Metode Trachtenberg - perkalian dengan 11 dan 12

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1. © ar i e 2. Perkalian dengan 11 <ul><li>Aturannya sebagai berikut : </li></ul><ul><li>Angka terakhir dari bilangan yang dikalikan…

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  • 1. © ar i e
  • 2. Perkalian dengan 11 <ul><li>Aturannya sebagai berikut : </li></ul><ul><li>Angka terakhir dari bilangan yang dikalikan ditulis sebagai angka paling kanan dari jawabannya </li></ul><ul><li>Tiap angka selanjutnya ditambahkan pada angka di sebelah kanannya </li></ul><ul><li>Angka pertama bilangan yang dikalikan menjadi angka paling kiri pada jawabannya </li></ul>
  • 3. <ul><li>Marilah kita mulai dengan contoh sederhana : </li></ul><ul><li>#1. 6 3 3 x 11 </li></ul><ul><li>  </li></ul><ul><li>6 3 3 x 1 1 </li></ul><ul><li>------------- </li></ul><ul><li> 3 </li></ul><ul><li>3 + 3 = 6 6 3 3 x 1 1 </li></ul><ul><li>------------- </li></ul><ul><li> 6 3 </li></ul><ul><li>  </li></ul><ul><li>6 + 3 = 9 6 3 3 x 1 1 </li></ul><ul><li>------------- </li></ul><ul><li>9 6 3 </li></ul><ul><li>  </li></ul><ul><li>6 3 3 x 1 1 </li></ul><ul><li> --------------- </li></ul><ul><li> 6 9 6 3 </li></ul>
  • 4. <ul><li>#2. 7 2 1 . 3 2 4 x 11 </li></ul><ul><li>  7 2 1 3 2 4 x 1 1 </li></ul><ul><li>------------------- </li></ul><ul><li> 4 </li></ul><ul><li>2 + 4 = 6 7 2 1 3 2 4 x 1 1 </li></ul><ul><li>------------------- </li></ul><ul><li> 6 4 </li></ul><ul><li>  </li></ul><ul><li>3 + 2 = 5 7 2 1 3 2 4 x 1 1 </li></ul><ul><li>------------------- </li></ul><ul><li> 5 6 4 </li></ul><ul><li>  </li></ul><ul><li>1 + 3 = 4 7 2 1 3 2 4 x 1 1 </li></ul><ul><li>------------------- </li></ul><ul><li> 4 5 6 4 </li></ul><ul><li>  </li></ul>
  • 5. <ul><li>2 + 1 = 3 7 2 1 3 2 4 x 1 1 </li></ul><ul><li>------------------- </li></ul><ul><li> 3 4 5 6 4 </li></ul><ul><li>  </li></ul><ul><li>7 + 2 = 9 7 2 1 3 2 4 x 1 1 </li></ul><ul><li>------------------- </li></ul><ul><li>9 3 4 5 6 4 </li></ul><ul><li>  </li></ul><ul><li>7 2 1 3 2 4 x 1 1 </li></ul><ul><li> --------------------- </li></ul><ul><li> 7 9 3 4 5 6 4 </li></ul>
  • 6. <ul><li>#3. 1 . 7 5 4 x 11 </li></ul><ul><li>1 7 5 4 x 1 1 </li></ul><ul><li>--------------- </li></ul><ul><li> 4 </li></ul><ul><li>  </li></ul><ul><li>5 + 4 = 9 1 7 5 4 x 1 1 </li></ul><ul><li>--------------- </li></ul><ul><li> 9 4 </li></ul><ul><li>  </li></ul><ul><li>7 + 5 = 12 1 7 5 4 x 1 1 </li></ul><ul><li>(tulis 2, --------------- </li></ul><ul><li>simpan 1 ) 2 9 4 </li></ul><ul><li>  </li></ul>
  • 7. <ul><li>1 + 7 = 8 </li></ul><ul><li>8 + 1 = 9 1 7 5 4 x 1 1 </li></ul><ul><li>--------------- </li></ul><ul><li>9 2 9 4 </li></ul><ul><li>  </li></ul><ul><li>1 7 5 4 x 1 1 </li></ul><ul><li> ----------------- </li></ul><ul><li> 1 9 2 9 4 </li></ul><ul><li>  </li></ul>
  • 8. Perkalian dengan 12 <ul><li>Aturannya sebagai berikut : </li></ul><ul><li>Kalikan setiap angka dengan dua secara berturut-turut dan tambahkan pada angka di sebelah kanannya </li></ul>
  • 9. <ul><li>Mari kita mulai dengan contoh sederhana : </li></ul><ul><li>  </li></ul><ul><li>#1. 4 1 3 x 12 </li></ul><ul><li>3 x 2 = 6 0 4 1 3 x 1 2 </li></ul><ul><li>--------------- </li></ul><ul><li> 6 </li></ul><ul><li>  </li></ul><ul><li>1 x 2 + 3 = 5 0 4 1 3 x 1 2 </li></ul><ul><li>--------------- </li></ul><ul><li> 5 6 </li></ul><ul><li>  </li></ul><ul><li>4 x 2 + 1 = 9 0 4 1 3 x 1 2 </li></ul><ul><li>--------------- </li></ul><ul><li> 9 5 6 </li></ul><ul><li>  </li></ul><ul><li>0 x 2 + 4 = 4 0 4 1 3 x 1 2 </li></ul><ul><li>--------------- </li></ul><ul><li>4 9 5 6 </li></ul>
  • 10. <ul><li>#2. 6 3 . 2 4 7 x 12 </li></ul><ul><li>  </li></ul><ul><li>7 x 2 = 14 0 6 3 2 4 7 x 1 2 </li></ul><ul><li>(tulis 4, ------------------- </li></ul><ul><li>simpan 1 ) 4 </li></ul><ul><li>  </li></ul><ul><li>4 x 2 + 7 + 1 = 16 0 6 3 2 4 7 x 1 2 </li></ul><ul><li>(tulis 6, ------------------- </li></ul><ul><li>simpan 1 ) 6 4 </li></ul><ul><li>  </li></ul><ul><li>2 x 2 + 4 + 1 = 9 0 6 3 2 4 7 x 1 2 </li></ul><ul><li>------------------- </li></ul><ul><li> 9 6 4 </li></ul><ul><li>3 x 2 + 2 = 8 0 6 3 2 4 7 x 1 2 </li></ul><ul><li>------------------- </li></ul><ul><li> 8 9 6 4 </li></ul>
  • 11. <ul><li>  </li></ul><ul><li>6 x 2 + 3 = 15 0 6 3 2 4 7 x 1 2 </li></ul><ul><li>(tulis 5, ------------------- </li></ul><ul><li>simpan 1 ) 5 8 9 6 4 </li></ul><ul><li>  </li></ul><ul><li>0 x 2 + 6 + 1 = 7 0 6 3 2 4 7 x 1 2 </li></ul><ul><li>------------------- </li></ul><ul><li> 7 5 8 9 6 4 </li></ul>
  • 12. Selamat berhitung ! ( bersambung ) © ar i e 140908
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