Whakaoti i te -1/10+7/8-314/100=782/1000+frac{628}{100}

$$- \frac { 1 } { 10 } + \frac { 7 } { 8 } - \frac { 314 } { 100 } = \frac { 782 } { 1000 } + \frac { 628 } { 100 }$$

Manatoko

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 10 me 8 ko 40. Me tahuri -\frac{1}{10} me \frac{7}{8} ki te hautau me te tautūnga 40.

$$-\frac{4}{40}+\frac{35}{40}-\frac{314}{100}=\frac{782}{1000}+\frac{628}{100}$$

Tā te mea he rite te tauraro o -\frac{4}{40} me \frac{35}{40}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-4+35}{40}-\frac{314}{100}=\frac{782}{1000}+\frac{628}{100}$$

Tāpirihia te -4 ki te 35, ka 31.

$$\frac{31}{40}-\frac{314}{100}=\frac{782}{1000}+\frac{628}{100}$$

Whakahekea te hautanga \frac{314}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{31}{40}-\frac{157}{50}=\frac{782}{1000}+\frac{628}{100}$$

Ko te maha noa iti rawa atu o 40 me 50 ko 200. Me tahuri \frac{31}{40} me \frac{157}{50} ki te hautau me te tautūnga 200.

$$\frac{155}{200}-\frac{628}{200}=\frac{782}{1000}+\frac{628}{100}$$

Tā te mea he rite te tauraro o \frac{155}{200} me \frac{628}{200}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{155-628}{200}=\frac{782}{1000}+\frac{628}{100}$$

Tangohia te 628 i te 155, ka -473.

$$-\frac{473}{200}=\frac{782}{1000}+\frac{628}{100}$$

Whakahekea te hautanga \frac{782}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$-\frac{473}{200}=\frac{391}{500}+\frac{628}{100}$$

Whakahekea te hautanga \frac{628}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$-\frac{473}{200}=\frac{391}{500}+\frac{157}{25}$$

Ko te maha noa iti rawa atu o 500 me 25 ko 500. Me tahuri \frac{391}{500} me \frac{157}{25} ki te hautau me te tautūnga 500.

$$-\frac{473}{200}=\frac{391}{500}+\frac{3140}{500}$$

Tā te mea he rite te tauraro o \frac{391}{500} me \frac{3140}{500}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$-\frac{473}{200}=\frac{391+3140}{500}$$

Tāpirihia te 391 ki te 3140, ka 3531.

$$-\frac{473}{200}=\frac{3531}{500}$$

Ko te maha noa iti rawa atu o 200 me 500 ko 1000. Me tahuri -\frac{473}{200} me \frac{3531}{500} ki te hautau me te tautūnga 1000.

$$-\frac{2365}{1000}=\frac{7062}{1000}$$

Whakatauritea te -\frac{2365}{1000} me te \frac{7062}{1000}.

$$\text{false}$$