Whakaoti i te n/4frac{1{5}}=62/7/3frac{1{4}}

$$\frac { n } { 4 \frac { 1 } { 5 } } = \frac { 6 \frac { 2 } { 7 } } { 3 \frac { 1 } { 4 } }$$

Whakaoti mō n

$$n = \frac{528}{65} = 8\frac{8}{65} \approx 8.123076923$$

Ngā Upane mō te Whakaoti Whārite Rārangi

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

$$\frac{n\times 5}{4\times 5+1}=\frac{\frac{6\times 7+2}{7}}{\frac{3\times 4+1}{4}}$$

Whakareatia te 4 ki te 5, ka 20.

$$\frac{n\times 5}{20+1}=\frac{\frac{6\times 7+2}{7}}{\frac{3\times 4+1}{4}}$$

Tāpirihia te 20 ki te 1, ka 21.

$$\frac{n\times 5}{21}=\frac{\frac{6\times 7+2}{7}}{\frac{3\times 4+1}{4}}$$

Whakawehe \frac{6\times 7+2}{7} ki te \frac{3\times 4+1}{4} mā te whakarea \frac{6\times 7+2}{7} ki te tau huripoki o \frac{3\times 4+1}{4}.

$$\frac{n\times 5}{21}=\frac{\left(6\times 7+2\right)\times 4}{7\left(3\times 4+1\right)}$$

Whakareatia te 6 ki te 7, ka 42.

$$\frac{n\times 5}{21}=\frac{\left(42+2\right)\times 4}{7\left(3\times 4+1\right)}$$

Tāpirihia te 42 ki te 2, ka 44.

$$\frac{n\times 5}{21}=\frac{44\times 4}{7\left(3\times 4+1\right)}$$

Whakareatia te 44 ki te 4, ka 176.

$$\frac{n\times 5}{21}=\frac{176}{7\left(3\times 4+1\right)}$$

Whakareatia te 3 ki te 4, ka 12.

$$\frac{n\times 5}{21}=\frac{176}{7\left(12+1\right)}$$

Tāpirihia te 12 ki te 1, ka 13.

$$\frac{n\times 5}{21}=\frac{176}{7\times 13}$$

Whakareatia te 7 ki te 13, ka 91.

$$\frac{n\times 5}{21}=\frac{176}{91}$$

Me whakarea ngā taha e rua ki te 21.

$$n\times 5=\frac{176}{91}\times 21$$

Tuhia te \frac{176}{91}\times 21 hei hautanga kotahi.

$$n\times 5=\frac{176\times 21}{91}$$

Whakareatia te 176 ki te 21, ka 3696.

$$n\times 5=\frac{3696}{91}$$

Whakahekea te hautanga \frac{3696}{91} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 7.

$$n\times 5=\frac{528}{13}$$

Whakawehea ngā taha e rua ki te 5.

$$n=\frac{\frac{528}{13}}{5}$$

Tuhia te \frac{\frac{528}{13}}{5} hei hautanga kotahi.

$$n=\frac{528}{13\times 5}$$

Whakareatia te 13 ki te 5, ka 65.

$$n=\frac{528}{65}$$