 27 m Base 12 dm 10 cm 16 1/2 m

a = 26 dm

b = 17 dm

A = ?

A = ab

A = x 26 x 17

A=221sqdm

Measuring the Area of a Triangleb b

26dm

17 dm

,

-

1 2

1 2

1 21 2

19

, Points to remember: Theareaofatrapezoidisequaltotheheighttimestheaverage ofthetwoparallelsides(bases).

Formula:A=hxb1 + b2

34dm

29 dm

42 dm

Findtheareaofatrapezoidwithbasesof42dmand34dmandaheightof29dm.

h=29dmb1 = 42 dmb2 = 34 dmA =?

A = 29 x 38A=1102sqdm

Directions: Solve.

1. Whatistheareaofatrapezoidiftheheightis7mandtheparallel sides are 8 m and 14 m?

2. Findtheareasoftrapezoidshavingthefollowingdimensions:

a) b) c)

Height 8 m 5 cm 18 dm

Upper Base 4 m 9 cm 29 dm

Lower Base 10 m 13 cm 36 dm

A=hxb1 + b22

2

A = 29 x 42 + 34

-

Measuring the Area of a Trapezoidb b

2

20

, Points to remember: Theareaofacircleisequaltopi()timestheradiussquared.

Formula: A = r2

Anyoneofthefollowingvaluesofmaybeused:3 oror3.14or,forgreateraccuracy,3.1416.

Findtheareaofacirclehavingaradiusof5meters.

A = r2 A=3.14x(5)2 A = 3.14 x 25 A=78.5sqm

Or,theareaofacircleisequaltoonefourthtimespi( ) timesthediametersquared. Formula: A = Formula: A = .7854 d2 is also used.

Findtheareaofacirclehavingadiameterof14dm.

d = 14 dm A = d2

= A=xx(14)2

A=? A=154sqdm

Directions: Solve.

1. Whatistheareaofacirclewhoseradiusis6meters?

2. Findtheareasofcircleshavingthefollowingradii:

a)13cm b)28m c)1.375dm

3. Whatistheareaofacirclewhosediameteris24meters?

4. Whichislarger:theareaofacircle6cmindiameterortheareaof asquarewhosesideis6cm.Howmuchlarger?

r = 5 m = 3.14A =?

5 m

14 dm

Measuring the Area of a Circleb b

-

227

17

227

1414

227

14 d2

21

, Points to remember: Thevolume,alsocalledcubicalcontentsorcapacity,isthenumber ofunitsofcubicmeasurecontainedinagivenspace. Whencomputingthevolumeofageometricfigure, expressall linearunitsinthesamedenominationandincubicunits. Thevolumeofarectangularsolidisequaltothelengthtimesthe widthtimestheheight. Formula:V=lwh

Findthevolumeofarectangularsolid8mlong,5mwideand7m high.

V=lwh V = 8 x 5 x 7 V = 280 cu m

Directions: Solve.

1. Whatisthevolumeofarectangularsolidifitis7cmlong, 4cmwide,and9cmhigh?

2. Findthevolumesofrectangularsolidshavingthefollowing dimensions:

Length 8dm 12cm 17m

Width 3dm 9cm 18m

Height 6dm 10cm 14m

, Point to remember: Thevolumeofacubeisequaltothelengthoftheedgetimes itselfortheedgeorsidecubed.

Formula: V = e3 or V = s3

Findthevolumeofacubewhoseedgemeasures17cm. e = 17 cm V = e3 V=? V=(17)3 V = 17 x 17 x 17 V = 4 913 cu cm

85

7

l = 8 mw = 5 mh=7mV = ?

Measuring Volume of a Rectangular Solidb b

-

Measuring the Volume of a Cubeb b

a. c.b.

17

1717

22

Directions: Solve.

1. Whatisthevolumeofacubewhoseedgeis25dm?

2. Findthevolumesofcubeswhoseedgesmeasure:

a)9m b)14cm c)11m d)27dm e)1.09m

f)0.39m g)2m h)4dm i)5m

, Points to remember: Thevolumeofacylinderisequaltopi( )timesthesquareof theradiusofthebasetimestheheight.

Formula: V = r2 h

Whenthediameterisknown,gettheradiusbydividingthe diameterby2.Thenusetheformulaabove.

Findthevolumeofacylinder75mhighwithitsbasehavinga radiusof30m.

r = 30 m V = r2h h=75m V=3.14x(30)2 x 75 = 3.14 V = 3.14 x 900 x 75 V = ? V = 211 950 cu m

Findthevolumeofthecylinderwhoseheightis47cmwitha basehavingadiameterof32cm. Step A Step B d = 32 cm 32 2 V = r2h h=47cm 16(radius) V=3.14x(16)2 x 47 V = ? = 3.14 x 256 x 47 V = 803.84 x 47 = 37780.48 cu cm

Directions:Solve.

1. Whatisthevolumeofacylinderiftheradiusofitsbaseis 3dmandtheheightis6dm?

2. Whatisthevolumeofacylinderifthediameterofitsbase is10mandtheheightis16m? 3. Findthevolumesofcylindershavingthefollowingdimensions:

a)radius=5dm b)diameter=4cm height=8dm height=6cm

75

-

Measuring the Volume of a Circular Cylinderb b

12

34

-

30

47

32

23

Measure of Time

, Points to remember: Inchanging:

yearstomonths,multiplythenumberofyearsby12 monthstoyears,dividethenumberofmonthsby12 yearstoweeks,multiplythenumberofyearsby52 weekstoyears,dividethenumberofweeksby52 yearstodays,multiplythenumberofyearsby365 daystoyears,decidethenumberofdaysby365 weekstodays,multiplythenumberofweeksby7 daystoweeks,dividethenumberofdaysby24 daystohours,multiplythenumberofdaysby24 hourstodays,dividethenumberofhoursby24 hourstominutes,multiplythenumberofhoursby60 minutestohours,dividethenumberofminutesby60 minutestoseconds,multiplythenumberofminutesby60 secondstominutes,dividethenumberofsecondsby60.

A. Directions: Changetomonths:

1. 3years 4. 4years4months 2. year 5. 1year6months 3. 9years7months 6. 5years9months

B. Directions: Changetoweeks:

1. 2years 4. 3years16weeks 2. 3years 5. 5years23weeks 3. 4years 6. 1year41weeks

C. Directions: Changetohours:

1. 2days4hours 4. 14days16hours 2. 4days 5. 11days9hours 3. 30days 6. 8days

Graphs

, Points to remember: Agraphisadrawingwhichusuallydescribesnumericalrelationships. Abargraphisagraphinwhichvaluesofvariablesare representedby bars.Thebarsmaybedrawnverticallyorhorizontally.Thelengthof abarindicatesavalue. Tocreateabargraph: a)arrangethegivenvaluesandvariablesinalogicalorderpreferably inatableofvaluestoorganizeandsimplifyplotting.

b b

-

-

-

34

12

14

The Bar Graphb b

24

b) decidewhichvariable(s)tolocateonthex-axis(the horizontalaxis)andwhichtolocateonthey-axis(the verticalaxis) c) labelthex-axisandthey-axisandassignthevaluesto thespaceonthescalesconvenientlychosen.These assignedvaluesonthegraphshouldconvenientlyrepresent thevaluestobeplotted d) draweachbartothelengthorheightcorrespondingtoits value. Tointerpretabargraph,determinethevalueofeachspaceon theaxis.Ifthebarsarehorizontal,determinethespace valueon thehorizontalscale.Ifthebarsarevertical, determinetheplace valueontheverticalscale.Iftheendofthebarisnotona graphline,thevalueisapproximated.

Directions: Studythegraphbelow.

Answerthefollowingquestionsaboutthegraphshownabove.

1. Whatisthetitleofthebargraph?

2. Whatisrepresentedonthex-axis?

3. Onwhatdaydidthegreatestnumberofstudentsusethe library?

4. Onwhatdaydidtheleastnumberofstudentsusethelibrary?

5. Onwhattwodaysdidthesamenumberofstudentsusethe library?

6. HowmanystudentsusedthelibraryonMonday?onThursday?

Number of Students Using the Library (1st week of June,

Days of the week

nu

mb

er

of

stu

den

ts in

th

e

lib

rary

-

35

30

25

20

15

10

5

0

Mon. Tues. Wed. Thurs. Fri.

25

The Line Graph

, Points to remember: Agraphinwhichpointsrepresentingquantitiesare connectedbyline segmentsiscalledalinegraph.Linegraphsshowtherelationshipand changebetweenquantities. Tomakealinegraph,arrangethegivenvaluesinalogicalorder,from smallesttolargestorviceversa,orfrombeginningtoendofatime period. Agraphingpaperorcoordinatepaperwhoseintersectingverticaland horizontallinesareequaldistancesapartisusedtoplotlinegraphs. Spacesonthecoordinatepaperareassignedvaluesaccordingtothe valuesofthequantitiesinvolved. Alinewhichservesasabasisfromwhichtocounttherequirednumberof spacesiscalledanaxis.Thex-axisis thehorizontalaxis.They-axis istheverticalaxis.Thepointwherethetwoaxesmeetistheorigin (0,0)

Directions: Refertothegraphbelowandanswerthequestionsthat follow.

1. Whatwasthepulserateatthestart?

2. Howmuchdidthepulseraterisebytheendofthefirstminuteof exercise?

3. Estimatethehighestpulserateshownbythelinegraph. Afterhowmanyminutesdidthisrateoccur?

4. Whatwasthepulserateattheendof10minutes?

b b

-

Exercise Time in Minutes

Exercise Pulse Rate

130

120

110

100

9080

70

60

1 2 3 4 5 6 7 8 9 10

Pu

lse R

ate

per

Min

ute

26

The Circle Graph

, Points to remember: Acirclegraphisagraphinwhichthecirclerepresents100%ofatotal quantity.Sectorsarepartsofacircularregion.Valuesaredetermined bythesizesofthesectors.Circlegraphsarealsoknownaspiecharts. Acirclecontains3600 whichis100%ofthetotal.Usually,acirclegraph hasapercentageofatotalineachsector. Tofindthesectorvaluewhenthetotalisknown,multiply thetotalby thesectorpercentageindecimalform.

Example: ThecirclegraphbelowshowsMrs.Reyesmonthlybudget.

1. Howmuchmoneyisspentforhousing? 30%forhousing percentxtotal 30%xP7100 =.30xP7100 =P2130

2. Howmuchmoremoneyisspentforfoodthanforsavings? A.Forfood:25%xP7100=.25xP7100=P1775

B.Forsavings:10%xP7100=.10xP7100=P710

C.P1771-P710=P1065

Thus,P1065moreisspentforfoodthansavings.

3. Howmuchmoneyisspentforclothing?

8%forclothing: .08xP7100=P568

A. Directions: Eachsectorinthecirclegraphbelowshows10%.Copy andcompletethecirclegraphusingthedatainthetable. Usethedottedlinesasaguidetoshowtheapproximate sizeofeachsector.

MonthlyBudgetTotal:P7100

FAVORITE TV SHOWS OF 100 STUDENTS

PublicAffairs 10%

TalkShow 40%

Drama 10%

Comedy 20%

VarietyShow 20%

b b

-

others27%

housing30%

clothing8%

savings10%

food25%

27

1. Howmanystudentsfavoredpublicaffairsprogram?

2. Howmanymorestudentswatchedtalkshowsthanpublic affairs program?

3. Howmanystudentswatcheddrama?comedy?varietyshows?

4. Howmanymorestudentswatchedvarietyshowsthanpublicaffairs program?

5. Howmanymorestudentswatchedtalkshowsthancomedyshows?

Naming Angles

, Points to remember: Anangleisformedbytwononcollinearraysfromthesame endpoint. Thetworaysarecalledsidesoftheangleandthecommon endpointiscalledvertexoftheangle. Anangleisdenotedbythesymbol . Therearevariouswaysofnamingangles: a) usingthecapitalletteratthevertex,

b) usingasmallletteroranumeral,

c) usingthethreelettersassociatedwiththesidesandthevertex. (Note:Thevertexisalwaysthemiddle letter.)

Angle B

m1

Angle m and angle 1

b b

R

S

T

Angle RST or Angle TSR

28

Inthefiguresattheright,howmany angleshavepointOasvertex?Willyoube abletodistinguishwhichangleisbeing referredtoifeachisnamedsimplyasO? Why?

Thecorrectsetofthreeletters,therefore,mustbeusedto indicateanyparticularone,say,TOPfortheanglewhich opensupwardandPOSfortheonewhichopenstothe right.Wemayalsousesmalllettersornumbersto simplifyreferencetoindividualangles. Anangleseparatesthepointsintheplaneintothreesub sets,namely: a)pointsintheinterioroftheangle b)pointsontheangleitself c)pointsintheexterioroftheangle

Directions: Studytheillustrations,thenanswerthequestionsthat follow.

interior

exterior

1. Howmanydifferent anglesareformed bythethreerays frompointO? Nameeachangle.

2. Howmanydifferent anglesareformedbythe fourraysfrompointP? Nameeachangle.

-

Q

RS

TP

AB

CO

T

O S

12

P

29

Directions: Solvefortheanswerofthefollowing.

1. Whichisabetterbuy:Asinglediscountof25%onP2450ortwo successivediscountsof15%and10%? 2. Whatrateofdiscountisgivenifaladysbagwhichissoldata regularpriceofP750.00isnowsoldforP660.00? 3. BlousesareonsaleforP99.95.Theyaremarkedasbeing27%off. Whatwastheregularprice?

, Points to remember: Discountreferstothereductioninprices. Adiscount rateistheamounttobedeductedperP100ofthe originalprice. Theregularpriceofanitemiscalledits list price or marked price. Thepriceofanitemafterdeductingthediscountisitsnet price or sale price.

Example: During a sale at the LSC department store, a dress was sold at a 20% discount. If the regular price of the dress was P 699.75, how much did the buyer pay for the dress?

Solution: Sale Price = Regular Price - Discount = P 699.75 - (20% of P 699.75) = P 699.75 - P 139.95 = P 559.80

Tofindthediscountwhenthemarkedpriceandtherateofdiscount aregiven,multiplythemarkedpricebytherateofdiscount. Discount = marked price x r%

Tofindthesaleprice,subtractthediscountfromthemarkedprice. Sale price = marked price - discount

Tofindtherateofdiscount,findwhatpercentofthemarkedprice thediscountis. r% of marked price = discount r% = discount marked price

Tofindthemarkedpricewhenthesalepriceandrateofdiscount aregiven,subtractthegivenratefrom100%thendividethesale pricebytheresult. marked price = sale price 100% - r%

-

b bDISCOUNT

30

, Points to remember: Acommission isacertainpercentofthetotalsalesearnedbyan agentorasalespersonwhobuysorsellsgoodsfor another.This amountisdeductedfromthetotalorgrosssalesandgoestothe agent. Theamountthatgoestotheownerofthegoodsafterthe commissionhasbeendeductediscalledthenet proceeds. Thepercentofsalesthatdeterminesthecommissioniscalledthe rate of commission. Example: An agent for an appliance store works for a commission of 9.75% of sales. If his total sales for the month amounts to P 37 485, how much commission will he receive?

Solution: r = 9.75% or .0975 Commission = 0.0975 x P 37 485 = P 3 654.79

b bCOMMISSION

Directions: Solve:

1. Ifaninsurancebrokerreceives18%ofthepremiumashis commission,howmuchmoneyisduehimwhenthepremiumonafire insurancepolicyisP183.50?

2. AusedcarsalesmanearnedP6265.00commission forsellingacarfor P89550.00.Whatwastherateofcommission?

-

31

, Points to remember: Interestistheamountchargedformoneydepositedinthebanks orforthemoneyborrowed(loan). Theprincipal istheamountofmoneyborrowed. Thetimeistheperiodallottedfortherepaymentoftheprincipal plusinterest. TheamounttobepaidbackperP100istherate of interest. Iftheinterestdoesnotbecomepartoftheprincipal,theinterest is called simple interest. Examples: 1. Find the interest at 14% on a P 5 000 loan for 3 years.

Solution: Principal = P 5 000 with interest rate of 14% Time = 3 years Interest = Principal x Rate x Time = P 5 000 x .14 x 3 = P 2 100

2. Find the principal if the interest for 6 years is P 7 132 at 12%.

Solution: Interest = P 7 132, rate = 12%, time = 6 years Principal = Interest Rate x Time = P 7 132 12% x 6

= P 7 132 .12 x 6

= P 5 135.04

3. Find the interest rate of a 2-year loan of P15000 with P1 800interest. Solution: Principal = P 15 000, interest = P 1 800, time = 2 years

Rate = Interest Principal x Time

= P 1 800 P 15 000 x 2

= .06

= 6%

b bSimple Interest

32

4. Find the time for P 2000 to gain P 450 at a 5% interest rate. Solution: Principal = P 2 000, Interest = P 450, rate = 5%

Time = Interest Principal x Rate

= P 450 P 2 000 x 5%

= P 450 P 2 000 x .05

= 4.5 or 4 1/2 years

Ourformulaforsimpleinterestthenis: I=Prt,thatis, Interest = principal x rate x time

Directions: Solvefortheanswers.

1. Mrs.GilleraborrowedP25000tostartasmallbusinessat14% simpleinterest.IfshepaidP10000everyfourmonths,howmany timesdidshepay?Howmuchdidshepayinthelastpayment?

2. Readtheadvertisements.WithaP5000depositforone year,how muchinterestwillyouearnoneachaccount?

PREMIER SAVINGS a. Invest P 5 000 for 1 year at 9% per annum

CARE SAVINGS b. Invest Here! All accounts earn 8% per annum.

-

33

Answer KeyElementary Mathematics

(Part I-Content and Practice Exercises)

Whole Numbers

A. 1. fourhundredseventy-sixthousand,ninehundredtwenty-three 2. onehundredforty-sevenbillion,onehundredninety-four million,sixhundredfifty-twothousand,eight hundredfive 3. fivebillion 4. twohundredforty-onemillion,eighthundredforty-nine thousand

B. 1. 6 843 2. 2 725 235 3. 6 450 000 000 4. 406 923 685

Addition of Fractions and Mixed Numbers

A. 1. 14 5. 25 2. 6. 3. 7 7. 1 4. 12 8. 8

B. 1. 4 2. 7 3. 16

Borrowing in Subtraction of Fractions

A. 1. 2 5. 3 2. 3 6. 4 3. 8 7. 13 4. 19 8. 5

B. 1. 3. 5 2. 8 4. 2

C. 1. 5 2. 10 3. 4

Comparing Fractions

A. 1. 5.

2. 6.

3. 7.

4. 8.

23

14

12

14

142534

78

1924

141316

13

4713

34

58

47

25

131271656

16

110

45

23

34

B. 1. 5.

2. 6.

3. 7.

4. 8.

C. 1. ,, 5. ,,

2. ,, 6. ,,

3. ,, 7. ,,

4. ,, 8. ,,

Multiplication of Fractions and Mixed Numbers 1. 2 6. 1 2. 1 7. 3

3. 8. 1

4. 1 9. 1

5. 2 10. 24

Division of Fractions and Mixed Numbers

1. 4 5. 2 2. 6. 3. 9 7. 2 4. 8. 8

Reading and Writing Decimals

A. 1. twotenths 2. sixhundredths

3. fifty-eighthundredths

4. oneandfivetenths

5. threeandseventy-threehundredths

6. seventy-sixthousandths

7. twohundredeighty-ninethousandths

8. fourteenandsevenhundredeightthousandths

9. thirty-sevententhousandths

10. seventeenthousand,ninehundredtwenty-fivehundred

thousandths

910

37

12

1598

161811038

142371215

12

15

13

23

58

35

34

712

916

34

58

35

12

14

16

12

25

310

34

1116

58

38

516

14

7912

532

56

132411121116

35

332

38

13

35

B. 1. 6.04 6. .0494 2. 5.62 7. .300 3. .069 8. 19.122 4. 73.18 9. .00042 5. 36.253 10. 407.25

Addition of Decimals

1. 11.282 5. 12.174 2. 10.246 6. 41.32 3. 1.08 7. 40.64 4. 221.376 8. 8.25

Multiplication of Decimals

1. .247632 4. 22.160758 2. 19.635 5. .00716 3. .12756 6. .00628

Division of Decimals

1. 19 4. 300 2. 60.83 5. 20 3. .092 6. 2.8

Changing Common Fractions to Decimals

1. .9 6. .83 2. .5 7. 1.25 3. .27 8. .375 4. .25 9. .89 5. .875 10. .8

Changing Decimals to Common Fractions

1. 6. 1

2. 7. 2

3. 8. 1

4. 9.

5. 10.

Finding a Percent of a Number

A. 1. 8.28 6. 1.44 2. 2.6325 7. 413 3. .48 8. 18.81 4. 6 9. .846 5. 4.5 10. 150

B. 1. 17 2. 68

23

3 5

125

1 4

3 10

38

1 7

910

6721

281 000

36

Finding What Percent One Number is of Another

A. 1. 80% 3. 83% 5. 57% 2. 50% 4. 56% B. 1. 60% 2. 76% 3. 40%

Finding a Number When a Percent of it is Known

1. 200 4. 21 2. 50 5. 200 3. 24 6. 100 7. 70Perimeter

1. 136 cm 2. 90 m 3. 149 cm

Circumference

1. a)14m b)46cm c)13cm 2. a)19m b)2.5cm c)4.45m 3. 188.4 cm 4. a)15.7cm c)816.4dm e)1381.6cm b)109.9m d)153.86m Measuring Area of a Rectangle

1. 126sqm 2. a)391sqm b)11875sqcm

MeasuringAreaofaSquare

1. 529sqm 2. a)100sqm b).3844sqdm c)1764sqcm d)36966400sqcm

Measuring Area of a Parallelogram

1. 48sqm 2. 270sqm 3. a)364sqm b)7350sqcm c)39.01sqm Measuring Area of a Triangle

1. 40sqcm 2. a)108sqdm b)65sqcm c)222.75sqm

Measuring the Area of a Trapezoid

1. 77sqm 2. a)56sqm b)55sqcm c)585sqdm

37

Measuring the Area of a Circle

1. 113.04sqm 2. a)530.66sqcm b)2461.76sqm c)5.9365625sqdm 3. 452.16sqm 4. square;7.74sqcm

Measuring the Volume of a Rectangular Solid

1. 252 cu cm 2. a)144cudm b)1080cucm c)4284cum

Measuring the Volume of a Cube

1. 15 625 cu dm 2. a)729cum b)2744cucm c)1331cum d)19683cudm e)1.295029cum f).059319cum g)15.625cum h)107.171875cudm i)125cum

Measuring the Volume of a Circular Cylinder

1. 169.56 cu dm 2. 1256 cu m 3. a)628cudm b)75.36cucm

Measure of Time

A. 1. 36months 4. 52months 2. 9months 5. 18months 3. 115months 6. 69months

B. 1. 104 weeks 4. 172 weeks 2. 182 weeks 5. 283 weeks 3. 208 weeks 6. 53 weeks

C. 1. 52hours 4. 352hours 2. 96hours 5. 273hours 3. 720hours 6. 198hours

38

Graphs

Bar Graph

1. NameofStudentsUsingtheLibrary 2. DaysoftheWeek 3. Thursday 4. Tuesday 5. WednesdayandFriday 6. 23; 30

Line Graph

1. 70 3. 129; 6 2. 18 4. 100

Circle Graph

1. 10 2. 30 3. 10; 20; 20 4. 10 5. 20

Naming Angles

1. 3; AOB; BOC; AOC

2. 7; QPR; RPS;SPT;QPS;QPT;RPT; QPT

Discount

1. thesame 2. 12% 3. P370.19

Commission

1. P33.03 2. 7%

Simple Interest

1. 3times;P8500 2. a)P450 b)P400

PublicAffairs10%

Talk Show40%

Vari-etyShow

Comedy20%

Drama10%

39

PART II

Practice Test Questions

d = 8 m = 3.14c = ?

8 m

c = dc = 3.14 x 8c = 25.12 m

40

Practice Test Questions

Directions: Eachiteminthistestconsistsofaquestionorincomplete statementwithfouroptionsnumbered1,2,3,and4. Choosethecorrectanswerandthenblackenthenumberof yourchosenanswerfortheitemonyourAnswerSheet.

1. Whatistheplacevalueof3in34192?

1. hundredthousands 2. millions 3. tenthousands 4. thousands

2. 815-387isclosestto

1. 800-300 2. 800-400 3. 900-300 4. 900-400

3. 253569roundedtothenearestthousandis

1. 253 000 2. 253 500 3. 253 600 4. 254 000

4. 507200isthesameas

1. (5x10000)+(7x100)+(2x10) 2. (5x10000)+(7x1000)+(2x100) 3. (5x100000)+(7x10000)+(2x100) 4. (5x100000)+(7x1000)+(2x100)

5. Whatnumbershouldbeinthebox?258-=135

1. 123 2. 193 3. 323 4. 393

6. Whichisthenextnumberinthepattern? 1,4,7,10

1. 11 2. 13 3. 14 4. 15

7. Thegreatestcommonfactorof24and60is

1. 15 2. 12 3. 6 4. 4

-

41

8. Theleastcommonmultipleof8and4is

1. 32 2. 16 3. 8 4. 4

9. Theprimefactorizationof84is

1. 2 x 6 x 7 2. 2 x 3 x 3 x 7 3. 2 x 2 x 2 x 7 4. 2 x 2 x 3 x 7

10. isequalto

1.

2.

3.

4.

11. Whichsymbolshouldbeinthecircle?5/92/3

1. < 2. > 3. = 4.

12. 2isequalto

1.

2.

3.

4.

13. Whichdecimaltellshowmuchisshaded?

1. .001 2. .01 3. .1 4. 1.1

1215915

1225

910

35

256

176146

1012

26

42

14. Whatistheplacevalueof4in2.045?

1. tenths 2. hundredths 3. thousandths 4. tens

15. Whatistheplacevalueof9in3.0019?

1. tenthousandths 2. thousandths 3. hundredths 4. tenths

16. .03isequalto

1.

2.

3.

4.

17. isequalto

1. .00048 2. .0048 3. .048 4. .48

18. Whichsymbolshouldbeinthecircle? .11.101

1. < 2. > 3. = 4.

19. Writethemissingnumberforthis:=

1. 10 2. 9 3. 8 4. 4

20. 75%isequalto

1.

2.

3.

4.

21. Writethemissingnumberforthis:9-n=3

1. 3 3. 12 2. 6 4. 27

3

310

14

13

3 4

2 3

45

32

x6

481 000

43

22. Howdoyouwrite209051685inwords?

1. twohundredninetymillion,fifty-onethousand,sixhundred eighty-five 2. twohundredninemillion,fifty-onethousand,sixhundred eighty-five 3. twohundredninemillion,fivehundredonethousand, sixhundredeighty-five 4. twohundredninemillion,fifty-onethousand,eight hundred fifty-six

23. Roundofftothenearesttenthousand:65838049

1. 65 840 000 2. 65 838 050 3. 65 800 000 4. 61 000 000

24. Findthesumof25,463,7589,38906,and5627

1. 52 610 2. 53 610 3. 52 160 4. 53 600

25. Take84582from204291.

1. 119 690 2. 129 691 3. 119 691 4. 119 961

26. Multiply1760by48.

1. 84 480 2. 8 480 3. 844 080 4. 84 840

27. Expressasadecimal:Twohundredthirty-seventhousandths.

1. 237 000 2. .0237 3. 2.037 4. .237

28. Add: .68 + 1.26 + 9.98

1. 1.192 3. 11.912 2. 11.92 4. 11 921 29. Reduce to lowest terms.

1. 3.

2. 4.

4 53 5

2 6

810

4860

44

30. Add: 3 + 1 +

1. 2

2. 4

3. 6

4. 6

31. Subtract:2-1

1.

2. 1

3. 2

4.

32. Divide:31

1. 2

2. 2

3.

4. 5

33. Whatkindofangleistheoneshownbelow?

1. acute 2. obtuse 3. right 4. straight

34. Whatgeometricfigureissimilartotheillustrationbelow? 1. cone 2. cylinder 3. prism 4. sphere

35. Whatgeometricfigureissimilartotheillustrationbelow? 1. cone 2. cylinder 3. prism 4. sphere

36. UsingtheformulaA=(bh),findtheareaofatrianglewitha baseof8cmandaheightof17cm.

1. 64 cm2 3. 68 cm2

2. 66 cm2 4. 680 cm2

78

712

712

712

516

512

12

1516

516

3716

516

56

1712

34

23

520

14

14

4520

12

45

37. Findtheareaofthetrapezoidgivenbelow.Usetheformula A=1/2xh(b1 + b2)orhx(b1 + b2).

1. 1.17sqm 2. 1.30sqm 3. 2.06sqm 4. 5.40sqm

38. Findtheareaofatrapezoidwithanaltitudeof3.36cm,withbases of7.25cmand9.64cm.

1. 26.38 cm2

2. 28.00 cm2 3. 28.38 cm2 4. 283.75 cm2

39. FindtheenergyconsumptionfromNovember1toDecember1ifthe electric meter readings are:

1. 245kwh 2. 254kwh 3. 524kwh 4. 452kwh

40. Findthecostoftheelectricityconsumedforthemonthiftherate isP4.59perkilowatthour.

1. P112.46 2. P1124.55 3. P1125.00 4. P2124.55

November1

December1

0

36

7

98

5

2

4

10

74

3

12

5

8

6

90

74

3

12

5

8

6

90

36

7

98

5

2

4

1

0

36

7

98

5

2

4

10

74

3

12

5

8

6

90

74

3

12

5

8

6

90

36

7

98

5

2

4

1

2

5.4 m

2.4 m

.3 m

46

41. TheSarmagofamilyearnsP620000.00ayear.Thepiechartbelowshows thefamilybudget.Howmuchisallottedforotherexpenses?

1. P93000 3. P903000 2. P930000 4. P9300 Situation I

The sixth grade class at Little Jesus Child Development Center put on a play to raise moneyfornewsportsequipment.

42. Junexmadehisowncostumefortheschoolplay.Heused1.5metersof yellowmaterialand2.25metersofblackmaterial.Howmanymetersof materialdidJunexuseinall?

1. .75 meters 2. 2.4 meters 3. 3.375 meters 4. 3.75 meters

43. ArchieandRheamade8piratecostumes.Theyused2.3metersof materialforeachcostume.Tofindouthowmanymetersofmaterial ArchieandRheausedalltogether,youshouldfindtheanswerto

1. 8 2.3 2. 8 x 2.3 3. 8 + 2.3 4. 2.3 8

44. The20studentsintheticketcommitteehadtofindouthowmanyseats t herewereintheschoolauditorium.Therewere25 rowsofseats,with40 seatsineachrow.Tofindouthowmanyseatstherewereinthe auditorium,youshouldfindtheanswerto

1. 40 x 25 2. 20x(40+25) 3. 20 x 40 x 25 4. 40 + 25

45. The20membersoftheticketcommitteehopedtosell350ticketsfor adultsatP1.20perticket,and550lowerpricedticketsforstudents.How manyticketsdidthecommitteeplantosellaltogether?

1. 900 2. 920 3. 1020 4. 1080

Food 25%

Clo

thin

g

12

%

Oth

er

Exp

en

ses

15

%

Family car

10 %

Shelter20 % Operating

Expenses 8 %

savin

gs

10%

47

46. TicketsforstudentscostP1.20each.Adultticketscost3timesmore. Howmuchdidanadultticketcost?

1. P3.60 2. P1.60 3. P.80 4. P.40

Situation 2

The six students who sold the most tickets to the play were Clara, Susie, Mila, Tata, Ernie and Ali. The graph below shows how many tickets they sold.

47. Whichisthebestestimateofthegreatestnumberofticketssoldbyany ofthesixstudents?

1. 78 2. 74 3. 72 4. 68

48. Whichnumberisthebestestimateofthedifferencebetweenthenumber ofticketsClarasoldandthenumberofticketsMilasold?

1. 9 2. 12 3. 14 4. 17

Situation 3

A Halloween party for 80 people was planned at the Maligaya Recreation Center. Three committees planned the party. No one was on more than one committee. There were 12 people on the decoration committee, 15 on the food committee, and 10 on the games and entertainment committee.

49. Howmanypeoplewerethereinallonthecommitteesplanningtheparty?

1. 25 2. 37 3. 80 4. 117

Nu

mb

er

of

tick

ets

TICKETS SOLD

Clara Su- Mila Tata Er- Ali

70

50

40

30

20

10

60

48

50. Howmanypeoplewereexpectedtocometothepartyotherthanthoseon thefoodcommittee?

1. 95 2. 65 3. 63 4. 60

51. Themembersofthefoodcommitteeboughtenoughapplejuice foreachof the80peopletohave3glasses.Thereare4glassesinaliter.Tofind outhowmanylitersofjuicethecommitteebought,youshouldfindthe answer to

1. (4x80)3 2. (803)x4 3. (3x80)4 4. (3x80)x4

52. ThegamesandentertainmentcommitteeplannedtoplayCDtapesatthe party.Isabelle,Nicole,andSameachpromisedtobring8tapes,and4 othercommitteememberspromisedtobring6tapeseach.Howmany tapesinalldidthesepeoplepromisetobring?

1. 48 2. 38 3. 32 4. 18

53. Thedecorationcommitteehad4rollsofnarrowcrepepapertouseto decoratefortheparty.Eachrollcontained20.5metersofcrepepaper. Howmanymetersofcrepepaperdidthecommitteehaveinall?

1. 5.1 2. 24.5 3. 80.5 4. 82

54. AaronandByronboughtonesquashthatweighed3.3kilogramsand anotherthatweighed1.8kilograms.Howmuchdidthetwosquashweigh together?

1. 1.5 kilograms 2. 3.56 kilograms 3. 5.1 kilograms 4. 5.94 kilograms

55. ThedecorationcommitteehadP250.00tospend.Theyspentonly85%of themoney.Howmuchmoneydidthedecorationcommitteehaveleft?

1. P37.50 2. P39.50 3. P212.50 4. P165.00

49

56. Thegamesandentertainmentcommitteeplannedtogiveprizestosome luckypersonsattheparty.Eachpersonwouldwritehisorhernameon theticketandputitinthebox.Later,thenameofthewinnerwouldbe drawnfromthebox.IfRoseisoneof80peoplewhoplacedtheirnames inthebox,whatistheprobabilitythatRosesnamewillbedrawn?

1.

2.

3.

4.

Situation 4

The social studies classes at Langtad Elementary School went on a trip to the museum.

57. Inall,125studentsand35adultswenttothemuseum.Theywenton buses.Eachbuscouldtake40people.Howmanybusesdidtheyuse?

1. 3 2. 4 3. 5 4. 6

58. TheroutefromLangtadtothemuseummeasured11cmonHarveysroad map.Thescaleofthemapwas:1cm=5km.Howfarwasitfrom Langtadtothemuseum?

1. 40 km 2. 26 km 3. 55 km 4. 105km

59. Fiveguidesmetthematthemuseum,and1/5ofthe125studentswent witheachguide.Howmanystudentswentwitheachguide?

1. 5 2. 25 3. 50 4. 625

60. Risasgroupsawalargemapofacountry.Thecountryisrectangularin shape.Itslengthandwidthareshowninthe figurebelow.

Tofindtheareaofthecountryinsquarekilometers,youshould findtheanswerto

1. 387 + 276 3. 2 x 387 x 276 2. 2x(387+276) 4. 387 x 276

387 kilometers

276 kilometers

8081

7980180

181

50

61. InthecapitalcityofacertainAmericanstate,thenormalJanuaryhigh temperatureis43.50 F.ThenormalJanuarylowis16.20F.Whatisthe differencebetweenthenormallowtemperatureandthenormal high temperature?

1. 27.30 F 2. 29.70 F 3. 37.30 F 4. 59.70 F

62. Thereareabout30000farmsinacertaincountry.Theaveragesizeofthe farmis1300sqmeters.Toestimatethenumberofsquaremetersof farmlandsinthecountry,youshould

1. add 30 000 and 1 300 2. subtract1300from30000 3. multiply30000by1300 4. divide30000by1300

63. Maymay,Brian,BambiandFrancisatelunchtogetherattheschool canteen.Eachofthemorderedthesamething.Thetotalcostforthe4 luncheswasP159.80.Whatwasthecostofonelunch?

1. P18.75 2. P26.50 3. P30.00 4. P39.95

64. Joy,Gay,RyanandJollywenttotheHandyHobbyStoretobuy crafts supplies.Joyneededsandpaper.Thepriceofsandpaper was3sheetsforP25.Shebought12sheets.Howmuchdid12sheetsofsandpapercost?

1. P75 2. P100 3. P150 4. P200

65. AlargepadofdrawingpapercostP2.75.Ryanwantedtobuy one,but whenhecountedhismoney,hehadonlyP2.45.Tofind outhowmuch moremoneyRyanneededtobuythedrawing paper,youshould

1. add 2. divide 3. multiply 4. subtract

66. Thepriceofdrawingpencilswas2forP1.75.Cynthiabought6drawing pencils.Howmuchdidthe6drawingpencilscost?

1. P5.25 2. P5.75 3. P5.95 4. P5.99

51

67. Jollymadeasmallrectangulartable.Shewantedtocoverthetopof the tablewithtiles.Thefigurebelowshowsthesizeofthetable.

Thestorehadsquaretileswithsides1centimeterlong.Howmanyof thesetileswouldJollyneedtocoverthetopofhertable?

1. 240 2. 1 000 3. 1 200 4. 2 400

68. Gaywantedtobuyasetoftoolsforcarvingwood,butshedidnthave enoughmoney.ThesetcostsP240.30.ThesalespersontoldGaythat thesetwouldsoonbeonsalefor20%lessthantheregularprice. Whenthesetoftoolsisonsale,itscostwillbe

1. P150.85 2. P192.24 3. P205.40 4. P292.24

69. Carlosplannedtostainanoldtable.Thestorehadtwodifferentbrands ofwoodstain.

Whichbrandcostlesspergram?Howmuchless?

1. BrandXcost1centavolesspergram. 2. BrandXcost10centavoslesspergram. 3. BrandYcost1centavolesspergram. 4. BrandYcost11centavoslesspergram.

70. JoyspentP43.76,GayspentP29.35,andJollyspentP63.37inall theirpurchases.Whatwastheaverageamountofmoneyspentby thesepeople?

1. P45.49 2. P136.48 3. P148.63 4. P157.19

40 centimeters

60 centimeters

Brand XStain

P 16.45(170.1grams)

Brand YStain

P 25.95(226.8grams)

52

71. Onamap,1.5cmrepresents210km.Whatactualdistancecorresponds toamapdistanceof30cm?

1. 420 km 2. 430 km 3. 4 200 km 4. 4 300 km

72. Arecipecallsfor2spoonfulsofbutterforeacheggused.One eggisused forevery3servingstobemade.Howmuchbutterisneededfor6 servings?

1. 1spoonful 2. 2spoonfuls 3. 3spoonfuls 4. 4spoonfuls

73. Atreecastsashadowof12meterswhena5-meterpolecastsashadow of4meters.Howtallisthetree?

1. 14 m 2. 15 m 3. 16 m 4. 17 m

74. Puregoldis24karats.Ifapieceofjewelryismarked18-karatgold, whatpercentpureisit?

1. 25% 2. 50% 3. 70% 4. 75%

75. Whatrateofdiscountisgivenifapairofladysshoeswhichissoldata regularpriceofP499.95isnowsoldforP299.95?

1. 40% 2. 45% 3. 47% 4. 50%

76. TextbooksareonsaleforP125.Theyaremarkedasbeing20% off.Whatistheregularprice?

1. P145.56 2. P152.75 3. P156.25 4. P160.50

77. Aninsuranceagentworksforacommissionrateof8.25%ofsales.Ifhis totalsalesforthismonthamountstoP21685,howmuchcommissionwill hereceive?

1. P1789 2. P2897 3. P3400 4. P4368

53

78. ThetotalenrolmentofSt.IgnatiusParochialSchoolforthemonthofJune is2565.Duetofinancialproblems,changeofresidence,andother reasons,somestudentsdroppedout.Thetotalenrolmentforthemonth ofJanuaryis2273.Whatpercentofthetotalenrolmentdroppedout?

1. 9% 2. 10% 3. 11% 4. 12%

79. ThestocksofanoilcompanysoldforP27ashareayearago. Today,its priceisP12.50ashare.Whatisthepercentofdecrease?

1. 54% 2. 64% 3. 74% 4. 85%

80. AmathematicsmagazinewhichusuallycostP15isnowsoldatP18. Whatpercentwastheincrease?

1. 5% 2. 15% 3. 20% 4. 25%

81. Senenearnsacommissionof12%onwhathesells.Lastmonth,hissales totaledP15400.Howmuchdidheearn?

1. P1488 2. P8488 3. P4188 4. P1848

82.Findthesimpleinterestat13%onaP2000loanfor2years.

1. P420 2. P520 3. P535 4. P550

83. JunputP4325inasavingsaccount5yearsago,at8%interestrateper annum.Howmuchsimpleinterestdidhismoneyearn?

1. P1730 2. P1945 3. P2340 4. P1635

84. DeannaborrowedP7500attherateof15%perannumfor4years.What isthetotalamountthatshemustpay?

1. P12000 2. P12500

54

85. Ifittakes6minutestocutaloginto3pieces,howlongwillittaketo cutalogofthesamekindintofourpieces?

1. 8 2. 18 3. 28 4. 81

86. 60iswhatpercentof240?

1. 15% 2. 20% 3. 25% 4. 30%

87. Whatisthecircumferenceofapipe90cmindiameter?

1. 282.3 cm 2. 282.6 cm 3. 28.26 cm 4. 2.82 cm

88. Carton A is 30 cm x 41 cm x 61 cm. Carton B is 36 cm x 36 cm x 61 cm. CartonCis32cmx40cmx61cm,whileCartonDis30cmx40cmx61 cm.Whichcartonhasthelargestcapacity?

1. A 2. B 3. C 4. D

89.Findtheareaofthiscircle:

1. 706.5 cm2 2. 706.5 cm2

3. 70.65 cm2

4. 70.65 cm2

90. OnacoldnightinBaguio,thetemperaturedroppedfrom200 Cby80 C. Whatwasthetemperaturethatnight?

1. 280 C 2. 180 C 3. 120 C 4. 2080 C

91. Anuclearpoweredsubmarineisabout300mdeepdowntheMarianas Trench,whichisabout11034mdeep.Howfaristhesubmarinefrom t hedeepestpartofthetrench?

1. 300 m 2. 8 734 m 3. 9 237 m 4. 10 734 m

15 cm

55

92. EddiedepositedP1500inabank.HewithdrewP200onthefirstmonth, depositedP300onthesecondmonthandmakeaP700withdrawalonthe thirdmonth.Howmuchmoneydidhehaveinthebankafterthethird month?

1. P300 2. P500 3. P700 4. P900

93. Ifoneworkercanfinishapieceofworkin10days,howmanyworkers, eachworkingatthesamerateasthefirst,willbeneededtofinishtheworkin50days?

1. 5 2. 7 3. 9 4. 12

94. Inamathematicsclassof60students,36aregirls.Whatistheratioof boystogirls?

1. 36:24 2. 24:60 3. 36:60 4. 24:36

95. AcomputertechnicianchargedP450forlaborthattook3hours.What washishourlyrateforlabor?

1. P24 2. P150 3. P212 4. P300

96. PatandMilausedthefollowingconcretemixformulafortheirhouse:4 partssand,4partsgravel,3partscementand1partwater.Whatisthe ratioofwatertocement?

1. 1:1 2. 1:2 3. 1.3 4. 3:1

97. Amelonweighs.69kilograms.Howmanygramsisthis?

1. 690 g 2. 609 g 3. 69 g 4. 6 900 g

98. Vitalefthomeat10:45a.m.andarrivedatafriendshouseat 1:15p.m. Howlongdidthetriptake?

1. 2hours 2. 2hoursand30minutes 3. 2hoursand45minutes 4. 3hours

56

99. Mr.Villegasfilledhiscarwith60Lofgasoline.HealsospentP30fora canofoilandP60forcarwax.HespentatotalofP660.Whatwasthe costofgasolineperliter?

1. P8.50 2. P9.50 3. P10.50 4. P10.45

100. Vic,Leo,Johnny,andBongarelinedupinthesepositions,midway throughatrackmeet:

Vicis20mbehindLeo. Leois50maheadofJohnny. Johnnyis10mbehindBong. Jessis30maheadofVic. Bongis50mbehindJess.

Atthispointintherace,whoiswinning?

1. Bong 2. Jess 3. Johnny 4. Leo

57

Answer KeyElementary Mathematics

(Practice Test Questions)

1. 3 26. 1 51. 3 76. 32. 2 27. 4 52. 1 77. 13. 4 28. 2 53. 4 78. 34. 4 29. 1 54. 3 79. 15. 1 30. 4 55. 1 80. 36. 2 31. 1 56. 4 81. 47. 4 32. 2 57. 4 82. 28. 1 33. 2 58. 3 83. 19. 4 34. 1 59. 2 84. 110. 3 35. 2 60. 4 85. 111. 1 36. 3 61. 1 86. 312. 3 37. 1 62. 3 87. 213. 3 38. 3 63. 4 88. 214. 2 39. 1 64. 2 89. 115. 1 40 2 65. 4 90. 316. 4 41. 1 66. 1 91. 417. 3 42. 4 67. 4 92. 418. 2 43. 2 68. 2 93. 119. 2 44. 1 69. 1 94. 420. 3 45. 1 70. 2 95. 221. 2 46. 1 71. 3 96. 322. 1 47. 1 72. 4 97. 123. 1 48. 4 73. 2 98. 224. 1 49. 2 74. 4 99. 225. 3 50. 4 75. 1 100. 2

References

DeSagun,PriscillaC.,1997. Dynamic Math I.DiwaScholasticPress.

Naslund,RobertA.,et.al.1978.SRA Achievement Series. ScienceResearch Associates,Inc. Stein,EdwinI.,1957. Refresher Arithmetic with Practical Applications.Allyn andBacon,Inc.,(Publishedinthe Philippinesby PhoenixPress,Inc.)

CONTENTS

Part I. Content and Practice Exercises 1

WholeNumbers 2 ReadingandWritingLargeNumbers 2 Common Fractions 3 AdditionofFractionsandMixedNumbers 3 BorrowinginSubtractionofFractions 4 ComparingFractions 5 MultiplicationofFractionsandMixedNumbers 6 DivisionofFractionsandMixedNumbers 7 DecimalFractions 7 ReadingandWritingDecimals 7 AdditionofDecimals 9 MultiplicationofDecimals 10 DivisionofDecimals 10 ChangingCommonFractionstoDecimals 11 ChangingDecimalstoCommonFractions 12 FindingaPercentofaNumber 13 FindingWhatPercentOneNumberisofAnother 13 FindingaNumberWhenaPercentofitisKnown 14 Perimeter 15 CircumferenceofaCircle 15 MeasuringAreaofaRectangle 16 MeasuringAreaofaSquare 17 MeasuringAreaofaParallelogram 17 MeasuringAreaofaTriangle 18 MeasuringAreaofaTrapezoid 19 MeasuringAreaofaCircle 20 MeasuringVolumeofaRectangularSolid 21 MeasuringVolumeofaCube 21 MeasuringtheVolumeofaCircularCylinder 22 MeasureofTime 23 TheBarGraph 23 TheLineGraph 25 TheCircleGraph 26 Naming Angles 27 Discount 29 Commission 30 SimpleInterest 31 AnswerKey(PartI-ContentandPracticeExercises) 33

Part II. Practice Test Questions 39

AnswerKey 57 References 58

60

Points to remember:

Changethepercenttoadecimalorcommonfraction. Multiplythegivennumberbythisdecimalorcommonfraction.

Find23%of64.

64 x .23 1 92 12 8 14.72

A. Directions:Findthefollowing:

1. 18%of46 6. 6%of24 2. 39%of6.75 7. 140%of295 3. .3%of160 8. 25%of75.24 4. 3%of200 9. 18%of4.7 5. 9%of50 10. 200%of75

B. Directions: Solve.

1. Ofthe20problemsgiven,Joancorrectlyanswered85%. Howmanyproblemsdidsheanswercorrectly? 2. Theenrolmentinacertainhighschoolis850.Iftheattendance forthemonthofMarchwas92%,howmanyabsenceswerethere duringthemonth?

Finding What Percent One Number is of Another

Points to remember:

Tofindwhatpercentonenumberisofanother: makeafraction,indicatingwhatfractionalpartonenumber isofanother changethefractiontoapercent,usingthepercentequivalentif itisknown;otherwisechangethefractionfirsttoa2-place decimalbydividingthenumeratorbythedenominator,the changethedecimaltoapercent.

27iswhatpercentof36? = = 75% .75 = 75% = 36) 27.00 25.2 1 80 1 80

Finding a Percent of a Numberb b

,

-

-

b b

,

2736

34

2736

61