Whakaoti i te a-r/a=n/1

$$\frac { a - r } { a } = \frac { n } { 1 }$$

Whakaoti mō a

$$\left\{\begin{matrix}a=\frac{r}{1-n}\text{, }&r\neq 0\text{ and }n\neq 1\\a\neq 0\text{, }&r=0\text{ and }n=1\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tē taea kia ōrite te tāupe a ki 0 nā te kore tautuhi i te whakawehenga mā te kore. Whakareatia ngā taha e rua o te whārite ki te a.

$$a-r=an$$

Tangohia te an mai i ngā taha e rua.

$$a-r-an=0$$

Me tāpiri te r ki ngā taha e rua. Ko te tau i tāpiria he kore ka hua koia tonu.

$$a-an=r$$

Pahekotia ngā kīanga tau katoa e whai ana i te a.

$$\left(1-n\right)a=r$$

Whakawehea ngā taha e rua ki te 1-n.

$$\frac{\left(1-n\right)a}{1-n}=\frac{r}{1-n}$$

Mā te whakawehe ki te 1-n ka wetekia te whakareanga ki te 1-n.

$$a=\frac{r}{1-n}$$

Tē taea kia ōrite te tāupe a ki 0.

$$a=\frac{r}{1-n}\text{, }a\neq 0$$

Whakaoti mō n

$$n=\frac{a-r}{a}$$

$$a\neq 0$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia ngā taha e rua o te whārite ki te a.

$$a-r=an$$

Whakawhitihia ngā taha kia puta ki te taha mauī ngā kīanga tau taurangi katoa.

$$an=a-r$$

Whakawehea ngā taha e rua ki te a.

$$\frac{an}{a}=\frac{a-r}{a}$$

Mā te whakawehe ki te a ka wetekia te whakareanga ki te a.

$$n=\frac{a-r}{a}$$