Whakaoti i te 31/4/2frac{1{4}}=191/2/11frac{1{4}}

$$\frac { 3 \frac { 1 } { 4 } } { 2 \frac { 1 } { 4 } } = \frac { 19 \frac { 1 } { 2 } } { 11 \frac { 1 } { 4 } }$$

Manatoko

Ngā Upane Otinga

Whakawehe \frac{3\times 4+1}{4} ki te \frac{2\times 4+1}{4} mā te whakarea \frac{3\times 4+1}{4} ki te tau huripoki o \frac{2\times 4+1}{4}.

$$\frac{\left(3\times 4+1\right)\times 4}{4\left(2\times 4+1\right)}=\frac{\frac{19\times 2+1}{2}}{\frac{11\times 4+1}{4}}$$

Me whakakore tahi te 4 i te taurunga me te tauraro.

$$\frac{1+3\times 4}{1+2\times 4}=\frac{\frac{19\times 2+1}{2}}{\frac{11\times 4+1}{4}}$$

Whakareatia te 3 ki te 4, ka 12.

$$\frac{1+12}{1+2\times 4}=\frac{\frac{19\times 2+1}{2}}{\frac{11\times 4+1}{4}}$$

Tāpirihia te 1 ki te 12, ka 13.

$$\frac{13}{1+2\times 4}=\frac{\frac{19\times 2+1}{2}}{\frac{11\times 4+1}{4}}$$

Whakareatia te 2 ki te 4, ka 8.

$$\frac{13}{1+8}=\frac{\frac{19\times 2+1}{2}}{\frac{11\times 4+1}{4}}$$

Tāpirihia te 1 ki te 8, ka 9.

$$\frac{13}{9}=\frac{\frac{19\times 2+1}{2}}{\frac{11\times 4+1}{4}}$$

Whakawehe \frac{19\times 2+1}{2} ki te \frac{11\times 4+1}{4} mā te whakarea \frac{19\times 2+1}{2} ki te tau huripoki o \frac{11\times 4+1}{4}.

$$\frac{13}{9}=\frac{\left(19\times 2+1\right)\times 4}{2\left(11\times 4+1\right)}$$

Me whakakore tahi te 2 i te taurunga me te tauraro.

$$\frac{13}{9}=\frac{2\left(1+2\times 19\right)}{1+4\times 11}$$

Whakareatia te 2 ki te 19, ka 38.

$$\frac{13}{9}=\frac{2\left(1+38\right)}{1+4\times 11}$$

Tāpirihia te 1 ki te 38, ka 39.

$$\frac{13}{9}=\frac{2\times 39}{1+4\times 11}$$

Whakareatia te 2 ki te 39, ka 78.

$$\frac{13}{9}=\frac{78}{1+4\times 11}$$

Whakareatia te 4 ki te 11, ka 44.

$$\frac{13}{9}=\frac{78}{1+44}$$

Tāpirihia te 1 ki te 44, ka 45.

$$\frac{13}{9}=\frac{78}{45}$$

Whakahekea te hautanga \frac{78}{45} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 3.

$$\frac{13}{9}=\frac{26}{15}$$

Ko te maha noa iti rawa atu o 9 me 15 ko 45. Me tahuri \frac{13}{9} me \frac{26}{15} ki te hautau me te tautūnga 45.

$$\frac{65}{45}=\frac{78}{45}$$

Whakatauritea te \frac{65}{45} me te \frac{78}{45}.

$$\text{false}$$