Extra oefeningen hoofdstuk 6: Gehele getallen
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Pienter 1ASO Extra oefeningen hoofdstuk 6 Extra oefeningen hoofdstuk 6: Gehele getallen 6.1 Gehele getallen 1 Onderlijn de gehele getallen in het rood en de natuurlijke getallen in het groen: 5 -369 -6 -5,2 8 0 321 6,0 2,5 -8,02 = …… = …… = …… = …… = …… = …… 2 De verzameling van de gehele getallen De verzameling van de gehele getallen zonder 0 De verzameling van de positieve gehele getallen De verzameling van de strikt positieve gehele getallen De verzameling van de negatieve gehele getallen De verzameling van de strikt negatieve gehele getallen 3 Vul in. a) |–5| = ………… d) – (–6) = ………… g) |–25| = ………… b) |7| = ………… e) – (2) = ………… h) –|+2| = ………… c) |0| = ………… f) – (+48) = ………… i) –|–9| = ………… 4 Vul in met < , > of = –3 … 5 –12 … – 15 6 … – (+ 5) 7 … 2 –30 … – 25 – |+ 25| … – (–7) 0 … –4 22 … |–22 | –5 … –4 5 … +5 – |–100| … |100| 8 … –7 –2 … –6 – 29 … – (|– 29|) –9 … –8 – 18 … |–18| +3 … 0 +4 … –4 +4 … 8 – (+ 5) … – (– 3) –8 … –7 – (|–25|) … – (– 25) Uitgeverij Van In – (–5) … –5 + 6 … – (+ 8) – (–12) … – 4 – 9 … –| 7 | – (+ 5) … 4 15 … |–25| –38 … – (|–36|) 8 … – |– (– 6)| 1 Pienter 1ASO 5 Extra oefeningen hoofdstuk 6 Rangschik de getallen telkens van klein naar groot. a) –5 , 8 , -6 , 0 , 12 en –7 -7 …………………………………………………… b) 45 , –78 , –1 , –5 , 4 en –35 ………………………………………………………… c) –4 , –8 , –5 , –10 , –7 en –6 ………………………………………………………… d) 1 , –1 , 5 , –5 , 6 , –9 en –3 ………………………………………………………… e) 74 , –36 , –15 , –45 , 24 , –17 en 0 ………………………………………………………… 6 Welke gehele getallen horen bij de aangeduide punten? … 0 1 … … … … ZZ –10 … … 2 … … … ZZ –6 … … … 2 … … ZZ … –17 … … … … 38 ZZ … –20 … … 36 … … ZZ … –16 … … … … 83 ZZ … –84 –45 … … … … ZZ … … … … … 3 36 ZZ –50 … … … … -11 … ZZ … … 1 … 13 … … ZZ Uitgeverij Van In 2 Pienter 1ASO 7 Extra oefeningen hoofdstuk 6 Noteer, indien mogelijk, alle gehele getallen die in de plaats van g kunnen gezet worden. – 2,3 g 5,2 …………………………………………………………………… –5 g 2 …………………………………………………………………… –7,2 g – 3,9 …………………………………………………………………… – 5 g – 3,2 …………………………………………………………………… –42 g – 37 …………………………………………………………………… Uitgeverij Van In 3 Pienter 1ASO Extra oefeningen hoofdstuk 6 6.2 Bewerkingen met gehele getallen 8 Bereken de volgende sommen. (5) + (–3) = ............................................................................................. –11 + (–15) = ............................................................................................. (+7) + (–7) = ............................................................................................. –69 + 6 = ............................................................................................. (+8) + (–12) = ............................................................................................. –47 + (–32) = ............................................................................................. 0 + (–9) = ............................................................................................. 35 + 17 = ............................................................................................. (–13) + (–12) = ............................................................................................. –6 + (–15) = ............................................................................................. (+36) + (+42) = ............................................................................................. 87 + (–58) = ............................................................................................. (–2) + (+7) = ............................................................................................. –36 + (–47) = ............................................................................................. (–7) + (–7) = ............................................................................................. (–48) + 25 = ............................................................................................. 8 + (–12) = ............................................................................................. 95 + (–47) = ............................................................................................. (+265) + (+984) = .......................................................................................... (–212) + (+120) = .......................................................................................... (+232) + (–584) = .......................................................................................... (–20) + (–20) = .......................................................................................... (–847) + (+963) = .......................................................................................... (+59) + (–47) = .......................................................................................... (–625) + (+25) = .......................................................................................... (–87) + (–83) = .......................................................................................... (+54) + (+36) = .......................................................................................... (+691) + (–47) = .......................................................................................... (–84) + (–435) = .......................................................................................... (385) + (–58) = .......................................................................................... (–57) + (–74) = .......................................................................................... (+123) + (–478) = .......................................................................................... (+135) + (–25) = ........................................................................................... (–254) + (–365) = .......................................................................................... (–584) + (–896) = .......................................................................................... (+416) + (–36) = .......................................................................................... (+874) + (–572) = .......................................................................................... (–587) + (+32) = .......................................................................................... Uitgeverij Van In 4 Pienter 1ASO 9 Extra oefeningen hoofdstuk 6 Bereken. (+2) – (–8) = .......................................................................................... (–15) – (–11) = .......................................................................................... (–3) – (+9) = .......................................................................................... (–37) – (+15) = .......................................................................................... (+5) – (–12) = .......................................................................................... (+28) – (–17) = .......................................................................................... (–7) – (–14) = .......................................................................................... (–27) – (+28) = ......................................................................................... (+20) – (+12) = .......................................................................................... (+13) – (+15) = .......................................................................................... (+35) – (–9) = .......................................................................................... (–10) – (–10) = .......................................................................................... (–16) – (–4) = .......................................................................................... (–25) – (+25) = .......................................................................................... (–38) – (–17) = .......................................................................................... (–18) – (+25) = .......................................................................................... (–28) – 0 = .......................................................................................... (–17) – (–23) = .......................................................................................... 0 – (–28) = .......................................................................................... (–27) – (–13) = .......................................................................................... (+100) – (–99) = ........................................................................................... 75 – 162 = .......................................................................................... 258 – (–167) = .......................................................................................... –48 – 136 = .......................................................................................... –148 – (–58) = .......................................................................................... 65 – (–78) = .......................................................................................... (+94) – (+45) = .......................................................................................... –93 – (–47) = .......................................................................................... (–205) – (+315) = .......................................................................................... –68 – (–72) = .......................................................................................... (+432) – (–218) = .......................................................................................... (–52) – (+78) = .......................................................................................... (–312) – (–213) = .......................................................................................... (+63) – (–45) = .......................................................................................... 546 – (–145) = .......................................................................................... +45 – 87 = .......................................................................................... –159 – 364 = .......................................................................................... –62 – (–46) = .......................................................................................... (–258) – (+112) = .......................................................................................... Uitgeverij Van In 5 Pienter 1ASO 10 11 Bereken. (+28) + (–12) (+19) – (–26) (–16) + (+4) (–57) + (–38) (–15) – (–16) (–28) – (–36) (–37) – (+15) (+84) + (+36) (+41) + (–19) (+53) – (–37) (–18) – (+25) (+17) + (–88) (–12) + (+7) (–17) – (–88) (–8) + (–27) –(–15) – (+10) (+17) – (–23) –(–53) + (–47) (+17) + (+53) –(–11) – (–10) (–78) + (–43) Extra oefeningen hoofdstuk 6 = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. = ............................................................................................. Vul de juiste term in. ……… + (–5) = 3 (–50) – ……… = –7 ……… + (–5) = 12 0 + ……… = –12 ……… – (–17) = –5 –8 – ……… = –25 ……… + (–8) = –35 (–13) – ……… = 2 …… – (–18) = 10 (–15) + ……… = 0 ……… – (+63) = –36 63 + ……… = 52 ……… + (–25) = –23 –85 – ……… = 1 …… – (–25) = –13 Uitgeverij Van In 6 Pienter 1ASO 12 Extra oefeningen hoofdstuk 6 Kleur de hokjes waar de som of het verschil negatief is. 2+5 14 + 36 17 – (–38) –8 + 9 47 – 25 25 + (–14) – 41 + 52 48 + 36 –8 + 9 4–5 6 – (+8) –6 – (–3) 18 – 21 45 + (–50) –36 – 25 67 – (–23) 18 – 14 –5 + 4 72 + 59 45 + (–46) 45 + 36 –42 + 78 73 – (–14) –27 + 38 28 + (–4) –8 – (–4) 0 – (–5) 5–9 91 – (–28) 5 – (–18) 25 – 19 28 – 16 36 + 1 12 – 16 7 + (–9) –4 + (–5) –5 + 4 –14 + (–1) 4–9 72 – 39 –71 +85 72 – (–38) –7 + 9 48 + 27 69 – 47 47 + (–39) –25 + 38 48 + 62 –3 – (–4) –6 – (–2) –5 + 0 8 – 11 5 + (–11) 3 + (–98) –4 + (–3) –18 + 92 –5 + 8 –5 – (–18) –9 – 5 26 – (–8) 58 – 36 –18 + 67 –4 – (–51) –16 + 68 9–2 0 – (–52) 18 – 6 –6 – 2 25 + 36 8 – (–25) –7 + 28 82 – (–68) 15 – (–5) –65 + 98 –15 + 58 48 – (–35) –5 + (–2) 25 + (–17) 123 – 89 58 – 47 –4 + 8 –25 + 37 42 + 98 –26 – 4 56 – 24 14 – (–36) –89 + 100 0 + 25 –19 + 37 87 – 69 25 – 36 41 + 97 78 + (–25) –7 + 28 –25 + 48 –4 –(–58) 87 – (–19) 47 – 52 47 + (–48) –18 – 36 –9 + 5 –14 – (–6) –8 – 26 –47 + 82 25 + (–13) 94 + 27 78 – (–4) –17 + 28 14 + 36 25 + (–22) –8 + 9 5 + 37 48 + 39 –4 + 3 –5 + (–7) 8 – 14 –9 – (–4) 7–9 9 – 21 69 – 48 73 + 82 –36 + 42 0 – (–18) 56 – (–27) 7–5 48 – 47 –59 + 73 38 – (–47) –5 + 59 –25 + 0 –38 + 25 17 + (–18) 27 + 83 –67 + 83 –8 + 6 3 – (–28) 12– 8 0 + (–58) 45 + 39 45 – 87 2 – (–18) –45 – 63 –5 + 36 –37 + 95 76 – (–18) 86 – 98 74 – (–28) 52 + (–60) –78 –36 49 – (–71) – 4 – (–5) 25 + (–14) –3 – (–9) –25 + 13 –47 – (–2) –7 – 8 5 + (–18) 62 – 85 –17 – (–1) 34 – 18 –28 + 39 –5 + 72 2 + 68 –47 + 58 28 – 13 47 + (–28) –54 + 63 74 + 58 32 + (–12) –8 + 0 17 – 25 68 + (–71) 47 + 65 58 – 39 14 + 95 –14 + 39 57 – 42 –35 + 28 –5 + 9 14 – 36 –47 + 85 –49 + 82 49 – (–14) 7+0 25 + (–15) 47 – 85 4 – (–8) –4 – (–2) 29 – (–78) 56 + (–28) –9 – (–10) –34 + 84 –47 + 59 1 + (–7) 5 – 19 –6 – 8 –71 + 6 –7 – 0 –8 + 6 42 – 36 17 – (–57) 63 + 47 72 + 86 –36 + 75 84 – 29 57 – (–67) –7 + 18 29 – (–69) Uitgeverij Van In 7 Pienter 1ASO Extra oefeningen hoofdstuk 6 13 Bereken de volgende producten. 3.5 = .................................................................................................. (–3) . (–3) = .................................................................................................. 2 . (–4) = .................................................................................................. –7 . 5 = .................................................................................................. (–15) . 6 = .................................................................................................. (–8) . 3 = .................................................................................................. 1 . (–15) = .................................................................................................. (–9) . (–1) = .................................................................................................. (–5) . 3 = .................................................................................................. 0 . (–93) = .................................................................................................. –12 . (–9) = .................................................................................................. 6 . (–15) = .................................................................................................. 18 . (–6) = .................................................................................................. –4 . (–12) = .................................................................................................. 13 . (–1) = .................................................................................................. 10 . (–6) = .................................................................................................. –1 . (–1) = .................................................................................................. (–45) . (–2) = .................................................................................................. 0 . (–2) = .................................................................................................. (8) . (–7) = .................................................................................................. –3 . 25 = .................................................................................................. 14 Bereken. 45 : (–9) = .................................................................................................. (–84) : (–7) = .................................................................................................. 117 : (–9) = .................................................................................................. 568 : (–1) = .................................................................................................. 0 : (–58) = .................................................................................................. –204 : 12 = .................................................................................................. –68 : 0 = .................................................................................................. –38 : 1 = .................................................................................................. –112 : (–8) = .................................................................................................. 63 : (–7) = .................................................................................................. 91 : (–7) = .................................................................................................. 296 : 8 = .................................................................................................. 25 : (–25) = .................................................................................................. –272 : 8 = .................................................................................................. (–748) : (–22) = .............................................................................................. Uitgeverij Van In 8 Pienter 1ASO Extra oefeningen hoofdstuk 6 15 Vul in. –7 . ……… = –28 126 : ……… = 6 127 ……… . 3 = –15 –5 . ……… = –5 ……… : 20 = –4 ……… . (–4) = 16 –12 . ……… = 0 –162 : ……… = 18 ……… . (–9) = 72 ……… : (–5) = 32 ……… . (–15) = –195 84 : ……… = –3 –12 . ……… = 144 ……… : (–12) = –8 …… . (–17) = –306 16 Bereken. 24 5 2 = ..................................................................................................... = ..................................................................................................... = ..................................................................................................... 7 5 2 2 0 = ..................................................................................................... 8 14 2 9 3 3 0 3 2 3 4 3 1 4 8 1 2 142 3 5 24 25 5 1 3 5 6 2 03 26 Uitgeverij Van In = ..................................................................................................... = ..................................................................................................... = ..................................................................................................... = ..................................................................................................... = ..................................................................................................... = ..................................................................................................... = ..................................................................................................... = ..................................................................................................... = = = = = = ..................................................................................................... ..................................................................................................... ..................................................................................................... ..................................................................................................... ..................................................................................................... ..................................................................................................... = = = = ..................................................................................................... ..................................................................................................... ..................................................................................................... ..................................................................................................... .. 9 Pienter 1ASO 43 2 5 = ..................................................................................................... = ..................................................................................................... 4 = ..................................................................................................... = ..................................................................................................... = ..................................................................................................... 2 16 2 6 2 5 8 2 18 2 13 3 5 1 7 0 4 2 4 3 00 17 Extra oefeningen hoofdstuk 6 = ..................................................................................................... = ..................................................................................................... = ..................................................................................................... = ..................................................................................................... = ..................................................................................................... = = = = ..................................................................................................... ..................................................................................................... ..................................................................................................... .................................................................................................... Vereenvoudig indien nodig en bereken daarna deze gedurige sommen. a) (+15) – (–5) + (–16) – (+12) = .................................................................................................................. b) 34 – 16 + 5 – 9 – 25 = .................................................................................................................. c) (–17) – (+20) + (–14) – (–26) = .................................................................................................................. d) (+20) + (–11) + (–15) + (+13) + (–14) = .................................................................................................................. e) (–28) – (–42) + (–32) – (+35) = .................................................................................................................. f) (+15) + (–23) – (–19) – (+13) = .................................................................................................................. g) – 86 + 52 – 117 + 38 – 43 = .................................................................................................................. h) (–11) + (–211) + (+105) + (–33) + 150 = .................................................................................................................. i) – 113 + 85 – 24 – 63 + 45 = .................................................................................................................. j) (+28) + (+228) + (–356) + (–100) = .................................................................................................................. Uitgeverij Van In 10 Pienter 1ASO Extra oefeningen hoofdstuk 6 18 Werk de haakjes weg met de haakjesregel en los (indien mogelijk) op. a) 5 + (–7 + 4) = ................................................................................................................... b) 20 – (14 – 7) = ................................................................................................................... c) –12 + (–4 – 7) = ................................................................................................................... d) –16 – (19 + 5) = ................................................................................................................... e) (–14 + 10) + (–3 – 28) = ................................................................................................................... 19 Vul aan tussen de haakjes. Gebruik de getallen uit de opgave. a) 3 + 4 + 5 = 3 + ( …………… ) a) b)12 + 5 – 36 = 12 + ( …………… ) b) 6 + 4 + 5 = 6 – ( …………… ) c) 78 + 23 – 45 = 78 – ( …………… ) d) 12 – 23 + 87 = 12 + ( …………… ) e) 32 – 58 – 36 = 32 – ( …………… ) f) 45 – 23 – 95 = 45 + ( …………… ) g) 14 + 56 – 86 = 14 – ( …………… ) h) 52 – 36 + 85 = 52 + ( …………… ) i) 62 – 75 – 28 = 62 – ( …………… ) 20 Bereken de volgende gedurige producten. a) 15 . 3 . (–2) . (–5) = ................................................................................................................ b) –4 . 7 . 25 . (–3) = ................................................................................................................ c) –10 . 2 . 4 . (–25) = ................................................................................................................ d) 5 . (–2) . (–3) . 6 = ................................................................................................................ e) 2 . (–15) . (–8) . (–1) = ................................................................................................................ f) 2 . 2 . 2 . (–2) . (–2) = ................................................................................................................ g) –1 . 2 . 3 . (–2) . (–1) . 3 . 2 = ................................................................................................................ h) (–1) . (–2) . (–3) . (–4) . (–5) = ................................................................................................................ i) 1 . (–1) . 1 . (–1) . 1 . (–1) . (–1) . (–1) . 1 = ................................................................................................................ Uitgeverij Van In 11 Pienter 1ASO 21 22 Bereken. –7 + 8 –15 + (–23) –3 . (–3) –7 . 8 –9 . 2 . (–3) –3 : (–3) –7 . (–8) –125 : (–5) –3 + (–3) 8:4 –8 + 5 –3 – (–3) –18 + 6 –17 – (–28) –24 – 39 Extra oefeningen hoofdstuk 6 = = = = = = = = = = = = = = = ............................................................................................ ............................................................................................ ............................................................................................ ............................................................................................ ............................................................................................ ............................................................................................ ............................................................................................ ............................................................................................ ............................................................................................ ............................................................................................ ............................................................................................ ............................................................................................ ............................................................................................ ............................................................................................ ............................................................................................ Schrijf deze vraagstukjes als een optelling of een aftrekking. Bereken daarna. a) Een schoolbus vertrekt met 15 leerlingen. Aan de eerste halte komen er 6 bij. Aan de kleuterschool stappen 7 kleuters af en komen er 4 leerlingen bij. Aan de volgende halte stappen er weer 6 op. Aan de basisschool gaan er 11 af en komen er 2 bij. Met hoeveel leerlingen komt de bus bij ons op school aan? b) In een casino begint een man met 400 euro. Bij het eerste spel verliest hij 120 euro. Bij het tweede nog eens 250 euro. Bij het derde spel wint hij 70 euro en bij het vierde verliest hij opnieuw 120 euro. Heeft hij winst of verlies na zo’n dagje in het casino? 23 Een reis begint op 2 april en eindigt op 18 april. a) Hoeveel dagen duurt de reis? En hoeveel nachten? b) En wat als de reis begint op 25 januari en stopt op 16 februari? 24 Een kanovaarder vaart 5 km. Door de stroming en de harde wind gaat hij vervolgens 8 km achteruit. Hij vaart opnieuw 7 km maar wordt dan weer 6 km achteruit geblazen. Hoeveel km is hij uiteindelijk vooruitgeraakt? Uitgeverij Van In 12 Pienter 1ASO 25 Extra oefeningen hoofdstuk 6 Tijdens een toets stelt de leraar 10 vragen. Hij geeft 5 punten voor elk goed antwoord en trekt 3 punten af voor elk fout antwoord. a) Hoeveel behalen Koen (5 juist, 5 fout), Sofie (8 juist, 2 fout) en Joris (4 juist, 6 fout)? b) Wat is de hoogste score die behaald kan worden? En de laagste? c) Hoeveel vragen moet Tom juist antwoorden om 26 te halen? 6.3 Eigenschappen van de bewerkingen met gehele getallen 26 Vul in. Als in een vermenigvuldiging één van de factoren nul is, dan is het product ook ……………... Daarom noemen we nul ………………………………… voor de vermenigvuldiging in . Omdat het product van een vermenigvuldiging van een geheel getal met 1 hetzelfde is als dat geheel getal, noemen we 1 …………………………….. voor de vermenigvuldiging in . Als we bij een optelling van gehele getallen de plaats van de getallen mogen veranderen, dan noemen we de optelling ……………….... in . Als we bij een vermenigvuldiging van gehele getallen de haakjes rond een bewerking met getallen mogen weglaten, dan is de vermenigvuldiging …………………….. in . 27 Welke eigenschappen werden er toegepast ? a) – 5 . (– 6) = – 6 . (– 5) …………………………………………………... b) – 4 + 0 = – 4 = 0 + (– 4) …………………………………………………... c) 4 . [(– 8) . 2] = [4 . (– 8)] . 2 …………………………………………………... d) 4 . (– 8 + 5) = 4 . (– 8) + 4 . 5 …………………………………………………... e) 2 + 5 + (– 3) = 2 + (– 3) + 5 …………………………………………………... f) – 89 . 1 = – 89 = 1 . (– 89) …………………………………………………... g) 5 . (– 3) . 4 . (– 6) = 5 . 4 . (– 3) . (– 6) ………………………………..………... h) – 5 . 0 = 0 = 0 . (– 5) …………………………………………………... i) (4 – 15) – 8 = 4 + (– 15 – 8) …………………………………………………... j) 4 – 5 = – 5 + 4 …………………………………………………... k) – 8 . 6 + 9 . 6 = (– 8 + 9) . 6 …………………………………………………... Uitgeverij Van In 13 Pienter 1ASO 28 Extra oefeningen hoofdstuk 6 Gebruik de distributiviteit om de volgende oefeningen gemakkelijk op te lossen. Voorbeeld: 17 . 9 = 17 . (10 – 1) = 17 . 10 – 17 . 1 = 170 – 17 = 153 a) 53 . 9 = ............................................................................................. b) –47 . 11 = ............................................................................................. c) –9 . (–67) = ............................................................................................. d) (–11) . (–120) = ......................................................................................... e) 16 . (–9) = ............................................................................................. f) 63 . (–11) = ............................................................................................ g) (–9) . (–24) = ............................................................................................ 6.4 Volgorde van bewerkingen met de gehele getallen 29 Bereken. Let op de volgorde van de bewerkingen. a) –6 + 2 . (–3) = ............................................................................................................... b) –28 + (–6): 2 = ............................................................................................................... c) 42 : (–6) – 36 = ............................................................................................................... d) –44 – (–36) + 12 . (–4) = ............................................................................................................... e) –22 . (–6) + (–33) . 4 = ............................................................................................................... f) 6 . (–4) . 2 – (8 – 4 . 5 ) = ............................................................................................................... g) –3 – [–6 + 5 . (–3) ] = ............................................................................................................... h) –(–6 + 2 . 3) + 4 = ............................................................................................................... i) 18 . (–3) – (–4 + 17) = ............................................................................................................... j) 12 : (–3) + 8 : (–2) = ............................................................................................................... Uitgeverij Van In 14 Pienter 1ASO Extra oefeningen hoofdstuk 6 30 Bereken. Let op de volgorde van de bewerkingen. a) 3(–5) – 6 . 2 = .................................................................................................................. b) 2 . 3 + (–6) : 3 = .................................................................................................................. c) 13(–3) + 25 : 5 = .................................................................................................................. d) 45 : (–5) – 6 = .................................................................................................................. e) –10 : (–2) – 2 . 5 = .................................................................................................................. f) 13 . (–5) + (–54) : 6 = .................................................................................................................. g) –100 . 6 : 3 = .................................................................................................................. h) –2 + 8 : (–2) – 3 . 4 = .................................................................................................................. i) 3 – 5 – 6 . 2 = .................................................................................................................. j) –12 + 8 . (–3) – 6 : 2 = .................................................................................................................. 31 Bereken, en let op de volgorde van de bewerkingen. a) (–3)² + 4² = .................................................................................................................. b) (–4)0 – (–1)² – 5² = .................................................................................................................. c) 2²(–4) = .................................................................................................................. d) (–4)³ : 8 – 6 = .................................................................................................................. e) (–2)² . (–5)² = .................................................................................................................. f) 196 + 5(–3)² : 9 – 8² = .................................................................................................................. g) 9 + 9 . (–9) – 9² : 9 = .................................................................................................................. h) –5 . 3² – 2³ . 7 – (–5)6 = .................................................................................................................. Uitgeverij Van In 15 Pienter 1ASO 32 Extra oefeningen hoofdstuk 6 Bereken, en let op de volgorde van de bewerkingen. a) –3 – (–2) . (–4) + (6 – 7) = .................................................................................................................. .................................................................................................................. b) –2 + [ –5 + (–6)(–3) : 2 – (–3) ] – (+6) = .................................................................................................................. .................................................................................................................. c) (4 – 2 . 4) : (3 – 49 ) = .................................................................................................................. .................................................................................................................. d) [8 – 4(–3) : 5]² + 3(6–2).7 = .................................................................................................................. .................................................................................................................. e) 2 . (–4) – 3(–3 – 5 + 9)² = .................................................................................................................. .................................................................................................................. f) 4 + 12(8 – 15 + 49 )³ = .................................................................................................................. .................................................................................................................. g) –8(9 – 2.6 + 2²)³ = .................................................................................................................. .................................................................................................................. h) (8 – 6.5) : [ 144 + 5 : (–12 + 7)] = .................................................................................................................. .................................................................................................................. i) –3² – [2² – 3² + 4²(–2) – (–6)5]² = .................................................................................................................. .................................................................................................................. Uitgeverij Van In 16 Pienter 1ASO 33 Extra oefeningen hoofdstuk 6 Bereken. Let op de volgorde van de bewerkingen. 7 2 52 a) 5 6 2 23 = ................................................................................................................ ............................................................................................................... 82 52 5.2 (5)(2) 3 = b) ................................................................................................................ ................................................................................................................ 5 25 3 : 17 2 4 c) = ................................................................................................................ ................................................................................................................ d) e) 2 3 3 2 5 43 25.3 3 5 10 = ................................................................................................................ ................................................................................................................ 72 23 23 92 82 23 = ................................................................................................................ ................................................................................................................ f) 8 62 13 3.( 4) 9. 1 6 = ................................................................................................................ ................................................................................................................ g) 121 144 61 82 24 = ................................................................................................................ ................................................................................................................ h) i) 5 121 6.52 6 5 = ................................................................................................................ ................................................................................................................ 7. 6 : 3 4 7 25 16 = 2 ................................................................................................................ ................................................................................................................ j) 8 62 13 3. 4 9. 1 6 = ................................................................................................................ ................................................................................................................ Uitgeverij Van In 17 Pienter 1ASO Extra oefeningen hoofdstuk 6 6.5 Lettervormen 34 Bereken de getalwaarde van de volgende lettervormen. a) a + b – c = voor a = – 36, b = 28 en c = –15 ………………… b) x – y – z² = voor x = 8, y = – 9 en z = – 10 ………………… c) – 4a + 3b – a² = voor a = – 3 en b = – 5 ………………… d) 7x – y² + 3y : x = voor x = – 9 en y = – 6 ………………… e) – 4a – 8b – 12c voor a = – 5, b = 7 en c = – 3 ………………… f) 3a² + 2b² = voor a = – 5 en b = 8 ………………… g) 2ab + 3c² = voor a = – 5, b = 3 en c = – 1 ………………… h) 2a – 4b² – 6c³ = voor a = 5, b = – 3 en c = 1 ………………… i) 2a(3b² – 4c) = voor a = – 5, b = – 7 en c = – 9 ………………… j) –3a(b² + 3c³) + a² = voor a = – 4, b = 0 en c = – 2 ………………… 35 Werk zo ver mogelijk uit.. a) 5b – 2 + 6a + b = ................................................................................... b) –2a + 7 + (–3a) + 4 = ............................................................................. c) 2x + 3y + z – 5x – z + 3y = ..................................................................... d) –4t + 8s + (–8t) + 4s = ........................................................................... e) –9q + 14h – 22q = .................................................................................. f) d – d + d + d + (–3d) = ........................................................................... g) –4f + 9g + 3g – (–4f) = ........................................................................... h) 52c – 19k + 28c – 11k = ......................................................................... i) –7p + (–3m) + 6m – (–5p) = ................................................................... j) 2b – b + 3c – c + 4a – 8a = .................................................................... Uitgeverij Van In 18 Pienter 1ASO Extra oefeningen hoofdstuk 6 36 Schrijf zonder haakjes en werk dan zo ver mogelijk uit. a) 4z + (–2y + 6z) = .................................................................................... b) –8x – (16 + 8x) = .................................................................................... c) 5w – (–2 + 7w + 3v) –v = ....................................................................... d) –16 + (–23 + 8u) – 16u = ....................................................................... e) t – (s + 2t) + (3t – s) = ............................................................................ f) –(2a + 3b) + 4b – a = ............................................................................. g) –19c + 3d – 14c + 5d = .......................................................................... h) –(19c + 3d) – 14c + 5d = ........................................................................ i) –(19c + 3d) – (14c + 5d) = ..................................................................... j) –(19c + 3d – 14c) + 5d = ........................................................................ 37 Bereken de volgende producten. a) 3 . (a + 8) = ............................................................................................ b) –2 . (4 – x) = ......................................................................................... c) a . (–4 + c) = .......................................................................................... d) 8 . (4x – 5) = .......................................................................................... e) –2p . (–3 – 2s) = .................................................................................... f) (–7x + 2y) . 5z = ..................................................................................... g) (9t – p) . (–3s) = ..................................................................................... h) 10f . (–5x + 6y – 2z) = ............................................................................ i) (13g – 8n) . 0 = ...................................................................................... j) (–9x . –5y) . (–z) = ................................................................................. 38 Werk zo ver mogelijk uit. a) 7a + 3 . (2a – 5) = .................................................................................. b) –5b + 6 . (4 – 8b) + 14 = ........................................................................ c) –5x . (7 + 8y) + 14xy = ........................................................................... d) 9a . (–3 + 8b) – (b – 27a) = .................................................................... e) 3 . (2x – 8) – (8 – 4x) = .......................................................................... f) (–4f + 3p) . (–2) + 7p – 6f = .................................................................... g) (8r – 2s + 4t) . (–6) + r + 2s – (–5t) = ..................................................... h) –5 . (8a + 6b) – 2 . (4b + a) = ................................................................. i) –6 . (2x – y) – 6x . (3 + 7y) = .................................................................. Uitgeverij Van In 19 Pienter 1ASO Extra oefeningen hoofdstuk 6 6.6 Vergelijkingen en vraagstukken 39 Los de volgende vergelijkingen op. a) x + 4 = – 25 ................................................................................................................ b) x – 39 = – 74 ................................................................................................................ c) x – 49 = 141 ................................................................................................................ d) x + 52 = 43 ................................................................................................................ e) x + 8 = 75 ................................................................................................................ f) –6 + x = 18 ................................................................................................................ g) x – 8 = – 36 ................................................................................................................ h) – 8 + x = – 13 ................................................................................................................ i) x – 15 = – 58 ................................................................................................................ 40 Gebruik een vergelijking om de volgende vraagstukken op te lossen. a) Als we een getal met 15 vermeerderen, dan is de uitkomst – 6. Wat is dat getal? b) Als we een getal met 36 verminderen dan is de uitkomst – 15. Wat is dat getal? c) Als Joris van de temperatuur van deze nacht 22°C aftrekt komt hij –30°C uit. Hoe koud was het deze nacht? d) Pienter en zijn papa zijn even oud als zijn papa en zijn zus samen. Hoe oud is zijn zus als Pienter 12 jaar is, mama 36 en papa 40? e) Kato betaalt voor 3 agenda’s even veel als Marleen, die een dagboek en een pen koopt. Hoeveel kost het dagboek als een agenda 13 euro kost en een pen 2 euro? Uitgeverij Van In 20
