Whakaoti i te (1/2+2/5)div(3/4-1/5)=frac{3}{7}

$$( \frac{ 1 }{ 2 } + \frac{ 2 }{ 5 } ) \div ( \frac{ 3 }{ 4 } - \frac{ 1 }{ 5 } )= \frac{ 3 }{ 7 }$$

Manatoko

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 2 me 5 ko 10. Me tahuri \frac{1}{2} me \frac{2}{5} ki te hautau me te tautūnga 10.

$$\frac{\frac{5}{10}+\frac{4}{10}}{\frac{3}{4}-\frac{1}{5}}=\frac{3}{7}$$

Tā te mea he rite te tauraro o \frac{5}{10} me \frac{4}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{5+4}{10}}{\frac{3}{4}-\frac{1}{5}}=\frac{3}{7}$$

Tāpirihia te 5 ki te 4, ka 9.

$$\frac{\frac{9}{10}}{\frac{3}{4}-\frac{1}{5}}=\frac{3}{7}$$

Ko te maha noa iti rawa atu o 4 me 5 ko 20. Me tahuri \frac{3}{4} me \frac{1}{5} ki te hautau me te tautūnga 20.

$$\frac{\frac{9}{10}}{\frac{15}{20}-\frac{4}{20}}=\frac{3}{7}$$

Tā te mea he rite te tauraro o \frac{15}{20} me \frac{4}{20}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{9}{10}}{\frac{15-4}{20}}=\frac{3}{7}$$

Tangohia te 4 i te 15, ka 11.

$$\frac{\frac{9}{10}}{\frac{11}{20}}=\frac{3}{7}$$

Whakawehe \frac{9}{10} ki te \frac{11}{20} mā te whakarea \frac{9}{10} ki te tau huripoki o \frac{11}{20}.

$$\frac{9}{10}\times \frac{20}{11}=\frac{3}{7}$$

Me whakarea te \frac{9}{10} ki te \frac{20}{11} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{9\times 20}{10\times 11}=\frac{3}{7}$$

Mahia ngā whakarea i roto i te hautanga \frac{9\times 20}{10\times 11}.

$$\frac{180}{110}=\frac{3}{7}$$

Whakahekea te hautanga \frac{180}{110} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$\frac{18}{11}=\frac{3}{7}$$

Ko te maha noa iti rawa atu o 11 me 7 ko 77. Me tahuri \frac{18}{11} me \frac{3}{7} ki te hautau me te tautūnga 77.

$$\frac{126}{77}=\frac{33}{77}$$

Whakatauritea te \frac{126}{77} me te \frac{33}{77}.

$$\text{false}$$