Whakaoti i te 31/2k+41/3=72/9

$$3 \frac{ 1 }{ 2 } k+4 \frac{ 1 }{ 3 } = 7 \frac{ 2 }{ 9 }$$

Whakaoti mō k

$$k=\frac{52}{63}\approx 0.825396825$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 18, arā, te tauraro pātahi he tino iti rawa te kitea o 2,3,9.

$$9\left(3\times 2+1\right)k+6\left(4\times 3+1\right)=2\left(7\times 9+2\right)$$

Whakareatia te 3 ki te 2, ka 6.

$$9\left(6+1\right)k+6\left(4\times 3+1\right)=2\left(7\times 9+2\right)$$

Tāpirihia te 6 ki te 1, ka 7.

$$9\times 7k+6\left(4\times 3+1\right)=2\left(7\times 9+2\right)$$

Whakareatia te 9 ki te 7, ka 63.

$$63k+6\left(4\times 3+1\right)=2\left(7\times 9+2\right)$$

Whakareatia te 4 ki te 3, ka 12.

$$63k+6\left(12+1\right)=2\left(7\times 9+2\right)$$

Tāpirihia te 12 ki te 1, ka 13.

$$63k+6\times 13=2\left(7\times 9+2\right)$$

Whakareatia te 6 ki te 13, ka 78.

$$63k+78=2\left(7\times 9+2\right)$$

Whakareatia te 7 ki te 9, ka 63.

$$63k+78=2\left(63+2\right)$$

Tāpirihia te 63 ki te 2, ka 65.

$$63k+78=2\times 65$$

Whakareatia te 2 ki te 65, ka 130.

$$63k+78=130$$

Tangohia te 78 mai i ngā taha e rua.

$$63k=130-78$$

Tangohia te 78 i te 130, ka 52.

$$63k=52$$

Whakawehea ngā taha e rua ki te 63.

$$k=\frac{52}{63}$$