Whakaoti i te {l}{5/7-1/3}{23/5-7/8}{4frac{1}{2}*1frac{3}{4}}{2frac{1}{3}divfrac{5}{7}}

$$\left. \begin{array} { l } { \frac { 5 } { 7 } - \frac { 1 } { 3 } } \\ { 2 \frac { 3 } { 5 } - \frac { 7 } { 8 } } \\ { 4 \frac { 1 } { 2 } \times 1 \frac { 3 } { 4 } } \\ { 2 \frac { 1 } { 3 } \div \frac { 5 } { 7 } } \end{array} \right.$$

Kōmaka

$$\frac{8}{21},\frac{69}{40},\frac{49}{15},\frac{63}{8}$$

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 7 me 3 ko 21. Me tahuri \frac{5}{7} me \frac{1}{3} ki te hautau me te tautūnga 21.

$$sort(\frac{15}{21}-\frac{7}{21},\frac{2\times 5+3}{5}-\frac{7}{8},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Tā te mea he rite te tauraro o \frac{15}{21} me \frac{7}{21}, me tango rāua mā te tango i ō raua taurunga.

$$sort(\frac{15-7}{21},\frac{2\times 5+3}{5}-\frac{7}{8},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Tangohia te 7 i te 15, ka 8.

$$sort(\frac{8}{21},\frac{2\times 5+3}{5}-\frac{7}{8},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Whakareatia te 2 ki te 5, ka 10.

$$sort(\frac{8}{21},\frac{10+3}{5}-\frac{7}{8},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Tāpirihia te 10 ki te 3, ka 13.

$$sort(\frac{8}{21},\frac{13}{5}-\frac{7}{8},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Ko te maha noa iti rawa atu o 5 me 8 ko 40. Me tahuri \frac{13}{5} me \frac{7}{8} ki te hautau me te tautūnga 40.

$$sort(\frac{8}{21},\frac{104}{40}-\frac{35}{40},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Tā te mea he rite te tauraro o \frac{104}{40} me \frac{35}{40}, me tango rāua mā te tango i ō raua taurunga.

$$sort(\frac{8}{21},\frac{104-35}{40},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Tangohia te 35 i te 104, ka 69.

$$sort(\frac{8}{21},\frac{69}{40},\frac{4\times 2+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Whakareatia te 4 ki te 2, ka 8.

$$sort(\frac{8}{21},\frac{69}{40},\frac{8+1}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Tāpirihia te 8 ki te 1, ka 9.

$$sort(\frac{8}{21},\frac{69}{40},\frac{9}{2}\times \frac{1\times 4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Whakareatia te 1 ki te 4, ka 4.

$$sort(\frac{8}{21},\frac{69}{40},\frac{9}{2}\times \frac{4+3}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Tāpirihia te 4 ki te 3, ka 7.

$$sort(\frac{8}{21},\frac{69}{40},\frac{9}{2}\times \frac{7}{4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Me whakarea te \frac{9}{2} ki te \frac{7}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$sort(\frac{8}{21},\frac{69}{40},\frac{9\times 7}{2\times 4},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Mahia ngā whakarea i roto i te hautanga \frac{9\times 7}{2\times 4}.

$$sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{\frac{2\times 3+1}{3}}{\frac{5}{7}})$$

Whakawehe \frac{2\times 3+1}{3} ki te \frac{5}{7} mā te whakarea \frac{2\times 3+1}{3} ki te tau huripoki o \frac{5}{7}.

$$sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{\left(2\times 3+1\right)\times 7}{3\times 5})$$

Whakareatia te 2 ki te 3, ka 6.

$$sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{\left(6+1\right)\times 7}{3\times 5})$$

Tāpirihia te 6 ki te 1, ka 7.

$$sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{7\times 7}{3\times 5})$$

Whakareatia te 7 ki te 7, ka 49.

$$sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{49}{3\times 5})$$

Whakareatia te 3 ki te 5, ka 15.

$$sort(\frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{49}{15})$$

Ko te tauraro noa iti rawa atu o ngā tau i te rārangi \frac{8}{21},\frac{69}{40},\frac{63}{8},\frac{49}{15} ko 840. Tahuritia ngā tau i te rārangi ki te hautanga me te tauraro 840.

$$\frac{320}{840},\frac{1449}{840},\frac{6615}{840},\frac{2744}{840}$$

Hei kōmaka i te rārangi, me tīmata mai i tētahi huānga \frac{320}{840} kotahi.

$$\frac{320}{840}$$

Me kōkuhu te \frac{1449}{840} ki te tauwāhi tika i te rārangi hōu.

$$\frac{320}{840},\frac{1449}{840}$$

Me kōkuhu te \frac{6615}{840} ki te tauwāhi tika i te rārangi hōu.

$$\frac{320}{840},\frac{1449}{840},\frac{6615}{840}$$

Me kōkuhu te \frac{2744}{840} ki te tauwāhi tika i te rārangi hōu.

$$\frac{320}{840},\frac{1449}{840},\frac{2744}{840},\frac{6615}{840}$$

Whakakapia ngā hautanga i whiwhi ki ngā uara tīmata.

$$\frac{8}{21},\frac{69}{40},\frac{49}{15},\frac{63}{8}$$

Aromātai

$$\frac{8}{21},\ \frac{69}{40},\ \frac{63}{8},\ \frac{49}{15}$$