Whakaoti i te ((11/7-23/49):22/147-(0.6:33/4)2frac{1}{2}+3.75:1frac{1}{2}):2.2

$$( ( 1 \frac { 1 } { 7 } - \frac { 23 } { 49 } ) : \frac { 22 } { 147 } - ( 0.6 : 3 \frac { 3 } { 4 } ) 2 \frac { 1 } { 2 } + 3.75 : 1 \frac { 1 } { 2 } ) : 2.2$$

Aromātai

$$3$$

Ngā Upane Otinga

Whakareatia te 1 ki te 7, ka 7.

$$\frac{\frac{\frac{7+1}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Tāpirihia te 7 ki te 1, ka 8.

$$\frac{\frac{\frac{8}{7}-\frac{23}{49}}{\frac{22}{147}}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

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.

$$\frac{\frac{\frac{56}{49}-\frac{23}{49}}{\frac{22}{147}}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

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.

$$\frac{\frac{\frac{56-23}{49}}{\frac{22}{147}}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Tangohia te 23 i te 56, ka 33.

$$\frac{\frac{\frac{33}{49}}{\frac{22}{147}}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

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

$$\frac{\frac{33}{49}\times \frac{147}{22}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

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

$$\frac{\frac{33\times 147}{49\times 22}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

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

$$\frac{\frac{4851}{1078}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

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

$$\frac{\frac{9}{2}-\frac{0.6}{\frac{3\times 4+3}{4}}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Whakawehe 0.6 ki te \frac{3\times 4+3}{4} mā te whakarea 0.6 ki te tau huripoki o \frac{3\times 4+3}{4}.

$$\frac{\frac{9}{2}-\frac{0.6\times 4}{3\times 4+3}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Whakareatia te 0.6 ki te 4, ka 2.4.

$$\frac{\frac{9}{2}-\frac{2.4}{3\times 4+3}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Whakareatia te 3 ki te 4, ka 12.

$$\frac{\frac{9}{2}-\frac{2.4}{12+3}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Tāpirihia te 12 ki te 3, ka 15.

$$\frac{\frac{9}{2}-\frac{2.4}{15}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Whakarohaina te \frac{2.4}{15} mā te whakarea i te taurunga me te tauraro ki te 10.

$$\frac{\frac{9}{2}-\frac{24}{150}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Whakahekea te hautanga \frac{24}{150} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 6.

$$\frac{\frac{9}{2}-\frac{4}{25}\times \frac{2\times 2+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Whakareatia te 2 ki te 2, ka 4.

$$\frac{\frac{9}{2}-\frac{4}{25}\times \frac{4+1}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Tāpirihia te 4 ki te 1, ka 5.

$$\frac{\frac{9}{2}-\frac{4}{25}\times \frac{5}{2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Me whakarea te \frac{4}{25} ki te \frac{5}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{\frac{9}{2}-\frac{4\times 5}{25\times 2}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Mahia ngā whakarea i roto i te hautanga \frac{4\times 5}{25\times 2}.

$$\frac{\frac{9}{2}-\frac{20}{50}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Whakahekea te hautanga \frac{20}{50} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 10.

$$\frac{\frac{9}{2}-\frac{2}{5}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Ko te maha noa iti rawa atu o 2 me 5 ko 10. Me tahuri \frac{9}{2} me \frac{2}{5} ki te hautau me te tautūnga 10.

$$\frac{\frac{45}{10}-\frac{4}{10}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Tā te mea he rite te tauraro o \frac{45}{10} me \frac{4}{10}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{\frac{45-4}{10}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Tangohia te 4 i te 45, ka 41.

$$\frac{\frac{41}{10}+\frac{3.75}{\frac{1\times 2+1}{2}}}{2.2}$$

Whakawehe 3.75 ki te \frac{1\times 2+1}{2} mā te whakarea 3.75 ki te tau huripoki o \frac{1\times 2+1}{2}.

$$\frac{\frac{41}{10}+\frac{3.75\times 2}{1\times 2+1}}{2.2}$$

Whakareatia te 3.75 ki te 2, ka 7.5.

$$\frac{\frac{41}{10}+\frac{7.5}{1\times 2+1}}{2.2}$$

Whakareatia te 1 ki te 2, ka 2.

$$\frac{\frac{41}{10}+\frac{7.5}{2+1}}{2.2}$$

Tāpirihia te 2 ki te 1, ka 3.

$$\frac{\frac{41}{10}+\frac{7.5}{3}}{2.2}$$

Whakarohaina te \frac{7.5}{3} mā te whakarea i te taurunga me te tauraro ki te 10.

$$\frac{\frac{41}{10}+\frac{75}{30}}{2.2}$$

Whakahekea te hautanga \frac{75}{30} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 15.

$$\frac{\frac{41}{10}+\frac{5}{2}}{2.2}$$

Ko te maha noa iti rawa atu o 10 me 2 ko 10. Me tahuri \frac{41}{10} me \frac{5}{2} ki te hautau me te tautūnga 10.

$$\frac{\frac{41}{10}+\frac{25}{10}}{2.2}$$

Tā te mea he rite te tauraro o \frac{41}{10} me \frac{25}{10}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{\frac{41+25}{10}}{2.2}$$

Tāpirihia te 41 ki te 25, ka 66.

$$\frac{\frac{66}{10}}{2.2}$$

Whakahekea te hautanga \frac{66}{10} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{\frac{33}{5}}{2.2}$$

Tuhia te \frac{\frac{33}{5}}{2.2} hei hautanga kotahi.

$$\frac{33}{5\times 2.2}$$

Whakareatia te 5 ki te 2.2, ka 11.

$$\frac{33}{11}$$

Whakawehea te 33 ki te 11, kia riro ko 3.

$$3$$

Tauwehe

$$3$$