Whakaoti i te [31/4div{11/4-1/2(21/2-frac{1}{4}-frac{1}{6})}]div(frac{1}{2}text{of}4frac{1}{3})

$$[ 3 \frac { 1 } { 4 } \div \{ 1 \frac { 1 } { 4 } - \frac { 1 } { 2 } ( 2 \frac { 1 } { 2 } - \frac { 1 } { 4 } - \frac { 1 } { 6 } ) \} ] \div ( \frac { 1 } { 2 } \text { of } 4 \frac { 1 } { 3 } )$$

Aromātai

$$\frac{36}{5}=7.2$$

Ngā Upane Otinga

Whakareatia te 3 ki te 4, ka 12.

$$\frac{\frac{\frac{12+1}{4}}{\frac{1\times 4+1}{4}-\frac{1}{2}\left(\frac{2\times 2+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Tāpirihia te 12 ki te 1, ka 13.

$$\frac{\frac{\frac{13}{4}}{\frac{1\times 4+1}{4}-\frac{1}{2}\left(\frac{2\times 2+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Whakareatia te 1 ki te 4, ka 4.

$$\frac{\frac{\frac{13}{4}}{\frac{4+1}{4}-\frac{1}{2}\left(\frac{2\times 2+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Tāpirihia te 4 ki te 1, ka 5.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{2\times 2+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Whakareatia te 2 ki te 2, ka 4.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{4+1}{2}-\frac{1}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Tāpirihia te 4 ki te 1, ka 5.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{5}{2}-\frac{1}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Ko te maha noa iti rawa atu o 2 me 4 ko 4. Me tahuri \frac{5}{2} me \frac{1}{4} ki te hautau me te tautūnga 4.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{10}{4}-\frac{1}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Tā te mea he rite te tauraro o \frac{10}{4} me \frac{1}{4}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{10-1}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Tangohia te 1 i te 10, ka 9.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{9}{4}-\frac{1}{6}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Ko te maha noa iti rawa atu o 4 me 6 ko 12. Me tahuri \frac{9}{4} me \frac{1}{6} ki te hautau me te tautūnga 12.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\left(\frac{27}{12}-\frac{2}{12}\right)}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Tā te mea he rite te tauraro o \frac{27}{12} me \frac{2}{12}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\times \frac{27-2}{12}}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Tangohia te 2 i te 27, ka 25.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1}{2}\times \frac{25}{12}}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Me whakarea te \frac{1}{2} ki te \frac{25}{12} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{1\times 25}{2\times 12}}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 25}{2\times 12}.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{4}-\frac{25}{24}}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Ko te maha noa iti rawa atu o 4 me 24 ko 24. Me tahuri \frac{5}{4} me \frac{25}{24} ki te hautau me te tautūnga 24.

$$\frac{\frac{\frac{13}{4}}{\frac{30}{24}-\frac{25}{24}}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Tā te mea he rite te tauraro o \frac{30}{24} me \frac{25}{24}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{\frac{13}{4}}{\frac{30-25}{24}}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Tangohia te 25 i te 30, ka 5.

$$\frac{\frac{\frac{13}{4}}{\frac{5}{24}}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Whakawehe \frac{13}{4} ki te \frac{5}{24} mā te whakarea \frac{13}{4} ki te tau huripoki o \frac{5}{24}.

$$\frac{\frac{13}{4}\times \frac{24}{5}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Me whakarea te \frac{13}{4} ki te \frac{24}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\frac{13\times 24}{4\times 5}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Mahia ngā whakarea i roto i te hautanga \frac{13\times 24}{4\times 5}.

$$\frac{\frac{312}{20}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Whakahekea te hautanga \frac{312}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\frac{\frac{78}{5}}{\frac{1}{2}\times \frac{4\times 3+1}{3}}$$

Whakareatia te 4 ki te 3, ka 12.

$$\frac{\frac{78}{5}}{\frac{1}{2}\times \frac{12+1}{3}}$$

Tāpirihia te 12 ki te 1, ka 13.

$$\frac{\frac{78}{5}}{\frac{1}{2}\times \frac{13}{3}}$$

Me whakarea te \frac{1}{2} ki te \frac{13}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\frac{78}{5}}{\frac{1\times 13}{2\times 3}}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 13}{2\times 3}.

$$\frac{\frac{78}{5}}{\frac{13}{6}}$$

Whakawehe \frac{78}{5} ki te \frac{13}{6} mā te whakarea \frac{78}{5} ki te tau huripoki o \frac{13}{6}.

$$\frac{78}{5}\times \frac{6}{13}$$

Me whakarea te \frac{78}{5} ki te \frac{6}{13} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{78\times 6}{5\times 13}$$

Mahia ngā whakarea i roto i te hautanga \frac{78\times 6}{5\times 13}.

$$\frac{468}{65}$$

Whakahekea te hautanga \frac{468}{65} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 13.

$$\frac{36}{5}$$

Tauwehe

$$\frac{2 ^ {2} \cdot 3 ^ {2}}{5} = 7\frac{1}{5} = 7.2$$