Math NEAT.2010pdf
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Transcript of Math NEAT.2010pdf
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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
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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%
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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
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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
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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
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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
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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)
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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
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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
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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
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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
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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
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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
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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.)
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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
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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
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61