Whakaoti i te 14/50:x=18/30:10/6

$$\frac { 14 } { 50 } : x = \frac { 18 } { 30 } : \frac { 10 } { 6 }$$

Whakaoti mō x

$$x=\frac{7}{9}\approx 0.777777778$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$\frac{14}{50}=\frac{3}{5}x\times \frac{18}{30}$$

Whakahekea te hautanga \frac{14}{50} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{7}{25}=\frac{3}{5}x\times \frac{18}{30}$$

Whakahekea te hautanga \frac{18}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$\frac{7}{25}=\frac{3}{5}x\times \frac{3}{5}$$

Me whakarea te \frac{3}{5} ki te \frac{3}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{7}{25}=\frac{3\times 3}{5\times 5}x$$

Mahia ngā whakarea i roto i te hautanga \frac{3\times 3}{5\times 5}.

$$\frac{7}{25}=\frac{9}{25}x$$

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

$$\frac{9}{25}x=\frac{7}{25}$$

Me whakarea ngā taha e rua ki te \frac{25}{9}, te tau utu o \frac{9}{25}.

$$x=\frac{7}{25}\times \frac{25}{9}$$

Me whakarea te \frac{7}{25} ki te \frac{25}{9} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{7\times 25}{25\times 9}$$

Me whakakore tahi te 25 i te taurunga me te tauraro.

$$x=\frac{7}{9}$$