Whakaoti i te 6+20/100x/100+frac{20{100}}=16/100

$$\frac { 6 + \frac { 20 } { 100 } x } { 100 + \frac { 20 } { 100 } } = \frac { 16 } { 100 }$$

Whakaoti mō x

$$x = \frac{1254}{25} = 50\frac{4}{25} = 50.16$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakahekea te hautanga \frac{20}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 20.

$$\frac{6+\frac{1}{5}x}{100+\frac{20}{100}}=\frac{16}{100}$$

Whakahekea te hautanga \frac{20}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 20.

$$\frac{6+\frac{1}{5}x}{100+\frac{1}{5}}=\frac{16}{100}$$

Me tahuri te 100 ki te hautau \frac{500}{5}.

$$\frac{6+\frac{1}{5}x}{\frac{500}{5}+\frac{1}{5}}=\frac{16}{100}$$

Tā te mea he rite te tauraro o \frac{500}{5} me \frac{1}{5}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{6+\frac{1}{5}x}{\frac{500+1}{5}}=\frac{16}{100}$$

Tāpirihia te 500 ki te 1, ka 501.

$$\frac{6+\frac{1}{5}x}{\frac{501}{5}}=\frac{16}{100}$$

Whakahekea te hautanga \frac{16}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{6+\frac{1}{5}x}{\frac{501}{5}}=\frac{4}{25}$$

Whakawehea ia wā o 6+\frac{1}{5}x ki te \frac{501}{5}, kia riro ko \frac{6}{\frac{501}{5}}+\frac{\frac{1}{5}x}{\frac{501}{5}}.

$$\frac{6}{\frac{501}{5}}+\frac{\frac{1}{5}x}{\frac{501}{5}}=\frac{4}{25}$$

Whakawehe 6 ki te \frac{501}{5} mā te whakarea 6 ki te tau huripoki o \frac{501}{5}.

$$6\times \frac{5}{501}+\frac{\frac{1}{5}x}{\frac{501}{5}}=\frac{4}{25}$$

Tuhia te 6\times \frac{5}{501} hei hautanga kotahi.

$$\frac{6\times 5}{501}+\frac{\frac{1}{5}x}{\frac{501}{5}}=\frac{4}{25}$$

Whakareatia te 6 ki te 5, ka 30.

$$\frac{30}{501}+\frac{\frac{1}{5}x}{\frac{501}{5}}=\frac{4}{25}$$

Whakahekea te hautanga \frac{30}{501} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{10}{167}+\frac{\frac{1}{5}x}{\frac{501}{5}}=\frac{4}{25}$$

Whakawehea te \frac{1}{5}x ki te \frac{501}{5}, kia riro ko \frac{1}{501}x.

$$\frac{10}{167}+\frac{1}{501}x=\frac{4}{25}$$

Tangohia te \frac{10}{167} mai i ngā taha e rua.

$$\frac{1}{501}x=\frac{4}{25}-\frac{10}{167}$$

Ko te maha noa iti rawa atu o 25 me 167 ko 4175. Me tahuri \frac{4}{25} me \frac{10}{167} ki te hautau me te tautūnga 4175.

$$\frac{1}{501}x=\frac{668}{4175}-\frac{250}{4175}$$

Tā te mea he rite te tauraro o \frac{668}{4175} me \frac{250}{4175}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{1}{501}x=\frac{668-250}{4175}$$

Tangohia te 250 i te 668, ka 418.

$$\frac{1}{501}x=\frac{418}{4175}$$

Me whakarea ngā taha e rua ki te 501, te tau utu o \frac{1}{501}.

$$x=\frac{418}{4175}\times 501$$

Tuhia te \frac{418}{4175}\times 501 hei hautanga kotahi.

$$x=\frac{418\times 501}{4175}$$

Whakareatia te 418 ki te 501, ka 209418.

$$x=\frac{209418}{4175}$$

Whakahekea te hautanga \frac{209418}{4175} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 167.

$$x=\frac{1254}{25}$$