Whakaoti i te 21/13*(1/5-1/12)-7:31/2

$$2 \frac { 1 } { 13 } \cdot ( \frac { 1 } { 5 } - \frac { 1 } { 12 } ) - 7 : 3 \frac { 1 } { 2 }$$

Aromātai

$$-\frac{457}{260}\approx -1.757692308$$

Ngā Upane Otinga

Whakareatia te 2 ki te 13, ka 26.

$$\frac{26+1}{13}\left(\frac{1}{5}-\frac{1}{12}\right)-\frac{7}{\frac{3\times 2+1}{2}}$$

Tāpirihia te 26 ki te 1, ka 27.

$$\frac{27}{13}\left(\frac{1}{5}-\frac{1}{12}\right)-\frac{7}{\frac{3\times 2+1}{2}}$$

Ko te maha noa iti rawa atu o 5 me 12 ko 60. Me tahuri \frac{1}{5} me \frac{1}{12} ki te hautau me te tautūnga 60.

$$\frac{27}{13}\left(\frac{12}{60}-\frac{5}{60}\right)-\frac{7}{\frac{3\times 2+1}{2}}$$

Tā te mea he rite te tauraro o \frac{12}{60} me \frac{5}{60}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{27}{13}\times \frac{12-5}{60}-\frac{7}{\frac{3\times 2+1}{2}}$$

Tangohia te 5 i te 12, ka 7.

$$\frac{27}{13}\times \frac{7}{60}-\frac{7}{\frac{3\times 2+1}{2}}$$

Me whakarea te \frac{27}{13} ki te \frac{7}{60} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{27\times 7}{13\times 60}-\frac{7}{\frac{3\times 2+1}{2}}$$

Mahia ngā whakarea i roto i te hautanga \frac{27\times 7}{13\times 60}.

$$\frac{189}{780}-\frac{7}{\frac{3\times 2+1}{2}}$$

Whakahekea te hautanga \frac{189}{780} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{63}{260}-\frac{7}{\frac{3\times 2+1}{2}}$$

Whakawehe 7 ki te \frac{3\times 2+1}{2} mā te whakarea 7 ki te tau huripoki o \frac{3\times 2+1}{2}.

$$\frac{63}{260}-\frac{7\times 2}{3\times 2+1}$$

Whakareatia te 7 ki te 2, ka 14.

$$\frac{63}{260}-\frac{14}{3\times 2+1}$$

Whakareatia te 3 ki te 2, ka 6.

$$\frac{63}{260}-\frac{14}{6+1}$$

Tāpirihia te 6 ki te 1, ka 7.

$$\frac{63}{260}-\frac{14}{7}$$

Whakawehea te 14 ki te 7, kia riro ko 2.

$$\frac{63}{260}-2$$

Me tahuri te 2 ki te hautau \frac{520}{260}.

$$\frac{63}{260}-\frac{520}{260}$$

Tā te mea he rite te tauraro o \frac{63}{260} me \frac{520}{260}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{63-520}{260}$$

Tangohia te 520 i te 63, ka -457.

$$-\frac{457}{260}$$

Tauwehe

$$-\frac{457}{260} = -1\frac{197}{260} = -1.7576923076923077$$