Whakaoti i te (2+4/5):(7-7/5)=5^2/2^3*2^2:x

$$( 2 + \frac { 4 } { 5 } ) : ( 7 - \frac { 7 } { 5 } ) = \frac { 5 ^ { 2 } } { 2 ^ { 3 } \cdot 2 ^ { 2 } } : x$$

Whakaoti mō x

$$x = \frac{25}{16} = 1\frac{9}{16} = 1.5625$$

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.

$$\frac{5}{28}x\left(2+\frac{4}{5}\right)=\frac{5^{2}}{2^{3}\times 2^{2}}$$

Hei whakarea i ngā pū o te pūtake kotahi, me tāpiri ō rātou taupū. Tāpiria te 3 me te 2 kia riro ai te 5.

$$\frac{5}{28}x\left(2+\frac{4}{5}\right)=\frac{5^{2}}{2^{5}}$$

Me tahuri te 2 ki te hautau \frac{10}{5}.

$$\frac{5}{28}x\left(\frac{10}{5}+\frac{4}{5}\right)=\frac{5^{2}}{2^{5}}$$

Tā te mea he rite te tauraro o \frac{10}{5} me \frac{4}{5}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{5}{28}x\times \frac{10+4}{5}=\frac{5^{2}}{2^{5}}$$

Tāpirihia te 10 ki te 4, ka 14.

$$\frac{5}{28}x\times \frac{14}{5}=\frac{5^{2}}{2^{5}}$$

Me whakarea te \frac{5}{28} ki te \frac{14}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{5\times 14}{28\times 5}x=\frac{5^{2}}{2^{5}}$$

Me whakakore tahi te 5 i te taurunga me te tauraro.

$$\frac{14}{28}x=\frac{5^{2}}{2^{5}}$$

Whakahekea te hautanga \frac{14}{28} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 14.

$$\frac{1}{2}x=\frac{5^{2}}{2^{5}}$$

Tātaihia te 5 mā te pū o 2, kia riro ko 25.

$$\frac{1}{2}x=\frac{25}{2^{5}}$$

Tātaihia te 2 mā te pū o 5, kia riro ko 32.

$$\frac{1}{2}x=\frac{25}{32}$$

Me whakarea ngā taha e rua ki te 2, te tau utu o \frac{1}{2}.

$$x=\frac{25}{32}\times 2$$

Tuhia te \frac{25}{32}\times 2 hei hautanga kotahi.

$$x=\frac{25\times 2}{32}$$

Whakareatia te 25 ki te 2, ka 50.

$$x=\frac{50}{32}$$

Whakahekea te hautanga \frac{50}{32} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$x=\frac{25}{16}$$