Whakaoti i te 1+1/4/frac{frac{1{2}}{1+2/3}-1-frac{1/4}{frac{1}{3}}}*(10frac{1}{3}-3frac{2}{3})

$$\frac { 1 + \frac { 1 } { 4 } } { \frac { \frac { 1 } { 2 } } { 1 + \frac { 2 } { 3 } } - \frac { 1 - \frac { 1 } { 4 } } { \frac { 1 } { 3 } } } \times ( 10 \frac { 1 } { 3 } - 3 \frac { 2 } { 3 } )$$

Aromātai

$$-\frac{500}{117}\approx -4.273504274$$

Ngā Upane Otinga

Me tahuri te 1 ki te hautau \frac{4}{4}.

$$\frac{\frac{4}{4}+\frac{1}{4}}{\frac{\frac{1}{2}}{1+\frac{2}{3}}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Tā te mea he rite te tauraro o \frac{4}{4} me \frac{1}{4}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{4+1}{4}}{\frac{\frac{1}{2}}{1+\frac{2}{3}}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Tāpirihia te 4 ki te 1, ka 5.

$$\frac{\frac{5}{4}}{\frac{\frac{1}{2}}{1+\frac{2}{3}}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Me tahuri te 1 ki te hautau \frac{3}{3}.

$$\frac{\frac{5}{4}}{\frac{\frac{1}{2}}{\frac{3}{3}+\frac{2}{3}}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Tā te mea he rite te tauraro o \frac{3}{3} me \frac{2}{3}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{5}{4}}{\frac{\frac{1}{2}}{\frac{3+2}{3}}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Tāpirihia te 3 ki te 2, ka 5.

$$\frac{\frac{5}{4}}{\frac{\frac{1}{2}}{\frac{5}{3}}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Whakawehe \frac{1}{2} ki te \frac{5}{3} mā te whakarea \frac{1}{2} ki te tau huripoki o \frac{5}{3}.

$$\frac{\frac{5}{4}}{\frac{1}{2}\times \frac{3}{5}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Me whakarea te \frac{1}{2} ki te \frac{3}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\frac{5}{4}}{\frac{1\times 3}{2\times 5}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 3}{2\times 5}.

$$\frac{\frac{5}{4}}{\frac{3}{10}-\frac{1-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Me tahuri te 1 ki te hautau \frac{4}{4}.

$$\frac{\frac{5}{4}}{\frac{3}{10}-\frac{\frac{4}{4}-\frac{1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Tā te mea he rite te tauraro o \frac{4}{4} me \frac{1}{4}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{5}{4}}{\frac{3}{10}-\frac{\frac{4-1}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Tangohia te 1 i te 4, ka 3.

$$\frac{\frac{5}{4}}{\frac{3}{10}-\frac{\frac{3}{4}}{\frac{1}{3}}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Whakawehe \frac{3}{4} ki te \frac{1}{3} mā te whakarea \frac{3}{4} ki te tau huripoki o \frac{1}{3}.

$$\frac{\frac{5}{4}}{\frac{3}{10}-\frac{3}{4}\times 3}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Tuhia te \frac{3}{4}\times 3 hei hautanga kotahi.

$$\frac{\frac{5}{4}}{\frac{3}{10}-\frac{3\times 3}{4}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Whakareatia te 3 ki te 3, ka 9.

$$\frac{\frac{5}{4}}{\frac{3}{10}-\frac{9}{4}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Ko te maha noa iti rawa atu o 10 me 4 ko 20. Me tahuri \frac{3}{10} me \frac{9}{4} ki te hautau me te tautūnga 20.

$$\frac{\frac{5}{4}}{\frac{6}{20}-\frac{45}{20}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Tā te mea he rite te tauraro o \frac{6}{20} me \frac{45}{20}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{5}{4}}{\frac{6-45}{20}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Tangohia te 45 i te 6, ka -39.

$$\frac{\frac{5}{4}}{-\frac{39}{20}}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Whakawehe \frac{5}{4} ki te -\frac{39}{20} mā te whakarea \frac{5}{4} ki te tau huripoki o -\frac{39}{20}.

$$\frac{5}{4}\left(-\frac{20}{39}\right)\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Me whakarea te \frac{5}{4} ki te -\frac{20}{39} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{5\left(-20\right)}{4\times 39}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Mahia ngā whakarea i roto i te hautanga \frac{5\left(-20\right)}{4\times 39}.

$$\frac{-100}{156}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Whakahekea te hautanga \frac{-100}{156} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 4.

$$-\frac{25}{39}\left(\frac{10\times 3+1}{3}-\frac{3\times 3+2}{3}\right)$$

Whakareatia te 10 ki te 3, ka 30.

$$-\frac{25}{39}\left(\frac{30+1}{3}-\frac{3\times 3+2}{3}\right)$$

Tāpirihia te 30 ki te 1, ka 31.

$$-\frac{25}{39}\left(\frac{31}{3}-\frac{3\times 3+2}{3}\right)$$

Whakareatia te 3 ki te 3, ka 9.

$$-\frac{25}{39}\left(\frac{31}{3}-\frac{9+2}{3}\right)$$

Tāpirihia te 9 ki te 2, ka 11.

$$-\frac{25}{39}\left(\frac{31}{3}-\frac{11}{3}\right)$$

Tā te mea he rite te tauraro o \frac{31}{3} me \frac{11}{3}, me tango rāua mā te tango i ō raua taurunga.

$$-\frac{25}{39}\times \frac{31-11}{3}$$

Tangohia te 11 i te 31, ka 20.

$$-\frac{25}{39}\times \frac{20}{3}$$

Me whakarea te -\frac{25}{39} ki te \frac{20}{3} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{-25\times 20}{39\times 3}$$

Mahia ngā whakarea i roto i te hautanga \frac{-25\times 20}{39\times 3}.

$$\frac{-500}{117}$$

Ka taea te hautanga \frac{-500}{117} te tuhi anō ko -\frac{500}{117} mā te tango i te tohu tōraro.

$$-\frac{500}{117}$$

Tauwehe

$$-\frac{500}{117} = -4\frac{32}{117} = -4.273504273504273$$