Whakaoti i te .1(.94)+.25(18.5div25+.01)+.25(6div16+.02)+.4x=.7

$$.1(.94)+.25(18.5 \div 25+.01)+.25(6 \div 16+.02)+.4x=.7$$

Whakaoti mō x

$$x=0.799375$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakareatia te 0.1 ki te 0.94, ka 0.094.

$$0.094+0.25\left(\frac{18.5}{25}+0.01\right)+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Whakarohaina te \frac{18.5}{25} mā te whakarea i te taurunga me te tauraro ki te 10.

$$0.094+0.25\left(\frac{185}{250}+0.01\right)+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Whakahekea te hautanga \frac{185}{250} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 5.

$$0.094+0.25\left(\frac{37}{50}+0.01\right)+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Me tahuri ki tau ā-ira 0.01 ki te hautau \frac{1}{100}.

$$0.094+0.25\left(\frac{37}{50}+\frac{1}{100}\right)+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Ko te maha noa iti rawa atu o 50 me 100 ko 100. Me tahuri \frac{37}{50} me \frac{1}{100} ki te hautau me te tautūnga 100.

$$0.094+0.25\left(\frac{74}{100}+\frac{1}{100}\right)+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Tā te mea he rite te tauraro o \frac{74}{100} me \frac{1}{100}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$0.094+0.25\times \frac{74+1}{100}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Tāpirihia te 74 ki te 1, ka 75.

$$0.094+0.25\times \frac{75}{100}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Whakahekea te hautanga \frac{75}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$0.094+0.25\times \frac{3}{4}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Me tahuri ki tau ā-ira 0.25 ki te hautau \frac{25}{100}. Whakahekea te hautanga \frac{25}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$0.094+\frac{1}{4}\times \frac{3}{4}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

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

$$0.094+\frac{1\times 3}{4\times 4}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

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

$$0.094+\frac{3}{16}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Me tahuri ki tau ā-ira 0.094 ki te hautau \frac{94}{1000}. Whakahekea te hautanga \frac{94}{1000} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{47}{500}+\frac{3}{16}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Ko te maha noa iti rawa atu o 500 me 16 ko 2000. Me tahuri \frac{47}{500} me \frac{3}{16} ki te hautau me te tautūnga 2000.

$$\frac{188}{2000}+\frac{375}{2000}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Tā te mea he rite te tauraro o \frac{188}{2000} me \frac{375}{2000}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{188+375}{2000}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Tāpirihia te 188 ki te 375, ka 563.

$$\frac{563}{2000}+0.25\left(\frac{6}{16}+0.02\right)+0.4x=0.7$$

Whakahekea te hautanga \frac{6}{16} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{563}{2000}+0.25\left(\frac{3}{8}+0.02\right)+0.4x=0.7$$

Me tahuri ki tau ā-ira 0.02 ki te hautau \frac{2}{100}. Whakahekea te hautanga \frac{2}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$\frac{563}{2000}+0.25\left(\frac{3}{8}+\frac{1}{50}\right)+0.4x=0.7$$

Ko te maha noa iti rawa atu o 8 me 50 ko 200. Me tahuri \frac{3}{8} me \frac{1}{50} ki te hautau me te tautūnga 200.

$$\frac{563}{2000}+0.25\left(\frac{75}{200}+\frac{4}{200}\right)+0.4x=0.7$$

Tā te mea he rite te tauraro o \frac{75}{200} me \frac{4}{200}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{563}{2000}+0.25\times \frac{75+4}{200}+0.4x=0.7$$

Tāpirihia te 75 ki te 4, ka 79.

$$\frac{563}{2000}+0.25\times \frac{79}{200}+0.4x=0.7$$

Me tahuri ki tau ā-ira 0.25 ki te hautau \frac{25}{100}. Whakahekea te hautanga \frac{25}{100} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 25.

$$\frac{563}{2000}+\frac{1}{4}\times \frac{79}{200}+0.4x=0.7$$

Me whakarea te \frac{1}{4} ki te \frac{79}{200} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$\frac{563}{2000}+\frac{1\times 79}{4\times 200}+0.4x=0.7$$

Mahia ngā whakarea i roto i te hautanga \frac{1\times 79}{4\times 200}.

$$\frac{563}{2000}+\frac{79}{800}+0.4x=0.7$$

Ko te maha noa iti rawa atu o 2000 me 800 ko 4000. Me tahuri \frac{563}{2000} me \frac{79}{800} ki te hautau me te tautūnga 4000.

$$\frac{1126}{4000}+\frac{395}{4000}+0.4x=0.7$$

Tā te mea he rite te tauraro o \frac{1126}{4000} me \frac{395}{4000}, me tāpiri rāua mā te tāpiri i ō raua taurunga.

$$\frac{1126+395}{4000}+0.4x=0.7$$

Tāpirihia te 1126 ki te 395, ka 1521.

$$\frac{1521}{4000}+0.4x=0.7$$

Tangohia te \frac{1521}{4000} mai i ngā taha e rua.

$$0.4x=0.7-\frac{1521}{4000}$$

Me tahuri ki tau ā-ira 0.7 ki te hautau \frac{7}{10}.

$$0.4x=\frac{7}{10}-\frac{1521}{4000}$$

Ko te maha noa iti rawa atu o 10 me 4000 ko 4000. Me tahuri \frac{7}{10} me \frac{1521}{4000} ki te hautau me te tautūnga 4000.

$$0.4x=\frac{2800}{4000}-\frac{1521}{4000}$$

Tā te mea he rite te tauraro o \frac{2800}{4000} me \frac{1521}{4000}, me tango rāua mā te tango i ō raua taurunga.

$$0.4x=\frac{2800-1521}{4000}$$

Tangohia te 1521 i te 2800, ka 1279.

$$0.4x=\frac{1279}{4000}$$

Whakawehea ngā taha e rua ki te 0.4.

$$x=\frac{\frac{1279}{4000}}{0.4}$$

Tuhia te \frac{\frac{1279}{4000}}{0.4} hei hautanga kotahi.

$$x=\frac{1279}{4000\times 0.4}$$

Whakareatia te 4000 ki te 0.4, ka 1600.

$$x=\frac{1279}{1600}$$