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

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

Aromātai

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Ngā Upane Otinga

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

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

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.

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

Tāpirihia te 4 ki te 1, ka 5.

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

Whakawehe \frac{5}{4} ki te \frac{1}{2} mā te whakarea \frac{5}{4} ki te tau huripoki o \frac{1}{2}.

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

Tuhia te \frac{5}{4}\times 2 hei hautanga kotahi.

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

Whakareatia te 5 ki te 2, ka 10.

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

Whakahekea te hautanga \frac{10}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

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

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

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

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.

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

Tangohia te 1 i te 4, ka 3.

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

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

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

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

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

Whakareatia te 3 ki te 3, ka 9.

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

Ko te maha noa iti rawa atu o 2 me 4 ko 4. Me tahuri \frac{5}{2} me \frac{9}{4} ki te hautau me te tautūnga 4.

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

Tā te mea he rite te tauraro o \frac{10}{4} me \frac{9}{4}, me tango rāua mā te tango i ō raua taurunga.

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

Tangohia te 9 i te 10, ka 1.

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

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

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

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.

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

Tāpirihia te 3 ki te 2, ka 5.

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

Whakawehe \frac{1}{4} ki te \frac{5}{3} mā te whakarea \frac{1}{4} ki te tau huripoki o \frac{5}{3}.

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

Me whakarea te \frac{1}{4} ki te \frac{3}{5} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Mahia ngā whakarea i roto i te hautanga \frac{1\times 3}{4\times 5}.

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

Whakareatia te 10 ki te 3, ka 30.

$$\frac{3}{20}\left(\frac{30+1}{3}-\frac{3\times 3+2}{3}\right)$$

Tāpirihia te 30 ki te 1, ka 31.

$$\frac{3}{20}\left(\frac{31}{3}-\frac{3\times 3+2}{3}\right)$$

Whakareatia te 3 ki te 3, ka 9.

$$\frac{3}{20}\left(\frac{31}{3}-\frac{9+2}{3}\right)$$

Tāpirihia te 9 ki te 2, ka 11.

$$\frac{3}{20}\left(\frac{31}{3}-\frac{11}{3}\right)$$

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.

$$\frac{3}{20}\times \frac{31-11}{3}$$

Tangohia te 11 i te 31, ka 20.

$$\frac{3}{20}\times \frac{20}{3}$$

Me whakakore atu te \frac{3}{20} me tōna tau utu \frac{20}{3}.

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Tauwehe

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