Whakaoti i te 3/2:x=4/11:16/9

$$\frac { 3 } { 2 } : x = \frac { 4 } { 11 } : \frac { 16 } { 9 }$$

Whakaoti mō x

$$x = \frac{22}{3} = 7\frac{1}{3} \approx 7.333333333$$

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.

$$\frac{3}{2}=x\times \frac{\frac{4}{11}}{\frac{16}{9}}$$

Whakawehe \frac{4}{11} ki te \frac{16}{9} mā te whakarea \frac{4}{11} ki te tau huripoki o \frac{16}{9}.

$$\frac{3}{2}=x\times \frac{4}{11}\times \frac{9}{16}$$

Me whakarea te \frac{4}{11} ki te \frac{9}{16} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{3}{2}=x\times \frac{4\times 9}{11\times 16}$$

Mahia ngā whakarea i roto i te hautanga \frac{4\times 9}{11\times 16}.

$$\frac{3}{2}=x\times \frac{36}{176}$$

Whakahekea te hautanga \frac{36}{176} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{3}{2}=x\times \frac{9}{44}$$

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

$$x\times \frac{9}{44}=\frac{3}{2}$$

Me whakarea ngā taha e rua ki te \frac{44}{9}, te tau utu o \frac{9}{44}.

$$x=\frac{3}{2}\times \frac{44}{9}$$

Me whakarea te \frac{3}{2} ki te \frac{44}{9} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$x=\frac{3\times 44}{2\times 9}$$

Mahia ngā whakarea i roto i te hautanga \frac{3\times 44}{2\times 9}.

$$x=\frac{132}{18}$$

Whakahekea te hautanga \frac{132}{18} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$x=\frac{22}{3}$$