Whakaoti i te 3/5+25/7(-3/12)+(-5/12)=?

$$\frac { 3 } { 5 } + \frac { 25 } { 7 } ( - \frac { 3 } { 12 } ) + ( - \frac { 5 } { 12 } ) = ?$$

Aromātai

$$-\frac{149}{210}\approx -0.70952381$$

Ngā Upane Otinga

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

$$\frac{3}{5}+\frac{25}{7}\left(-\frac{1}{4}\right)-\frac{5}{12}$$

Me whakarea te \frac{25}{7} ki te -\frac{1}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{3}{5}+\frac{25\left(-1\right)}{7\times 4}-\frac{5}{12}$$

Mahia ngā whakarea i roto i te hautanga \frac{25\left(-1\right)}{7\times 4}.

$$\frac{3}{5}+\frac{-25}{28}-\frac{5}{12}$$

Ka taea te hautanga \frac{-25}{28} te tuhi anō ko -\frac{25}{28} mā te tango i te tohu tōraro.

$$\frac{3}{5}-\frac{25}{28}-\frac{5}{12}$$

Ko te maha noa iti rawa atu o 5 me 28 ko 140. Me tahuri \frac{3}{5} me \frac{25}{28} ki te hautau me te tautūnga 140.

$$\frac{84}{140}-\frac{125}{140}-\frac{5}{12}$$

Tā te mea he rite te tauraro o \frac{84}{140} me \frac{125}{140}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{84-125}{140}-\frac{5}{12}$$

Tangohia te 125 i te 84, ka -41.

$$-\frac{41}{140}-\frac{5}{12}$$

Ko te maha noa iti rawa atu o 140 me 12 ko 420. Me tahuri -\frac{41}{140} me \frac{5}{12} ki te hautau me te tautūnga 420.

$$-\frac{123}{420}-\frac{175}{420}$$

Tā te mea he rite te tauraro o -\frac{123}{420} me \frac{175}{420}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{-123-175}{420}$$

Tangohia te 175 i te -123, ka -298.

$$\frac{-298}{420}$$

Whakahekea te hautanga \frac{-298}{420} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$-\frac{149}{210}$$

Tauwehe

$$-\frac{149}{210} = -0.7095238095238096$$