Whakaoti i te (4/5*(1/6-3/8)):(5/12*(frac{1}{10}+frac{7}{4}))=

$$( \frac { 4 } { 5 } \cdot ( \frac { 1 } { 6 } - \frac { 3 } { 8 } ) ) : ( \frac { 5 } { 12 } \cdot ( \frac { 1 } { 10 } + \frac { 7 } { 4 } ) ) =$$

Aromātai

$$-\frac{8}{37}\approx -0.216216216$$

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 6 me 8 ko 24. Me tahuri \frac{1}{6} me \frac{3}{8} ki te hautau me te tautūnga 24.

$$\frac{\frac{4}{5}\left(\frac{4}{24}-\frac{9}{24}\right)}{\frac{5}{12}\left(\frac{1}{10}+\frac{7}{4}\right)}$$

Tā te mea he rite te tauraro o \frac{4}{24} me \frac{9}{24}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{4}{5}\times \frac{4-9}{24}}{\frac{5}{12}\left(\frac{1}{10}+\frac{7}{4}\right)}$$

Tangohia te 9 i te 4, ka -5.

$$\frac{\frac{4}{5}\left(-\frac{5}{24}\right)}{\frac{5}{12}\left(\frac{1}{10}+\frac{7}{4}\right)}$$

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

$$\frac{\frac{4\left(-5\right)}{5\times 24}}{\frac{5}{12}\left(\frac{1}{10}+\frac{7}{4}\right)}$$

Mahia ngā whakarea i roto i te hautanga \frac{4\left(-5\right)}{5\times 24}.

$$\frac{\frac{-20}{120}}{\frac{5}{12}\left(\frac{1}{10}+\frac{7}{4}\right)}$$

Whakahekea te hautanga \frac{-20}{120} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 20.

$$\frac{-\frac{1}{6}}{\frac{5}{12}\left(\frac{1}{10}+\frac{7}{4}\right)}$$

Ko te maha noa iti rawa atu o 10 me 4 ko 20. Me tahuri \frac{1}{10} me \frac{7}{4} ki te hautau me te tautūnga 20.

$$\frac{-\frac{1}{6}}{\frac{5}{12}\left(\frac{2}{20}+\frac{35}{20}\right)}$$

Tā te mea he rite te tauraro o \frac{2}{20} me \frac{35}{20}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-\frac{1}{6}}{\frac{5}{12}\times \frac{2+35}{20}}$$

Tāpirihia te 2 ki te 35, ka 37.

$$\frac{-\frac{1}{6}}{\frac{5}{12}\times \frac{37}{20}}$$

Me whakarea te \frac{5}{12} ki te \frac{37}{20} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{-\frac{1}{6}}{\frac{5\times 37}{12\times 20}}$$

Mahia ngā whakarea i roto i te hautanga \frac{5\times 37}{12\times 20}.

$$\frac{-\frac{1}{6}}{\frac{185}{240}}$$

Whakahekea te hautanga \frac{185}{240} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\frac{-\frac{1}{6}}{\frac{37}{48}}$$

Whakawehe -\frac{1}{6} ki te \frac{37}{48} mā te whakarea -\frac{1}{6} ki te tau huripoki o \frac{37}{48}.

$$-\frac{1}{6}\times \frac{48}{37}$$

Me whakarea te -\frac{1}{6} ki te \frac{48}{37} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{-48}{6\times 37}$$

Mahia ngā whakarea i roto i te hautanga \frac{-48}{6\times 37}.

$$\frac{-48}{222}$$

Whakahekea te hautanga \frac{-48}{222} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$-\frac{8}{37}$$

Tauwehe

$$-\frac{8}{37} = -0.21621621621621623$$