Whakaoti i te (1/2+2/3-3/3)*(2+1/3-2frac{1}{9})

$$( \frac { 1 } { 2 } + \frac { 2 } { 3 } - \frac { 3 } { 3 } ) * ( 2 + \frac { 1 } { 3 } - 2 \frac { 1 } { 9 } )$$

Aromātai

$$\frac{1}{27}\approx 0.037037037$$

Ngā Upane Otinga

Whakawehea te 3 ki te 3, kia riro ko 1.

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

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

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

Tā te mea he rite te tauraro o \frac{3}{6} me \frac{4}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

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

Tāpirihia te 3 ki te 4, ka 7.

$$\left(\frac{7}{6}-1\right)\left(2+\frac{1}{3}-\frac{2\times 9+1}{9}\right)$$

Me tahuri te 1 ki te hautau \frac{6}{6}.

$$\left(\frac{7}{6}-\frac{6}{6}\right)\left(2+\frac{1}{3}-\frac{2\times 9+1}{9}\right)$$

Tā te mea he rite te tauraro o \frac{7}{6} me \frac{6}{6}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{7-6}{6}\left(2+\frac{1}{3}-\frac{2\times 9+1}{9}\right)$$

Tangohia te 6 i te 7, ka 1.

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

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

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

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.

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

Tāpirihia te 6 ki te 1, ka 7.

$$\frac{1}{6}\left(\frac{7}{3}-\frac{2\times 9+1}{9}\right)$$

Whakareatia te 2 ki te 9, ka 18.

$$\frac{1}{6}\left(\frac{7}{3}-\frac{18+1}{9}\right)$$

Tāpirihia te 18 ki te 1, ka 19.

$$\frac{1}{6}\left(\frac{7}{3}-\frac{19}{9}\right)$$

Ko te maha noa iti rawa atu o 3 me 9 ko 9. Me tahuri \frac{7}{3} me \frac{19}{9} ki te hautau me te tautūnga 9.

$$\frac{1}{6}\left(\frac{21}{9}-\frac{19}{9}\right)$$

Tā te mea he rite te tauraro o \frac{21}{9} me \frac{19}{9}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{1}{6}\times \frac{21-19}{9}$$

Tangohia te 19 i te 21, ka 2.

$$\frac{1}{6}\times \frac{2}{9}$$

Me whakarea te \frac{1}{6} ki te \frac{2}{9} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{1\times 2}{6\times 9}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 2}{6\times 9}.

$$\frac{2}{54}$$

Whakahekea te hautanga \frac{2}{54} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{1}{27}$$

Tauwehe

$$\frac{1}{3 ^ {3}} = 0.037037037037037035$$