Whakaoti i te 1/3/0,2=1/5-frac{a/7}{frac{1}{4}}

$$\frac { \frac { 1 } { 3 } } { 0,2 } = \frac { \frac { 1 } { 5 } - \frac { a } { 7 } } { \frac { 1 } { 4 } }$$

Whakaoti mō a

$$a = -\frac{91}{60} = -1\frac{31}{60} \approx -1.516666667$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Tuhia te \frac{\frac{1}{3}}{0.2} hei hautanga kotahi.

$$\frac{1}{3\times 0.2}=\frac{\frac{1}{5}-\frac{a}{7}}{\frac{1}{4}}$$

Whakareatia te 3 ki te 0.2, ka 0.6.

$$\frac{1}{0.6}=\frac{\frac{1}{5}-\frac{a}{7}}{\frac{1}{4}}$$

Whakarohaina te \frac{1}{0.6} mā te whakarea i te taurunga me te tauraro ki te 10.

$$\frac{10}{6}=\frac{\frac{1}{5}-\frac{a}{7}}{\frac{1}{4}}$$

Whakahekea te hautanga \frac{10}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{5}{3}=\frac{\frac{1}{5}-\frac{a}{7}}{\frac{1}{4}}$$

Hei tāpiri, hei tango kīanga rānei, me whakaroha ērā kia rite ā rātou tauraro. Ko te taurea pātahi iti rawa o 5 me 7 ko 35. Whakareatia \frac{1}{5} ki te \frac{7}{7}. Whakareatia \frac{a}{7} ki te \frac{5}{5}.

$$\frac{5}{3}=\frac{\frac{7}{35}-\frac{5a}{35}}{\frac{1}{4}}$$

Tā te mea he rite te tauraro o \frac{7}{35} me \frac{5a}{35}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{5}{3}=\frac{\frac{7-5a}{35}}{\frac{1}{4}}$$

Whakawehea ia wā o 7-5a ki te 35, kia riro ko \frac{1}{5}-\frac{1}{7}a.

$$\frac{5}{3}=\frac{\frac{1}{5}-\frac{1}{7}a}{\frac{1}{4}}$$

Whakawehea ia wā o \frac{1}{5}-\frac{1}{7}a ki te \frac{1}{4}, kia riro ko \frac{\frac{1}{5}}{\frac{1}{4}}+\frac{-\frac{1}{7}a}{\frac{1}{4}}.

$$\frac{5}{3}=\frac{\frac{1}{5}}{\frac{1}{4}}+\frac{-\frac{1}{7}a}{\frac{1}{4}}$$

Whakawehe \frac{1}{5} ki te \frac{1}{4} mā te whakarea \frac{1}{5} ki te tau huripoki o \frac{1}{4}.

$$\frac{5}{3}=\frac{1}{5}\times 4+\frac{-\frac{1}{7}a}{\frac{1}{4}}$$

Whakareatia te \frac{1}{5} ki te 4, ka \frac{4}{5}.

$$\frac{5}{3}=\frac{4}{5}+\frac{-\frac{1}{7}a}{\frac{1}{4}}$$

Whakawehea te -\frac{1}{7}a ki te \frac{1}{4}, kia riro ko -\frac{4}{7}a.

$$\frac{5}{3}=\frac{4}{5}-\frac{4}{7}a$$

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

$$\frac{4}{5}-\frac{4}{7}a=\frac{5}{3}$$

Tangohia te \frac{4}{5} mai i ngā taha e rua.

$$-\frac{4}{7}a=\frac{5}{3}-\frac{4}{5}$$

Ko te maha noa iti rawa atu o 3 me 5 ko 15. Me tahuri \frac{5}{3} me \frac{4}{5} ki te hautau me te tautūnga 15.

$$-\frac{4}{7}a=\frac{25}{15}-\frac{12}{15}$$

Tā te mea he rite te tauraro o \frac{25}{15} me \frac{12}{15}, me tango rāua mā te tango i ō raua taurunga.

$$-\frac{4}{7}a=\frac{25-12}{15}$$

Tangohia te 12 i te 25, ka 13.

$$-\frac{4}{7}a=\frac{13}{15}$$

Me whakarea ngā taha e rua ki te -\frac{7}{4}, te tau utu o -\frac{4}{7}.

$$a=\frac{13}{15}\left(-\frac{7}{4}\right)$$

Me whakarea te \frac{13}{15} ki te -\frac{7}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$a=\frac{13\left(-7\right)}{15\times 4}$$

Mahia ngā whakarea i roto i te hautanga \frac{13\left(-7\right)}{15\times 4}.

$$a=\frac{-91}{60}$$

Ka taea te hautanga \frac{-91}{60} te tuhi anō ko -\frac{91}{60} mā te tango i te tohu tōraro.

$$a=-\frac{91}{60}$$