Whakaoti i te 13/x=11/5:11/3

$$1 \frac { 3 } { x } = 1 \frac { 1 } { 5 } : 1 \frac { 1 } { 3 }$$

Whakaoti mō x

$$x = \frac{10}{3} = 3\frac{1}{3} \approx 3.333333333$$

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.

$$1\times 3=\frac{3}{4}x\times \frac{1\times 5+1}{5}$$

Whakareatia te 1 ki te 3, ka 3.

$$3=\frac{3}{4}x\times \frac{1\times 5+1}{5}$$

Whakareatia te 1 ki te 5, ka 5.

$$3=\frac{3}{4}x\times \frac{5+1}{5}$$

Tāpirihia te 5 ki te 1, ka 6.

$$3=\frac{3}{4}x\times \frac{6}{5}$$

Me whakarea te \frac{3}{4} ki te \frac{6}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$3=\frac{3\times 6}{4\times 5}x$$

Mahia ngā whakarea i roto i te hautanga \frac{3\times 6}{4\times 5}.

$$3=\frac{18}{20}x$$

Whakahekea te hautanga \frac{18}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$3=\frac{9}{10}x$$

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

$$\frac{9}{10}x=3$$

Me whakarea ngā taha e rua ki te \frac{10}{9}, te tau utu o \frac{9}{10}.

$$x=3\times \frac{10}{9}$$

Tuhia te 3\times \frac{10}{9} hei hautanga kotahi.

$$x=\frac{3\times 10}{9}$$

Whakareatia te 3 ki te 10, ka 30.

$$x=\frac{30}{9}$$

Whakahekea te hautanga \frac{30}{9} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$x=\frac{10}{3}$$