Whakaoti i te (12/3+41/2+25/6):(43/10+3frac{1}{5}+1frac{7}{20})

$$( 1 \frac { 2 } { 3 } + 4 \frac { 1 } { 2 } + 2 \frac { 5 } { 6 } ) : ( 4 \frac { 3 } { 10 } + 3 \frac { 1 } { 5 } + 1 \frac { 7 } { 20 } )$$

Aromātai

$$\frac{60}{59}\approx 1.016949153$$

Ngā Upane Otinga

Whakareatia te 1 ki te 3, ka 3.

$$\frac{\frac{3+2}{3}+\frac{4\times 2+1}{2}+\frac{2\times 6+5}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Tāpirihia te 3 ki te 2, ka 5.

$$\frac{\frac{5}{3}+\frac{4\times 2+1}{2}+\frac{2\times 6+5}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Whakareatia te 4 ki te 2, ka 8.

$$\frac{\frac{5}{3}+\frac{8+1}{2}+\frac{2\times 6+5}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Tāpirihia te 8 ki te 1, ka 9.

$$\frac{\frac{5}{3}+\frac{9}{2}+\frac{2\times 6+5}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Ko te maha noa iti rawa atu o 3 me 2 ko 6. Me tahuri \frac{5}{3} me \frac{9}{2} ki te hautau me te tautūnga 6.

$$\frac{\frac{10}{6}+\frac{27}{6}+\frac{2\times 6+5}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Tā te mea he rite te tauraro o \frac{10}{6} me \frac{27}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{10+27}{6}+\frac{2\times 6+5}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Tāpirihia te 10 ki te 27, ka 37.

$$\frac{\frac{37}{6}+\frac{2\times 6+5}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Whakareatia te 2 ki te 6, ka 12.

$$\frac{\frac{37}{6}+\frac{12+5}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Tāpirihia te 12 ki te 5, ka 17.

$$\frac{\frac{37}{6}+\frac{17}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Tā te mea he rite te tauraro o \frac{37}{6} me \frac{17}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{37+17}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Tāpirihia te 37 ki te 17, ka 54.

$$\frac{\frac{54}{6}}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Whakawehea te 54 ki te 6, kia riro ko 9.

$$\frac{9}{\frac{4\times 10+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Whakareatia te 4 ki te 10, ka 40.

$$\frac{9}{\frac{40+3}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Tāpirihia te 40 ki te 3, ka 43.

$$\frac{9}{\frac{43}{10}+\frac{3\times 5+1}{5}+\frac{1\times 20+7}{20}}$$

Whakareatia te 3 ki te 5, ka 15.

$$\frac{9}{\frac{43}{10}+\frac{15+1}{5}+\frac{1\times 20+7}{20}}$$

Tāpirihia te 15 ki te 1, ka 16.

$$\frac{9}{\frac{43}{10}+\frac{16}{5}+\frac{1\times 20+7}{20}}$$

Ko te maha noa iti rawa atu o 10 me 5 ko 10. Me tahuri \frac{43}{10} me \frac{16}{5} ki te hautau me te tautūnga 10.

$$\frac{9}{\frac{43}{10}+\frac{32}{10}+\frac{1\times 20+7}{20}}$$

Tā te mea he rite te tauraro o \frac{43}{10} me \frac{32}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{9}{\frac{43+32}{10}+\frac{1\times 20+7}{20}}$$

Tāpirihia te 43 ki te 32, ka 75.

$$\frac{9}{\frac{75}{10}+\frac{1\times 20+7}{20}}$$

Whakahekea te hautanga \frac{75}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\frac{9}{\frac{15}{2}+\frac{1\times 20+7}{20}}$$

Whakareatia te 1 ki te 20, ka 20.

$$\frac{9}{\frac{15}{2}+\frac{20+7}{20}}$$

Tāpirihia te 20 ki te 7, ka 27.

$$\frac{9}{\frac{15}{2}+\frac{27}{20}}$$

Ko te maha noa iti rawa atu o 2 me 20 ko 20. Me tahuri \frac{15}{2} me \frac{27}{20} ki te hautau me te tautūnga 20.

$$\frac{9}{\frac{150}{20}+\frac{27}{20}}$$

Tā te mea he rite te tauraro o \frac{150}{20} me \frac{27}{20}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{9}{\frac{150+27}{20}}$$

Tāpirihia te 150 ki te 27, ka 177.

$$\frac{9}{\frac{177}{20}}$$

Whakawehe 9 ki te \frac{177}{20} mā te whakarea 9 ki te tau huripoki o \frac{177}{20}.

$$9\times \frac{20}{177}$$

Tuhia te 9\times \frac{20}{177} hei hautanga kotahi.

$$\frac{9\times 20}{177}$$

Whakareatia te 9 ki te 20, ka 180.

$$\frac{180}{177}$$

Whakahekea te hautanga \frac{180}{177} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{60}{59}$$

Tauwehe

$$\frac{2 ^ {2} \cdot 3 \cdot 5}{59} = 1\frac{1}{59} = 1.0169491525423728$$