Whakaoti i te ((11/7-23/49):22/147-(06:33/4)2frac{1}{2}+375:1frac{1}{2}):22

$$( ( 1 \frac { 1 } { 7 } - \frac { 23 } { 49 } ) : \frac { 22 } { 147 } - ( 06 : 3 \frac { 3 } { 4 } ) 2 \frac { 1 } { 2 } + 375 : 1 \frac { 1 } { 2 } ) : 22$$

Aromātai

$$\frac{509}{44}\approx 11.568181818$$

Ngā Upane Otinga

Whakareatia te 1 ki te 7, ka 7.

$$\frac{\frac{\frac{7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Tāpirihia te 7 ki te 1, ka 8.

$$\frac{\frac{\frac{8}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Ko te maha noa iti rawa atu o 7 me 49 ko 49. Me tahuri \frac{8}{7} me \frac{23}{49} ki te hautau me te tautūnga 49.

$$\frac{\frac{\frac{56}{49}-\frac{23}{49}}{\frac{22}{147}}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Tā te mea he rite te tauraro o \frac{56}{49} me \frac{23}{49}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{\frac{56-23}{49}}{\frac{22}{147}}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Tangohia te 23 i te 56, ka 33.

$$\frac{\frac{\frac{33}{49}}{\frac{22}{147}}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Whakawehe \frac{33}{49} ki te \frac{22}{147} mā te whakarea \frac{33}{49} ki te tau huripoki o \frac{22}{147}.

$$\frac{\frac{33}{49}\times \frac{147}{22}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Me whakarea te \frac{33}{49} ki te \frac{147}{22} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\frac{33\times 147}{49\times 22}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Mahia ngā whakarea i roto i te hautanga \frac{33\times 147}{49\times 22}.

$$\frac{\frac{4851}{1078}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Whakahekea te hautanga \frac{4851}{1078} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 539.

$$\frac{\frac{9}{2}-\frac{0\times 6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Whakareatia te 0 ki te 6, ka 0.

$$\frac{\frac{9}{2}-\frac{0}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Whakareatia te 3 ki te 4, ka 12.

$$\frac{\frac{9}{2}-\frac{0}{\frac{12+3}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Tāpirihia te 12 ki te 3, ka 15.

$$\frac{\frac{9}{2}-\frac{0}{\frac{15}{4}}\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Ko te kore i whakawehea ki te tau ehara te kore ka hua ko te kore.

$$\frac{\frac{9}{2}-0\times \frac{2\times 2+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Whakareatia te 2 ki te 2, ka 4.

$$\frac{\frac{9}{2}-0\times \frac{4+1}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Tāpirihia te 4 ki te 1, ka 5.

$$\frac{\frac{9}{2}-0\times \frac{5}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Whakareatia te 0 ki te \frac{5}{2}, ka 0.

$$\frac{\frac{9}{2}-0+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Tangohia te 0 i te \frac{9}{2}, ka \frac{9}{2}.

$$\frac{\frac{9}{2}+\frac{375}{\frac{1\times 2+1}{2}}}{22}$$

Whakawehe 375 ki te \frac{1\times 2+1}{2} mā te whakarea 375 ki te tau huripoki o \frac{1\times 2+1}{2}.

$$\frac{\frac{9}{2}+\frac{375\times 2}{1\times 2+1}}{22}$$

Whakareatia te 375 ki te 2, ka 750.

$$\frac{\frac{9}{2}+\frac{750}{1\times 2+1}}{22}$$

Whakareatia te 1 ki te 2, ka 2.

$$\frac{\frac{9}{2}+\frac{750}{2+1}}{22}$$

Tāpirihia te 2 ki te 1, ka 3.

$$\frac{\frac{9}{2}+\frac{750}{3}}{22}$$

Whakawehea te 750 ki te 3, kia riro ko 250.

$$\frac{\frac{9}{2}+250}{22}$$

Me tahuri te 250 ki te hautau \frac{500}{2}.

$$\frac{\frac{9}{2}+\frac{500}{2}}{22}$$

Tā te mea he rite te tauraro o \frac{9}{2} me \frac{500}{2}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{9+500}{2}}{22}$$

Tāpirihia te 9 ki te 500, ka 509.

$$\frac{\frac{509}{2}}{22}$$

Tuhia te \frac{\frac{509}{2}}{22} hei hautanga kotahi.

$$\frac{509}{2\times 22}$$

Whakareatia te 2 ki te 22, ka 44.

$$\frac{509}{44}$$

Tauwehe

$$\frac{509}{2 ^ {2} \cdot 11} = 11\frac{25}{44} = 11.568181818181818$$