Download 1. Add three-hundred and fifty

Mathematics
Grade7
MentalMath:Wholenumbers,Factors&Multiples,Exponents
Calculatetheanswerstothefollowing,withoutusingacalculator:
(30)
1. Addthree-hundredandfifty-fivethousandtosixthousandsixhundredandtwentyfive.
________________________________________________________________________
2. Howmanyhundredsin3789000?
________________________________________________________________________
3. Listthefactorsof78.
________________________________________________________________________
4. Thenumber7820000,isthenumber7820297roundedtothenearest_____.
________________________________________________________________________
5. Simplify:
70 − 5×3 ÷ 5 + 3* = ___
________________________________________________________________________
6. Roundthenumber3004906tothenearestfive.
________________________________________________________________________
7. Calculatethedifferenceinvaluebetweenthe7inthesetwonumbers:
148073and870661
________________________________________________________________________
8. The6thmultipleof25is____.
________________________________________________________________________
9. Theproductof30and2500is____.
________________________________________________________________________
10. Simplify:
126 ÷ 6×3 + 100 ÷ 4 = ___
________________________________________________________________________
11. Calculatetheproductofthedigitinthetenthousandsplaceandthedigitinthetens
placeinthefollowingnumber:3090178
________________________________________________________________________
12. Calculatetheproductofalltheevendigitsinthefollowingnumber:164309
________________________________________________________________________
13. Findthenextnumberintherow: 25,100,400,_____
________________________________________________________________________
14. Arrangethesenumbersindescendingorder:
348942;384429;394824;349284;348492;384942
________________________________________________________________________
15. Howmanytensarethereinthequotientof36000and120?
________________________________________________________________________
1
Mathematics
Grade7
MentalMath:Wholenumbers,Factors&Multiples,Exponents
16. FindtheHCFof54and78.
________________________________________________________________________
________________________________________________________________________
17. Roundthenumber379798tothenearestthousand.
________________________________________________________________________
18. Listalltheprimenumbersbetween90and130.
________________________________________________________________________
2
19. Simplify:
150 + 500×100 ÷ 101 − 5× 216 = ___
________________________________________________________________________
20. FindtheLCMof24and9
________________________________________________________________________
________________________________________________________________________
21. Arrangethefollowingdigitstomakethebiggestoddnumberwitha9intheTens
place:6098257
________________________________________________________________________
22. Calculatetheanswer:1525+35650+200525
________________________________________________________________________
________________________________________________________________________
23. Calculatetheanswer:90725–25005–15750
________________________________________________________________________
________________________________________________________________________
24. Whatisthequotientofthefourthandsecondcubenumbers?
________________________________________________________________________
________________________________________________________________________
25. Show30asaproductofitsprimefactors.
________________________________________________________________________
26. Simplify:
8100 ÷ 30 + 60×4 = ___
________________________________________________________________________
27. FindtheLCMof15,100and2
________________________________________________________________________
________________________________________________________________________
28. Findtheproductofthefirstfivesquarenumbers.
________________________________________________________________________
________________________________________________________________________
29. Whataretheprimefactorsof140?
________________________________________________________________________
________________________________________________________________________
30. Findthenextnumberinthesequence:234870;235020;235320;235920;
________________________________________________________________________
2
Mathematics
Grade7
Calculations:Wholenumbers,Factors&Multiples,Exponents
Answerthefollowingquestions,usingacalculatorwherenecessary:
Question1: Giveadefinitionforeachofthefollowing: Term
Definition
(8)
1. Naturalnumbers(N) 2. Wholenumbers(N0) 3. Compositenumbers
4. Primenumbers
5. Multiples
6. Factors
7. LCM
8. HCF
9. Cuberoot
10. Cubenumber
11. Squarenumber
12. Squareroot
Question2: FindtheHCFofthefollowingnumbers:
(6)
1. 24,54and48
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
2. 110,66and88
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
3. 78,54and90
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
3
Mathematics
Grade7
Calculations:Wholenumbers,Factors&Multiples,Exponents
Question3: FindtheLCMofthefollowingnumbers:
(6)
1. 6,9and5
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
2. 15,20and2
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
3. 16,60and3
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
____________________________________________________________________
Question4: Forwhichthreenumbers(lessthan100)caneachofthesegroupsbefactors:
1. 2,13,26
_____________________________________________________________________
_____________________________________________________________________
__________________________________________________________________
2. 3,27,9
_____________________________________________________________________
_____________________________________________________________________
__________________________________________________________________
Question5: Writeeachofthefollowingnumbersasaproductofitsprimefactors(usea
factortree): (8)
1. 108 2.
210
3. 350 4.
360
4
Mathematics
Grade7
Calculations:Wholenumbers,Factors&Multiples,Exponents
Question6: Findtheanswerstothefollowing:(DONOTuseyourcalculator) (12)
1.
387098+2709898+78009
2.
4006712–376865–8009
3.
3607x283 4.
2809x405
5.
92246÷14 6.
225128÷15
Question7: Entera<,>or=tomaketheseequationstrue:
(6)
2
2
45 + 3×30 ÷ 216
45 + 3×(30 ÷ 216)
1
108 − (4 + 24) ÷ 2
108 − (41 + 24 ÷ 2)
(5×2)6 + 5×45×178 178 ×(5×2)6 + 5×45
2
2
18 + 91 ÷ 3×10: 10: ×18 + 91 ÷ 3
𝑥 * ×𝑥 < + 𝑥 1 𝑥= + 𝑥1
1
1
2
2
2×( 500) + 5×200
200×( 500) + 5
5
Mathematics
ProblemSolving:Wholenumbers,Factors&Multiples,Exponents
1. Highlightalltheequivalentnumbersinthesamecolour: 4* 2
27 + 8
31 2
21 3:
3*
37 256
2* + 2* 27×8
1
3
1
27
6
9
2
26 ( 16)* 27× 8
2
2
3*
31
15
6
1 each
2
Grade7
(7)
243
9
2* ×2* 9
27
2. Writefollowingcelestialdistancesasproductofanumberandan
exponentof10.
(3)
Distancetothemoon
384400km
DistancetotheSun
150millionkm
DistancetoMars
225millionkm
3. Howmanypeoplecanfillastadiumwith107rowsand5376seatsineachrow? (3)
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
4. Atachildren’sparty,thereareanumberofbicyclesandtricycles.Therearedouble
theamountofbicyclesthantricycles.IfIcount84wheelsintotal,howmanybicycles
andhowmanytricyclesarethere?(Useyourknowledgeofmultiplesandfactorsto
solvethisproblem.) (3)
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
5. Twelverugbyfieldsareexactlyadjacenttoeachother,withtwometres(inbreadth)
betweeneachfield.Thelengthoftherugbyfieldisexactlytwicethebreadthofthe
field.Ifthelengthofonerugbyfieldis110m,whatisthetotalperimeterof12rugby
fields. (4)
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
6
Mathematics
Grade7
MEMO:Wholenumber,FactorsandMultiples
Calculatetheanswerstothefollowing,withoutusingacalculator:
1. Addthree-hundredandfifty-fivethousandtosixthousandsixhundredandtwentyfive.
355000 + 6625 = 361625
2. Howmanyhundredsin3789000?
37890ℎ𝑢𝑛𝑑𝑟𝑒𝑑𝑠
3. Listthefactorsof78.
78:{1,78,2,39,3,26,6,13}
4. Thenumber7820000,isthenumber7820297roundedtothenearest_____.
Thousand
5. Simplify:
70 − 5×3 ÷ 5 + 3* = ___
70 − 5×3 ÷ 5 + 3* = 70 − 3 + 9 = 76
6. Roundthenumber3004906tothenearestfive.
3004905
7. Calculatethedifferenceinvaluebetweenthe7inthesetwonumbers:
148073and870661
70000 − 70 = 69930
8. The6thmultipleof25is____.
25×6 = 150
9. Theproductof30and2500is____.
30×2500 = 75000
10. Simplify:
126 ÷ 6×3 + 100 ÷ 4 = ___
(126 ÷ 6×3) + (100 ÷ 4) = 88
11. Calculatetheproductofthedigitinthetenthousandsplaceandthedigitinthetens
placeinthefollowingnumber:3090178
90000×70 = 6300000
12. Calculatetheproductofalltheevendigitsinthefollowingnumber:164309
6×4×0 = 0
13. Findthenextnumberintherow: 25,100,400,_____
400×4 = 1600
14. Arrangethesenumbersindescendingorder:
348942;384429;394824;349284;348492;384942
394824;384942;384429;349284;348942;348492
15. Howmanytensarethereinthequotientof36000and120?
3600 ÷ 12 = 300(Rememberthatazerocanberemovedfromboththenumbers
beforedividing)Thereare30tensin300.
7
Mathematics
Grade7
16. FindtheHCFof54and78.
54:{1,54,2,27,3,18,6,9}
78:{1,78,2,39,3,26,6,13} HCF(HighestCommonFactor)=6
17. Roundthenumber379798tothenearestthousand.
380000
18. Listalltheprimenumbersbetween90and130.
97,101,103,107,113,127
19. Simplify:
2
150 + 500×100 ÷ 101 − 5× 216 = ___
2
150 + 500×100 ÷ 101 − 5× 216 = 150 + 50000 ÷ 1000 − 5×6 = 170
20. FindtheLCMof24and9
9,18,27,36,45,54,63,72,81,90,99
24,48,72
LCM(LowestCommonMultiple)=72
21. Arrangethefollowingdigitstomakethebiggestoddnumberwitha9intheTens
place:6098257
8762095
22. Calculatetheanswer:1525+35650+200525
1525 + 35650 + 200525 = 237700
23. Calculatetheanswer:90725–25005–15750
90725 − 25005 + 15750 = 90725 − 40755 = 49970
24. Whatisthequotientofthefourthandsecondcubenumbers?
Firstfivecubenumbers:1,8,27,64,125 64 ÷ 8 = 8
25. Show30asaproductofitsprimefactors.
30=2x3x5
26. Simplify:
8100 ÷ 30 + 60×4 = ___
8100 ÷ 30 + 60×4 = 270 + 240 = 510
27. FindtheLCMof15,100and2.
LCM=300
28. Findtheproductofthefirstfivesquarenumbers.
1×4×9×16×25 = 14400
29. Whataretheprimefactorsof140?
40:{2,5,7}
30. Findthenextnumberinthesequence:234870;235020;235320;235920;
237120(+150,+300,+600,+1200)
8
Mathematics
Grade7
MEMO:Calculations–Wholenumbers,multiples&factors
Answerthefollowingquestions,usingacalculatorwherenecessary:
Question1: Giveadefinitionforeachofthefollowing: (8)
Term
Definition
1. Naturalnumbers(N)
Wholenumbersgreaterthanorequalto1
Countingnumbersthatarepositive,
2. Wholenumbers(N0)
including0
3. Compositenumbers
Numberswithtwoormorefactors
Numberswithonlytwofactors,1anditself
4. Primenumbers
(thenumber1isnotaprimenumber)
5. Multiples
Theproductoftwonaturalnumbers
Anumberthatdividesexactlyintoanother
6. Factors
numberwithoutaremainder
LowestCommonMultiple–thelowest
7. LCM
multiplecommontotwoormorenumbers
HighestCommonFraction–thehighest
8. HCF
factorcommontotwoormorenumbers
Anumberthatismultipliedbyitselftwice
9. Cuberoot
2
togiveacubenumbere.g. 8 = 2
Theproductofanumbermultipliedby
10. Cubenumber
itselftwice,e.g.21 = 2×2×2 = 8
Theproductofanumbermultipliedby
11. Squarenumber
itselfonce,e.g.2* = 2×2 = 4
Anumberismultipliedbyitselftogivea
12. Squareroot
squarenumber,e.g. 4 = 2
Question2: FindtheHCFofthefollowingnumbers:
(6)
4. 24,54and48
24:{1,24,2,12,3,8,4,6}
54:{1,54,2,27,3,18,6,9}
48:{1,48,2,24,3,16,4,12,6,8} HCF=6
5. 110,66and88
110:{1,110,2,55,5,22,11,10}
66:{1,66,2,33,3,22,6,11}
88:{1,88,2,44,4,22,8,11} HCF=22
6. 78,54and90
78:{1,78,2,39,3,26,6,13}
54:{1,54,2,27,3,18,6,9}
90:{1,90,2,45,3,30,5,18,6,15,9,10} HCF=6
9
Mathematics
Grade7
Question4: FindtheLCMofthefollowingnumbers:
1. 6,9and5
9:{9,18,27,36,45,54,63,72,81,90}
5:{5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90}
6:{6,12,18,24,30,36,42,48,54,60,66,72,78,84,90} LCM=90
(6)
Tip:Startwiththebiggestnumber.WritedownthemultiplesuntilyoufindthefirstLCMwithone
othernumbere.g.startwith9,youknowthatthefirstmultipleof9thatwillalsobeamultipleof5
willbe90,thenseeifthisnumberisalsomultipleofthe3rdnumber.Ifnot,findthenextmultiplefor
thetwonumbersandcontinueinthisway
2. 15,20and2
20:{20,40,60,80,100,120}
15:{15,30,45,60,75,90}
Weknow60isamultipleof2,thereforeLCM=60
3. 16,60and3
60:{60,120,180,240,300}
Testif16hasanyoftheabovemultiplesbydividingthenumbersby16.
240(16x15)andweknow240isamultipleof3,thereforeLCM=240
Question5: Forwhichthreenumbers(lessthan100)caneachofthesegroupsbefactors:
3. 2,13,26
26,78and52
Startbymultiplyingthelowestandhighestfactor,thenuseeliminationtofindthe
numbers
4. 3,27,9
27,81and54
Question6: Writeeachofthefollowingnumbersasaproductofitsprimefactors(usea
factortree): (8)
*
1
2. 108 108 = 2 ×3 2.
210210 = 2×3×5×7
108 210 54 2
2
105 2
27 21 5
3 9 3
7 3 3
3. 350
350 = 5* ×7×2
350 70 5
10 7
5 2 4.
360360 = 21 ×3* ×5
360 5
3
72 24 3 8 2 4 2 2
10
Mathematics
Grade7
Question6: Findtheanswerstothefollowing:(DONOTuseyourcalculator) (12)
2.
387098+2709898+78009
2.
4006712–376865–8009
=3175005 =3621838
3.
3607x283 4.
2809x405
=1020781 =1137645
5.
92246÷14 6.
225128÷15
=6589
=15008r8
Question7: Entera<,>or=tomaketheseequationstrue:
(5)
2
2
=
45 + 3×30 ÷ 216
45 + 3×(30 ÷ 216)
1
108 − (4 + 24) ÷ 2
>
108 − (41 + 24 ÷ 2)
=
(5×2)6 + 5×45×178 178 ×(5×2)6 + 5×45
2
2
<
18 + 91 ÷ 3×10: 10: ×18 + 91 ÷ 3
𝑥 * ×𝑥 < + 𝑥 1 =
𝑥= + 𝑥1
1
1
2
2
<
2×( 500) + 5×200
200×( 500) + 5
ProblemSolving:
1 each
1. Colouralltheequivalentnumbersthesame:
(7)
2
1
2
27×8
4* 21 3
6
3:
1
2
27 + 8
27
9
3*
243
26 31 ( 16)* 9
3*
27× 8
37 16* 31
9
15
2* + 2* 256
27
6
2. Writefollowingcelestialdistancesasproductofanumberandan
exponentof10.
(3)
Distancetothemoon
384400km
3844×10* 15×10< DistancetotheSun
150millionkm
DistancetoMars
225millionkm
225×10E 3. Howmanypeoplecanfillastadiumwith107rowsand5376seatsineachrow? (3)
107×5376 = 𝑥
107×5376 = 575232
Thestadiumcantake575232people
2
2
2
11
Mathematics
Grade7
1110m
4. Atachildren’sparty,thereareanumberofbicyclesandtricycles.Therearedouble
theamountofbicyclesthantricycles.IfIcount84wheelsintotal,howmanybicycles
andhowmanytricyclesarethere?(Useyourknowledgeofmultiplesandfactorsto
solvethisproblem.) (3)
Multiplesof3:3,6,9,12,15,18,21,24,27,30,33,36,39
Multiplesof2:2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,
42,44,46,48,50
Findallthethosewherethemultipleof2isexactlydoublethemultipleof3and
wherethenumberofwheelswilladduptothe84.(Therearemanysetsforwhich
thisapplies,youwillhavetotesteachpair)
12tricycles=36wheels
24bicycles=48wheels
36+48=84(theremaybeotherwaystosolvethis
problem)
5. Twelverugbyfieldsareexactlyadjacenttoeachother,withtwometres(inbreadth)
betweeneachfield.Thelengthoftherugbyfieldisexactlytwicethebreadthofthe
field.Ifthelengthofonerugbyfieldis110m,whatisthetotalperimeterof12rugby
fields.
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 2ℓ + 2𝑏
Lengthofonerugbyfield=110m,thereforebreadthofonerugbyfield=55m
Betweeneachfieldis2m
Breadthof12rugbyfields: 12×55𝑚 + 11×2𝑚 = 𝑥
660𝑚 + 22𝑚 = 682𝑚
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟 = 2 110𝑚 + 2 682𝑚 = 220𝑚 + 1364𝑚 = 1584𝑚
Thetotalperimeterofthe12rugbyfieldsis1584m
2m55m
12