Whakaoti i te (2/7*12/3+1/7*2/3)+(frac{2}{3}*2frac{1}{4}+frac{2}{3}*frac{3}{4})

$$( \frac { 2 } { 7 } \times 1 \frac { 2 } { 3 } + \frac { 1 } { 7 } \times \frac { 2 } { 3 } ) + ( \frac { 2 } { 3 } \times 2 \frac { 1 } { 4 } + \frac { 2 } { 3 } \times \frac { 3 } { 4 } )$$

Aromātai

$$\frac{18}{7}\approx 2.571428571$$

Ngā Upane Otinga

Whakareatia te 1 ki te 3, ka 3.

$$\frac{2}{7}\times \frac{3+2}{3}+\frac{1}{7}\times \frac{2}{3}+\frac{2}{3}\times \frac{2\times 4+1}{4}+\frac{2}{3}\times \frac{3}{4}$$

Tāpirihia te 3 ki te 2, ka 5.

$$\frac{2}{7}\times \frac{5}{3}+\frac{1}{7}\times \frac{2}{3}+\frac{2}{3}\times \frac{2\times 4+1}{4}+\frac{2}{3}\times \frac{3}{4}$$

Me whakarea te \frac{2}{7} ki te \frac{5}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{2\times 5}{7\times 3}+\frac{1}{7}\times \frac{2}{3}+\frac{2}{3}\times \frac{2\times 4+1}{4}+\frac{2}{3}\times \frac{3}{4}$$

Mahia ngā whakarea i roto i te hautanga \frac{2\times 5}{7\times 3}.

$$\frac{10}{21}+\frac{1}{7}\times \frac{2}{3}+\frac{2}{3}\times \frac{2\times 4+1}{4}+\frac{2}{3}\times \frac{3}{4}$$

Me whakarea te \frac{1}{7} ki te \frac{2}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{10}{21}+\frac{1\times 2}{7\times 3}+\frac{2}{3}\times \frac{2\times 4+1}{4}+\frac{2}{3}\times \frac{3}{4}$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 2}{7\times 3}.

$$\frac{10}{21}+\frac{2}{21}+\frac{2}{3}\times \frac{2\times 4+1}{4}+\frac{2}{3}\times \frac{3}{4}$$

Tā te mea he rite te tauraro o \frac{10}{21} me \frac{2}{21}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{10+2}{21}+\frac{2}{3}\times \frac{2\times 4+1}{4}+\frac{2}{3}\times \frac{3}{4}$$

Tāpirihia te 10 ki te 2, ka 12.

$$\frac{12}{21}+\frac{2}{3}\times \frac{2\times 4+1}{4}+\frac{2}{3}\times \frac{3}{4}$$

Whakahekea te hautanga \frac{12}{21} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{4}{7}+\frac{2}{3}\times \frac{2\times 4+1}{4}+\frac{2}{3}\times \frac{3}{4}$$

Whakareatia te 2 ki te 4, ka 8.

$$\frac{4}{7}+\frac{2}{3}\times \frac{8+1}{4}+\frac{2}{3}\times \frac{3}{4}$$

Tāpirihia te 8 ki te 1, ka 9.

$$\frac{4}{7}+\frac{2}{3}\times \frac{9}{4}+\frac{2}{3}\times \frac{3}{4}$$

Me whakarea te \frac{2}{3} ki te \frac{9}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{4}{7}+\frac{2\times 9}{3\times 4}+\frac{2}{3}\times \frac{3}{4}$$

Mahia ngā whakarea i roto i te hautanga \frac{2\times 9}{3\times 4}.

$$\frac{4}{7}+\frac{18}{12}+\frac{2}{3}\times \frac{3}{4}$$

Whakahekea te hautanga \frac{18}{12} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$\frac{4}{7}+\frac{3}{2}+\frac{2}{3}\times \frac{3}{4}$$

Ko te maha noa iti rawa atu o 7 me 2 ko 14. Me tahuri \frac{4}{7} me \frac{3}{2} ki te hautau me te tautūnga 14.

$$\frac{8}{14}+\frac{21}{14}+\frac{2}{3}\times \frac{3}{4}$$

Tā te mea he rite te tauraro o \frac{8}{14} me \frac{21}{14}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{8+21}{14}+\frac{2}{3}\times \frac{3}{4}$$

Tāpirihia te 8 ki te 21, ka 29.

$$\frac{29}{14}+\frac{2}{3}\times \frac{3}{4}$$

Me whakarea te \frac{2}{3} ki te \frac{3}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{29}{14}+\frac{2\times 3}{3\times 4}$$

Me whakakore tahi te 3 i te taurunga me te tauraro.

$$\frac{29}{14}+\frac{2}{4}$$

Whakahekea te hautanga \frac{2}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{29}{14}+\frac{1}{2}$$

Ko te maha noa iti rawa atu o 14 me 2 ko 14. Me tahuri \frac{29}{14} me \frac{1}{2} ki te hautau me te tautūnga 14.

$$\frac{29}{14}+\frac{7}{14}$$

Tā te mea he rite te tauraro o \frac{29}{14} me \frac{7}{14}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{29+7}{14}$$

Tāpirihia te 29 ki te 7, ka 36.

$$\frac{36}{14}$$

Whakahekea te hautanga \frac{36}{14} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{18}{7}$$

Tauwehe

$$\frac{2 \cdot 3 ^ {2}}{7} = 2\frac{4}{7} = 2.5714285714285716$$