Whakaoti i te (1/6+8/12)*(15/14-11/7)+(frac{10}{8}-frac{7}{6}):(-frac{1}{3})^3

$$( \frac { 1 } { 6 } + \frac { 8 } { 12 } ) \cdot ( \frac { 15 } { 14 } - \frac { 11 } { 7 } ) + ( \frac { 10 } { 8 } - \frac { 7 } { 6 } ) : ( - \frac { 1 } { 3 } ) ^ { 3 }$$

Aromātai

$$-\frac{8}{3}\approx -2.666666667$$

Ngā Upane Otinga

Whakahekea te hautanga \frac{8}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$\left(\frac{1}{6}+\frac{2}{3}\right)\left(\frac{15}{14}-\frac{11}{7}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

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

$$\left(\frac{1}{6}+\frac{4}{6}\right)\left(\frac{15}{14}-\frac{11}{7}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

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

$$\frac{1+4}{6}\left(\frac{15}{14}-\frac{11}{7}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Tāpirihia te 1 ki te 4, ka 5.

$$\frac{5}{6}\left(\frac{15}{14}-\frac{11}{7}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Ko te maha noa iti rawa atu o 14 me 7 ko 14. Me tahuri \frac{15}{14} me \frac{11}{7} ki te hautau me te tautūnga 14.

$$\frac{5}{6}\left(\frac{15}{14}-\frac{22}{14}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Tā te mea he rite te tauraro o \frac{15}{14} me \frac{22}{14}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{5}{6}\times \frac{15-22}{14}+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Tangohia te 22 i te 15, ka -7.

$$\frac{5}{6}\times \frac{-7}{14}+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Whakahekea te hautanga \frac{-7}{14} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 7.

$$\frac{5}{6}\left(-\frac{1}{2}\right)+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Me whakarea te \frac{5}{6} ki te -\frac{1}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{5\left(-1\right)}{6\times 2}+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Mahia ngā whakarea i roto i te hautanga \frac{5\left(-1\right)}{6\times 2}.

$$\frac{-5}{12}+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Ka taea te hautanga \frac{-5}{12} te tuhi anō ko -\frac{5}{12} mā te tango i te tohu tōraro.

$$-\frac{5}{12}+\frac{\frac{10}{8}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Whakahekea te hautanga \frac{10}{8} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$-\frac{5}{12}+\frac{\frac{5}{4}-\frac{7}{6}}{\left(-\frac{1}{3}\right)^{3}}$$

Ko te maha noa iti rawa atu o 4 me 6 ko 12. Me tahuri \frac{5}{4} me \frac{7}{6} ki te hautau me te tautūnga 12.

$$-\frac{5}{12}+\frac{\frac{15}{12}-\frac{14}{12}}{\left(-\frac{1}{3}\right)^{3}}$$

Tā te mea he rite te tauraro o \frac{15}{12} me \frac{14}{12}, me tango rāua mā te tango i ō raua taurunga.

$$-\frac{5}{12}+\frac{\frac{15-14}{12}}{\left(-\frac{1}{3}\right)^{3}}$$

Tangohia te 14 i te 15, ka 1.

$$-\frac{5}{12}+\frac{\frac{1}{12}}{\left(-\frac{1}{3}\right)^{3}}$$

Tātaihia te -\frac{1}{3} mā te pū o 3, kia riro ko -\frac{1}{27}.

$$-\frac{5}{12}+\frac{\frac{1}{12}}{-\frac{1}{27}}$$

Whakawehe \frac{1}{12} ki te -\frac{1}{27} mā te whakarea \frac{1}{12} ki te tau huripoki o -\frac{1}{27}.

$$-\frac{5}{12}+\frac{1}{12}\left(-27\right)$$

Whakareatia te \frac{1}{12} ki te -27, ka \frac{-27}{12}.

$$-\frac{5}{12}+\frac{-27}{12}$$

Whakahekea te hautanga \frac{-27}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$-\frac{5}{12}-\frac{9}{4}$$

Ko te maha noa iti rawa atu o 12 me 4 ko 12. Me tahuri -\frac{5}{12} me \frac{9}{4} ki te hautau me te tautūnga 12.

$$-\frac{5}{12}-\frac{27}{12}$$

Tā te mea he rite te tauraro o -\frac{5}{12} me \frac{27}{12}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{-5-27}{12}$$

Tangohia te 27 i te -5, ka -32.

$$\frac{-32}{12}$$

Whakahekea te hautanga \frac{-32}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$-\frac{8}{3}$$

Tauwehe

$$-\frac{8}{3} = -2\frac{2}{3} = -2.6666666666666665$$