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Negatieve getallen vermenigvuldigen en delen

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Negatieve getallen Vermenigvuldigen en delen
De heks koopt een emmer Met mijn nieuwe emmer kan ik meerdere blokjes tegelijk erin of eruit scheppen!
Blokjes erin scheppen β€’ De temperatuur moet 24Β°C stijgen – De heks doet steeds 8 warme blokjes in de emmer – Hoeveel emmers gevuld met 8 warme blokjes moet ze in de ketel gooien om de temperatuur 24Β°C te laten stijgen? 3 Γ— 8 = 24
3 Γ— 8 = 24 Positief getal, dus erbij scheppen! 3 keer de emmer gebruiken om blokjes erbij te scheppen Steeds 8 warme blokjes per schep. Ik doe er warme blokjes bij, dus de temp gaat omhoog! + Γ— + = +
Blokjes eruit scheppen β€’ Ze kan ook blokjes uit de ketel scheppen. β€’ De heks schept 3 Γ— 5 koude blokjes uit de ketel: β€’ Wat gebeurt er dan met de temperatuur? - - - -- De som die hierbij hoort is: -3 Γ— - 5 = 15
- 3 Γ— -5 = 15 Deze β€˜min’ staat voor ERUIT scheppen 3 keer de emmer gebruiken om blokjes eruit te halen Steeds 5 koude blokjes per schep. Ik haal koude blokjes eruit, dus de temp gaat omhoog! - Γ— - = +
Nog meer scheppen β€’ Op een dag schept ze 4 Γ— 6 koude blokjes erbij. β€’ Wat gebeurt er dan met de temperatuur? - -- - - - De som die hierbij hoort is: 4 Γ— - 6 = -24
4 Γ— -6 = -24 Positief getal, dus erbij scheppen! 4 keer de emmer gebruiken om blokjes erbij te scheppen Steeds 6 koude blokjes per schep. Ik doe er koude blokjes bij, dus de temp gaat omlaag! + Γ— - = -
Laatste keer scheppen! β€’ Op een dag schept ze 3 Γ— 7 warme blokjes eruit. β€’ Wat gebeurt er dan met de temperatuur? De som die hierbij hoort is: -3 Γ— 7= -21
- 3 Γ— 7 = -21 Deze β€˜min’ staat voor ERUIT scheppen 3 keer de emmer gebruiken om blokjes eruit te halen Steeds 7 warme blokjes per schep. Ik haal warme blokjes eruit, dus de temp gaat omlaag! - Γ— + = -
Vermenigvuldigen met negatieve getallen β€’ Door de heks met de emmer weten we nu de volgende regels: π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ Γ— π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ Γ— π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ Γ— π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ Γ— π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ 3 Γ— 4 = 12 βˆ’3 Γ— 4 = βˆ’12 3 Γ— βˆ’4 = βˆ’12 βˆ’3 Γ— βˆ’4 = 12 Regel Voorbeeld
Oefenen: neem over en vul in a) 3 Γ— -7 = b) -6 Γ— 8 = c) 7 Γ— -9 = d) -5 Γ— -2 = e) -4 Γ— -9 = f) … Γ— -8 = -64 g) … Γ— -1 𝟏 𝟐 = 3 h) -8 Γ— … = -4 π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ Γ— π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ Γ— π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ Γ— π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ Γ— π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“
Oefenen: neem over en vul in a) 3 Γ— -7 = b) -6 Γ— 8 = c) 7 Γ— -9 = d) -5 Γ— -2 = e) -4 Γ— -9 = f) … Γ— -8 = -64 g) … Γ— -1 𝟏 𝟐 = 3 h) -8 Γ— … = -4 -21 -48 -63 10 36 8 -2 𝟏 𝟐 π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ Γ— π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ Γ— π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ Γ— π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ Γ— π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“
Delen met negatieve getallen β€’ Het tegenovergestelde van vermenigvuldigen is delen. Voorbeeld 1) 6 Γ— 4 = 24 24 : 6 = 4 β€’ Dit werkt ook met negatieve getallen: Voorbeeld 2) -8 Γ— 5 = -40 -40 : -8 = 5
Delen met negatieve getallen β€’ De regels van het delen van getallen zijn hetzelfde als die van het vermenigvuldigen: π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ ∢ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ ∢ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ ∢ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ ∢ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ 24 ∢ 6 = 4 βˆ’24 ∢ 6 = βˆ’4 24 ∢ βˆ’6 = βˆ’4 βˆ’24 ∢ βˆ’6 = 4 Regel Voorbeeld
Oefenen: neem over en vul in a) 28 : -4 = b) -12 : -6 = c) -72 : 8 = d) -121 : -11 = e) -4 : 𝟏 πŸ‘ = f) … : -8 = 12 g) … : -1 𝟏 𝟐 = -20 h) -8 : … = -4 π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ ∢ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ ∢ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ ∢ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ ∢ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“
Oefenen: neem over en vul in a) 28 : -4 = b) -12 : -6 = c) -72 : 8 = d) -121 : -11 = e) -4 : 𝟏 πŸ‘ = f) … : -8 = 12 g) … : -1 𝟏 𝟐 = -20 h) -8 : … = -4 -7 2 -9 11 -12 -96 30 2 π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ ∢ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ ∢ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ ∢ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ ∢ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“

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Negatieve getallen havo

  • 2. De heks koopt een emmer Met mijn nieuwe emmer kan ik meerdere blokjes tegelijk erin of eruit scheppen!
  • 3. Blokjes erin scheppen β€’ De temperatuur moet 24Β°C stijgen – De heks doet steeds 8 warme blokjes in de emmer – Hoeveel emmers gevuld met 8 warme blokjes moet ze in de ketel gooien om de temperatuur 24Β°C te laten stijgen? 3 Γ— 8 = 24
  • 4. 3 Γ— 8 = 24 Positief getal, dus erbij scheppen! 3 keer de emmer gebruiken om blokjes erbij te scheppen Steeds 8 warme blokjes per schep. Ik doe er warme blokjes bij, dus de temp gaat omhoog! + Γ— + = +
  • 5. Blokjes eruit scheppen β€’ Ze kan ook blokjes uit de ketel scheppen. β€’ De heks schept 3 Γ— 5 koude blokjes uit de ketel: β€’ Wat gebeurt er dan met de temperatuur? - - - -- De som die hierbij hoort is: -3 Γ— - 5 = 15
  • 6. - 3 Γ— -5 = 15 Deze β€˜min’ staat voor ERUIT scheppen 3 keer de emmer gebruiken om blokjes eruit te halen Steeds 5 koude blokjes per schep. Ik haal koude blokjes eruit, dus de temp gaat omhoog! - Γ— - = +
  • 7. Nog meer scheppen β€’ Op een dag schept ze 4 Γ— 6 koude blokjes erbij. β€’ Wat gebeurt er dan met de temperatuur? - -- - - - De som die hierbij hoort is: 4 Γ— - 6 = -24
  • 8. 4 Γ— -6 = -24 Positief getal, dus erbij scheppen! 4 keer de emmer gebruiken om blokjes erbij te scheppen Steeds 6 koude blokjes per schep. Ik doe er koude blokjes bij, dus de temp gaat omlaag! + Γ— - = -
  • 9. Laatste keer scheppen! β€’ Op een dag schept ze 3 Γ— 7 warme blokjes eruit. β€’ Wat gebeurt er dan met de temperatuur? De som die hierbij hoort is: -3 Γ— 7= -21
  • 10. - 3 Γ— 7 = -21 Deze β€˜min’ staat voor ERUIT scheppen 3 keer de emmer gebruiken om blokjes eruit te halen Steeds 7 warme blokjes per schep. Ik haal warme blokjes eruit, dus de temp gaat omlaag! - Γ— + = -
  • 11. Vermenigvuldigen met negatieve getallen β€’ Door de heks met de emmer weten we nu de volgende regels: π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ Γ— π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ Γ— π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ Γ— π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ Γ— π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ 3 Γ— 4 = 12 βˆ’3 Γ— 4 = βˆ’12 3 Γ— βˆ’4 = βˆ’12 βˆ’3 Γ— βˆ’4 = 12 Regel Voorbeeld
  • 12. Oefenen: neem over en vul in a) 3 Γ— -7 = b) -6 Γ— 8 = c) 7 Γ— -9 = d) -5 Γ— -2 = e) -4 Γ— -9 = f) … Γ— -8 = -64 g) … Γ— -1 𝟏 𝟐 = 3 h) -8 Γ— … = -4 π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ Γ— π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ Γ— π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ Γ— π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ Γ— π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“
  • 13. Oefenen: neem over en vul in a) 3 Γ— -7 = b) -6 Γ— 8 = c) 7 Γ— -9 = d) -5 Γ— -2 = e) -4 Γ— -9 = f) … Γ— -8 = -64 g) … Γ— -1 𝟏 𝟐 = 3 h) -8 Γ— … = -4 -21 -48 -63 10 36 8 -2 𝟏 𝟐 π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ Γ— π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ Γ— π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ Γ— π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ Γ— π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“
  • 14. Delen met negatieve getallen β€’ Het tegenovergestelde van vermenigvuldigen is delen. Voorbeeld 1) 6 Γ— 4 = 24 24 : 6 = 4 β€’ Dit werkt ook met negatieve getallen: Voorbeeld 2) -8 Γ— 5 = -40 -40 : -8 = 5
  • 15. Delen met negatieve getallen β€’ De regels van het delen van getallen zijn hetzelfde als die van het vermenigvuldigen: π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ ∢ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ ∢ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ ∢ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ ∢ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ 24 ∢ 6 = 4 βˆ’24 ∢ 6 = βˆ’4 24 ∢ βˆ’6 = βˆ’4 βˆ’24 ∢ βˆ’6 = 4 Regel Voorbeeld
  • 16. Oefenen: neem over en vul in a) 28 : -4 = b) -12 : -6 = c) -72 : 8 = d) -121 : -11 = e) -4 : 𝟏 πŸ‘ = f) … : -8 = 12 g) … : -1 𝟏 𝟐 = -20 h) -8 : … = -4 π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ ∢ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ ∢ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ ∢ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ ∢ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“
  • 17. Oefenen: neem over en vul in a) 28 : -4 = b) -12 : -6 = c) -72 : 8 = d) -121 : -11 = e) -4 : 𝟏 πŸ‘ = f) … : -8 = 12 g) … : -1 𝟏 𝟐 = -20 h) -8 : … = -4 -7 2 -9 11 -12 -96 30 2 π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ ∢ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ ∢ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“ ∢ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ ∢ π‘›π‘’π‘”π‘Žπ‘‘π‘–π‘’π‘“ = π‘π‘œπ‘ π‘–π‘‘π‘–π‘’π‘“