Whakaoti i te [3/2+1/2+frac{1{3}}]div[1/frac{3{5}}+frac{2/5}{3}]

$$[ \frac { 3 } { 2 } + \frac { 1 } { 2 + \frac { 1 } { 3 } } ] \div [ \frac { 1 } { \frac { 3 } { 5 } } + \frac { \frac { 2 } { 5 } } { 3 } ]$$

Aromātai

$$\frac{15}{14}\approx 1.071428571$$

Ngā Upane Otinga

Me tahuri te 2 ki te hautau \frac{6}{3}.

$$\frac{\frac{3}{2}+\frac{1}{\frac{6}{3}+\frac{1}{3}}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

Tā te mea he rite te tauraro o \frac{6}{3} me \frac{1}{3}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{3}{2}+\frac{1}{\frac{6+1}{3}}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

Tāpirihia te 6 ki te 1, ka 7.

$$\frac{\frac{3}{2}+\frac{1}{\frac{7}{3}}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

Whakawehe 1 ki te \frac{7}{3} mā te whakarea 1 ki te tau huripoki o \frac{7}{3}.

$$\frac{\frac{3}{2}+1\times \frac{3}{7}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

Whakareatia te 1 ki te \frac{3}{7}, ka \frac{3}{7}.

$$\frac{\frac{3}{2}+\frac{3}{7}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

Ko te maha noa iti rawa atu o 2 me 7 ko 14. Me tahuri \frac{3}{2} me \frac{3}{7} ki te hautau me te tautūnga 14.

$$\frac{\frac{21}{14}+\frac{6}{14}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

Tā te mea he rite te tauraro o \frac{21}{14} me \frac{6}{14}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{21+6}{14}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

Tāpirihia te 21 ki te 6, ka 27.

$$\frac{\frac{27}{14}}{\frac{1}{\frac{3}{5}}+\frac{\frac{2}{5}}{3}}$$

Whakawehe 1 ki te \frac{3}{5} mā te whakarea 1 ki te tau huripoki o \frac{3}{5}.

$$\frac{\frac{27}{14}}{1\times \frac{5}{3}+\frac{\frac{2}{5}}{3}}$$

Whakareatia te 1 ki te \frac{5}{3}, ka \frac{5}{3}.

$$\frac{\frac{27}{14}}{\frac{5}{3}+\frac{\frac{2}{5}}{3}}$$

Tuhia te \frac{\frac{2}{5}}{3} hei hautanga kotahi.

$$\frac{\frac{27}{14}}{\frac{5}{3}+\frac{2}{5\times 3}}$$

Whakareatia te 5 ki te 3, ka 15.

$$\frac{\frac{27}{14}}{\frac{5}{3}+\frac{2}{15}}$$

Ko te maha noa iti rawa atu o 3 me 15 ko 15. Me tahuri \frac{5}{3} me \frac{2}{15} ki te hautau me te tautūnga 15.

$$\frac{\frac{27}{14}}{\frac{25}{15}+\frac{2}{15}}$$

Tā te mea he rite te tauraro o \frac{25}{15} me \frac{2}{15}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{27}{14}}{\frac{25+2}{15}}$$

Tāpirihia te 25 ki te 2, ka 27.

$$\frac{\frac{27}{14}}{\frac{27}{15}}$$

Whakahekea te hautanga \frac{27}{15} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{\frac{27}{14}}{\frac{9}{5}}$$

Whakawehe \frac{27}{14} ki te \frac{9}{5} mā te whakarea \frac{27}{14} ki te tau huripoki o \frac{9}{5}.

$$\frac{27}{14}\times \frac{5}{9}$$

Me whakarea te \frac{27}{14} ki te \frac{5}{9} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{27\times 5}{14\times 9}$$

Mahia ngā whakarea i roto i te hautanga \frac{27\times 5}{14\times 9}.

$$\frac{135}{126}$$

Whakahekea te hautanga \frac{135}{126} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 9.

$$\frac{15}{14}$$

Tauwehe

$$\frac{3 \cdot 5}{2 \cdot 7} = 1\frac{1}{14} = 1.0714285714285714$$