Whakaoti i te 3/2{(1/4-3/2)div(3/2+frac{1}{6})}=

$$\frac { 3 } { 2 } \{ ( \frac { 1 } { 4 } - \frac { 3 } { 2 } ) \div ( \frac { 3 } { 2 } + \frac { 1 } { 6 } ) \} =$$

Aromātai

$$-\frac{9}{8}=-1.125$$

Ngā Upane Otinga

Ko te maha noa iti rawa atu o 4 me 2 ko 4. Me tahuri \frac{1}{4} me \frac{3}{2} ki te hautau me te tautūnga 4.

$$\frac{3}{2}\times \frac{\frac{1}{4}-\frac{6}{4}}{\frac{3}{2}+\frac{1}{6}}$$

Tā te mea he rite te tauraro o \frac{1}{4} me \frac{6}{4}, me tango rāua mā te tango i ō raua taurunga.

$$\frac{3}{2}\times \frac{\frac{1-6}{4}}{\frac{3}{2}+\frac{1}{6}}$$

Tangohia te 6 i te 1, ka -5.

$$\frac{3}{2}\times \frac{-\frac{5}{4}}{\frac{3}{2}+\frac{1}{6}}$$

Ko te maha noa iti rawa atu o 2 me 6 ko 6. Me tahuri \frac{3}{2} me \frac{1}{6} ki te hautau me te tautūnga 6.

$$\frac{3}{2}\times \frac{-\frac{5}{4}}{\frac{9}{6}+\frac{1}{6}}$$

Tā te mea he rite te tauraro o \frac{9}{6} me \frac{1}{6}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{3}{2}\times \frac{-\frac{5}{4}}{\frac{9+1}{6}}$$

Tāpirihia te 9 ki te 1, ka 10.

$$\frac{3}{2}\times \frac{-\frac{5}{4}}{\frac{10}{6}}$$

Whakahekea te hautanga \frac{10}{6} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{3}{2}\times \frac{-\frac{5}{4}}{\frac{5}{3}}$$

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

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

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

$$\frac{3}{2}\times \frac{-5\times 3}{4\times 5}$$

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

$$\frac{3}{2}\times \frac{-15}{20}$$

Whakahekea te hautanga \frac{-15}{20} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$\frac{3}{2}\left(-\frac{3}{4}\right)$$

Me whakarea te \frac{3}{2} ki te -\frac{3}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

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

Mahia ngā whakarea i roto i te hautanga \frac{3\left(-3\right)}{2\times 4}.

$$\frac{-9}{8}$$

Ka taea te hautanga \frac{-9}{8} te tuhi anō ko -\frac{9}{8} mā te tango i te tohu tōraro.

$$-\frac{9}{8}$$

Tauwehe

$$-\frac{9}{8} = -1\frac{1}{8} = -1.125$$