Whakaoti i te (-122/3)div14-(-81/3)div(-14)+101/3div14

$$( - 12 \frac { 2 } { 3 } ) \div 14 - ( - 8 \frac { 1 } { 3 } ) \div ( - 14 ) + 10 \frac { 1 } { 3 } \div 14$$

Aromātai

$$-\frac{16}{21}\approx -0.761904762$$

Ngā Upane Otinga

Whakareatia te 12 ki te 3, ka 36.

$$\frac{-\frac{36+2}{3}}{14}-\frac{-\frac{8\times 3+1}{3}}{-14}+\frac{\frac{10\times 3+1}{3}}{14}$$

Tāpirihia te 36 ki te 2, ka 38.

$$\frac{-\frac{38}{3}}{14}-\frac{-\frac{8\times 3+1}{3}}{-14}+\frac{\frac{10\times 3+1}{3}}{14}$$

Tuhia te \frac{-\frac{38}{3}}{14} hei hautanga kotahi.

$$\frac{-38}{3\times 14}-\frac{-\frac{8\times 3+1}{3}}{-14}+\frac{\frac{10\times 3+1}{3}}{14}$$

Whakareatia te 3 ki te 14, ka 42.

$$\frac{-38}{42}-\frac{-\frac{8\times 3+1}{3}}{-14}+\frac{\frac{10\times 3+1}{3}}{14}$$

Whakahekea te hautanga \frac{-38}{42} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$-\frac{19}{21}-\frac{-\frac{8\times 3+1}{3}}{-14}+\frac{\frac{10\times 3+1}{3}}{14}$$

Whakareatia te 8 ki te 3, ka 24.

$$-\frac{19}{21}-\frac{-\frac{24+1}{3}}{-14}+\frac{\frac{10\times 3+1}{3}}{14}$$

Tāpirihia te 24 ki te 1, ka 25.

$$-\frac{19}{21}-\frac{-\frac{25}{3}}{-14}+\frac{\frac{10\times 3+1}{3}}{14}$$

Tuhia te \frac{-\frac{25}{3}}{-14} hei hautanga kotahi.

$$-\frac{19}{21}-\frac{-25}{3\left(-14\right)}+\frac{\frac{10\times 3+1}{3}}{14}$$

Whakareatia te 3 ki te -14, ka -42.

$$-\frac{19}{21}-\frac{-25}{-42}+\frac{\frac{10\times 3+1}{3}}{14}$$

Ka taea te hautanga \frac{-25}{-42} te whakamāmā ki te \frac{25}{42} mā te tango tahi i te tohu tōraro i te taurunga me te tauraro.

$$-\frac{19}{21}-\frac{25}{42}+\frac{\frac{10\times 3+1}{3}}{14}$$

Ko te maha noa iti rawa atu o 21 me 42 ko 42. Me tahuri -\frac{19}{21} me \frac{25}{42} ki te hautau me te tautūnga 42.

$$-\frac{38}{42}-\frac{25}{42}+\frac{\frac{10\times 3+1}{3}}{14}$$

Tā te mea he rite te tauraro o -\frac{38}{42} me \frac{25}{42}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{-38-25}{42}+\frac{\frac{10\times 3+1}{3}}{14}$$

Tangohia te 25 i te -38, ka -63.

$$\frac{-63}{42}+\frac{\frac{10\times 3+1}{3}}{14}$$

Whakahekea te hautanga \frac{-63}{42} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 21.

$$-\frac{3}{2}+\frac{\frac{10\times 3+1}{3}}{14}$$

Tuhia te \frac{\frac{10\times 3+1}{3}}{14} hei hautanga kotahi.

$$-\frac{3}{2}+\frac{10\times 3+1}{3\times 14}$$

Whakareatia te 10 ki te 3, ka 30.

$$-\frac{3}{2}+\frac{30+1}{3\times 14}$$

Tāpirihia te 30 ki te 1, ka 31.

$$-\frac{3}{2}+\frac{31}{3\times 14}$$

Whakareatia te 3 ki te 14, ka 42.

$$-\frac{3}{2}+\frac{31}{42}$$

Ko te maha noa iti rawa atu o 2 me 42 ko 42. Me tahuri -\frac{3}{2} me \frac{31}{42} ki te hautau me te tautūnga 42.

$$-\frac{63}{42}+\frac{31}{42}$$

Tā te mea he rite te tauraro o -\frac{63}{42} me \frac{31}{42}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{-63+31}{42}$$

Tāpirihia te -63 ki te 31, ka -32.

$$\frac{-32}{42}$$

Whakahekea te hautanga \frac{-32}{42} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$-\frac{16}{21}$$

Tauwehe

$$-\frac{16}{21} = -0.7619047619047619$$