Whakaoti i te 7/12*2/7+1/3div5/6quad(frac{2}{3}+frac{1}{6}+frac{3}{8})*24

$$\frac { 7 } { 12 } \times \frac { 2 } { 7 } + \frac { 1 } { 3 } \div \frac { 5 } { 6 } \quad ( \frac { 2 } { 3 } + \frac { 1 } { 6 } + \frac { 3 } { 8 } ) \times 24$$

Aromātai

$$\frac{353}{30}\approx 11.766666667$$

Ngā Upane Otinga

Me whakarea te \frac{7}{12} ki te \frac{2}{7} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{7\times 2}{12\times 7}+\frac{\frac{1}{3}}{\frac{5}{6}}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

Me whakakore tahi te 7 i te taurunga me te tauraro.

$$\frac{2}{12}+\frac{\frac{1}{3}}{\frac{5}{6}}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

Whakahekea te hautanga \frac{2}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{1}{6}+\frac{\frac{1}{3}}{\frac{5}{6}}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

Whakawehe \frac{1}{3} ki te \frac{5}{6} mā te whakarea \frac{1}{3} ki te tau huripoki o \frac{5}{6}.

$$\frac{1}{6}+\frac{1}{3}\times \frac{6}{5}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

Me whakarea te \frac{1}{3} ki te \frac{6}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{1}{6}+\frac{1\times 6}{3\times 5}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 6}{3\times 5}.

$$\frac{1}{6}+\frac{6}{15}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

Whakahekea te hautanga \frac{6}{15} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{1}{6}+\frac{2}{5}\left(\frac{2}{3}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

Ko te maha noa iti rawa atu o 3 me 6 ko 6. Me tahuri \frac{2}{3} me \frac{1}{6} ki te hautau me te tautūnga 6.

$$\frac{1}{6}+\frac{2}{5}\left(\frac{4}{6}+\frac{1}{6}+\frac{3}{8}\right)\times 24$$

Tā te mea he rite te tauraro o \frac{4}{6} me \frac{1}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1}{6}+\frac{2}{5}\left(\frac{4+1}{6}+\frac{3}{8}\right)\times 24$$

Tāpirihia te 4 ki te 1, ka 5.

$$\frac{1}{6}+\frac{2}{5}\left(\frac{5}{6}+\frac{3}{8}\right)\times 24$$

Ko te maha noa iti rawa atu o 6 me 8 ko 24. Me tahuri \frac{5}{6} me \frac{3}{8} ki te hautau me te tautūnga 24.

$$\frac{1}{6}+\frac{2}{5}\left(\frac{20}{24}+\frac{9}{24}\right)\times 24$$

Tā te mea he rite te tauraro o \frac{20}{24} me \frac{9}{24}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1}{6}+\frac{2}{5}\times \frac{20+9}{24}\times 24$$

Tāpirihia te 20 ki te 9, ka 29.

$$\frac{1}{6}+\frac{2}{5}\times \frac{29}{24}\times 24$$

Me whakarea te \frac{2}{5} ki te \frac{29}{24} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{1}{6}+\frac{2\times 29}{5\times 24}\times 24$$

Mahia ngā whakarea i roto i te hautanga \frac{2\times 29}{5\times 24}.

$$\frac{1}{6}+\frac{58}{120}\times 24$$

Whakahekea te hautanga \frac{58}{120} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{1}{6}+\frac{29}{60}\times 24$$

Tuhia te \frac{29}{60}\times 24 hei hautanga kotahi.

$$\frac{1}{6}+\frac{29\times 24}{60}$$

Whakareatia te 29 ki te 24, ka 696.

$$\frac{1}{6}+\frac{696}{60}$$

Whakahekea te hautanga \frac{696}{60} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 12.

$$\frac{1}{6}+\frac{58}{5}$$

Ko te maha noa iti rawa atu o 6 me 5 ko 30. Me tahuri \frac{1}{6} me \frac{58}{5} ki te hautau me te tautūnga 30.

$$\frac{5}{30}+\frac{348}{30}$$

Tā te mea he rite te tauraro o \frac{5}{30} me \frac{348}{30}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{5+348}{30}$$

Tāpirihia te 5 ki te 348, ka 353.

$$\frac{353}{30}$$

Tauwehe

$$\frac{353}{2 \cdot 3 \cdot 5} = 11\frac{23}{30} = 11.766666666666667$$